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margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.5px 8px; transform-origin: 127.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - test suite cleaned up on 2-9-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summation(n)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(isequal(summation(1),1))\r\n%%\r\nassert(isequal(summation(2),2))\r\n%%\r\nassert(isequal(summation(3),1))\r\n%%\r\nassert(isequal(summation(4),-1))\r\n%%\r\nassert(isequal(summation(5),-2))\r\n%%\r\nassert(isequal(summation(6),-1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2457030,"edited_by":223089,"edited_at":"2022-09-02T13:52:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2022-09-02T13:49:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T21:23:39.000Z","updated_at":"2026-03-04T13:46:29.000Z","published_at":"2022-07-13T21:23:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S be a sequence of numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1, a_2, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = a_{n-1} -a_{n-2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for some \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" 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takes a positive limit as input,\r\nAnd counts how many terms must be summed in the harmonic series:\r\n1/1, 1/2, 1/3, 1/4, ..., 1/N\r\nuntil the sum of the terms in the series is greater than the given limit.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 55.5px; transform-origin: 332px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function takes a positive limit as input,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAnd counts how many terms must be summed in the harmonic series:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1/1, 1/2, 1/3, 1/4, ..., 1/N\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003euntil the sum of the terms in the series is greater than the given limit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = count_of_harmonic_series(limit)\r\n sum_s = 1/1;\r\n n = 1;\r\nend","test_suite":"%%\r\nlimit = 2.0;\r\ny_correct = 4;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 10;\r\ny_correct = 12367;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 1.4;\r\ny_correct = 2;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 15;\r\ny_correct = 1835421;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 13.6;\r\ny_correct = 452609;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2710538,"edited_by":2710538,"edited_at":"2022-12-16T11:45:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-16T11:24:36.000Z","updated_at":"2026-02-19T15:16:16.000Z","published_at":"2022-12-16T11:40:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function takes a positive limit as input,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd counts how many terms must be summed in the harmonic series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1/1, 1/2, 1/3, 1/4, ..., 1/N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003euntil the sum of the terms in the series is greater than the given limit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44225,"title":"Sum of self power series","description":"The series, 1^1,2^2,3^3,4^4,....\r\n\r\nFind the sum of such series when x terms are given.","description_html":"\u003cp\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/p\u003e\u003cp\u003eFind the sum of such series when x terms are given.\u003c/p\u003e","function_template":"function y = sumofseries(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 5;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 288;\r\nassert(isequal(sumofseries(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":134801,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-05-25T05:40:41.000Z","updated_at":"2026-03-10T15:08:41.000Z","published_at":"2017-05-25T05:40:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of such series when x terms are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1485,"title":"Method of Common Differences part-1","description":"\r\nUse the method of common differences to output a vector containing the initial values and the nth order difference.\r\n\r\nex \r\n [ 1 4 9 16 25 36 ] has 1st differences [ 3 5 7 9 11 ] and second differences [2 2 2 2] . Therefore output [1 3 2] which is the 1st element of the above three vectors. \r\n\r\nThe use of this is that the sequence can be continued by using these differences. \r\n\r\nProblem 9) \r\nPrev: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1484 1484\u003e\r\nNext: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1486 1486\u003e\r\n\r\n","description_html":"\u003cp\u003eUse the method of common differences to output a vector containing the initial values and the nth order difference.\u003c/p\u003e\u003cp\u003eex \r\n [ 1 4 9 16 25 36 ] has 1st differences [ 3 5 7 9 11 ] and second differences [2 2 2 2] . Therefore output [1 3 2] which is the 1st element of the above three vectors.\u003c/p\u003e\u003cp\u003eThe use of this is that the sequence can be continued by using these differences.\u003c/p\u003e\u003cp\u003eProblem 9) \r\nPrev: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1484\"\u003e1484\u003c/a\u003e\r\nNext: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1486\"\u003e1486\u003c/a\u003e\u003c/p\u003e","function_template":"function y = seq2commondiff(x)\r\nt=[1];\r\nend","test_suite":"%%\r\nx = [1 4 9 16 25];\r\ny_correct = [1 3 2];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [1 9 29 67 129 221];\r\ny_correct = [1 8 12 6];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [3 4 9 23 51 98 169 269 403 576];\r\ny_correct = [3 1 4 5];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [1 8 27 64 125 216];\r\ny_correct = [1 7 12 6];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [2 0 2 9 22 42];\r\ny_correct = [2 -2 4 1];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx=[1 8 28 67 131 226]\r\ny_correct = [1 7 13 6];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":11275,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":"2013-05-01T18:21:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-01T17:52:16.000Z","updated_at":"2025-07-04T10:38:00.000Z","published_at":"2013-05-01T18:21:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the method of common differences to output a vector containing the initial values and the nth order difference.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eex [ 1 4 9 16 25 36 ] has 1st differences [ 3 5 7 9 11 ] and second differences [2 2 2 2] . Therefore output [1 3 2] which is the 1st element of the above three vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe use of this is that the sequence can be continued by using these differences.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 9) Prev:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1484\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1484\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Next:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1486\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1486\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54675,"title":"Define an arithmetic sequence","description":"Given three numbers n, a, and d, define an arithmetic sequence of n terms with a being the initial term of the sequence and d being the common difference of the sequence. If n = 0, then return an empty array since there would be no terms in the sequence.\r\nExamples:\r\nInput [n,a,d] = deal(10,5,2)\r\nOutput seq = [5 7 9 11 13 15 17 19 21 23]\r\n\r\nInput [n,a,d] = deal(5,2,-3)\r\nOutput seq = [2 -1 -4 -7 -10]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.875px; transform-origin: 407px 112.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven three numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, define an arithmetic sequence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e terms with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the initial term of the sequence and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the common difference of the sequence. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(10,5,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [5 7 9 11 13 15 17 19 21 23]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(5,2,-3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [2 -1 -4 -7 -10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = arithSequence(n,a,d)\r\n seq = [n a d];\r\nend","test_suite":"%%\r\n[n,a,d] = deal(10,5,2);\r\nseq_correct = [5 7 9 11 13 15 17 19 21 23];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(5,2,-3);\r\nseq_correct = [2 -1 -4 -7 -10];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(7,3,0.5);\r\nseq_correct = [3 3.5 4 4.5 5 5.5 6];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(0, 1, 2);\r\nassert(isempty(arithSequence(n,a,d)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":792819,"edited_by":792819,"edited_at":"2022-05-24T21:17:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-24T21:17:06.000Z","updated_at":"2026-03-05T13:32:48.000Z","published_at":"2022-05-24T21:17:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, define an arithmetic sequence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e terms with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the initial term of the sequence and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the common difference of the sequence. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input [n,a,d] = deal(10,5,2)\\nOutput seq = [5 7 9 11 13 15 17 19 21 23]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input [n,a,d] = deal(5,2,-3)\\nOutput seq = [2 -1 -4 -7 -10]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1486,"title":"Method of Common Differences part-2","description":"\r\nThis is the inverse problem to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1485 Problem 1485\u003e. Problem 1485 illustrates the method of differences takes a sequence and takes successive differences till it hits a constant. The output was the initial values and the final common difference. This output can be used to regenerate the original sequence. Thus this problem.\r\n\r\nUse the initial value and difference vector in the form output in 1485 and generate first n values of the sequence. \r\n\r\nEx: Consider the vector [1 3 2]. The last value '2' is the second order difference and the previous values are the initial values. This generates the sequence [1 4 9 16 25 36 ... ]\r\n\r\nProblem 10)\r\nPrev: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1485 1485\u003e \r\nPrev: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1496 1496\u003e ","description_html":"\u003cp\u003eThis is the inverse problem to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1485\"\u003eProblem 1485\u003c/a\u003e. Problem 1485 illustrates the method of differences takes a sequence and takes successive differences till it hits a constant. The output was the initial values and the final common difference. This output can be used to regenerate the original sequence. Thus this problem.\u003c/p\u003e\u003cp\u003eUse the initial value and difference vector in the form output in 1485 and generate first n values of the sequence.\u003c/p\u003e\u003cp\u003eEx: Consider the vector [1 3 2]. The last value '2' is the second order difference and the previous values are the initial values. This generates the sequence [1 4 9 16 25 36 ... ]\u003c/p\u003e\u003cp\u003eProblem 10)\r\nPrev: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1485\"\u003e1485\u003c/a\u003e \r\nPrev: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1496\"\u003e1496\u003c/a\u003e\u003c/p\u003e","function_template":"function y = commondiff2seq(x,n)\r\n y = [1 2 3];\r\nend","test_suite":"%%\r\nx = [1 3 2];\r\nn=5;\r\ny_correct = [1 4 9 16 25];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [1 4 6];\r\nn=6;\r\ny_correct = [1 5 15 31 53 81];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [10 -4 4];\r\nn=7;\r\ny_correct = [10 6 6 10 18 30 46];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [100 10 -5];\r\nn=5;\r\ny_correct = [100 110 115 115 110];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [0 -10 4 -2 6];\r\nn=10;\r\ny_correct = [ 0 -10 -16 -20 -18 0 50 154 340 642];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [3 0];\r\nn=4;\r\ny_correct = [3 3 3 3 ];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [6 1];\r\nn=4;\r\ny_correct = [6 7 8 9];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [-10 1 -5 2];\r\nn=10;\r\ny_correct = [-10 -9 -13 -20 -28 -35 -39 -38 -30 -13];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [ 1 3 -1 -2 2 1];\r\nn=10;\r\ny_correct = [ 1 4 6 5 1 -3 0 22 81 202];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [0 0 0];\r\nn=5;\r\ny_correct = [0 0 0 0 0];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":11275,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-01T18:40:08.000Z","updated_at":"2026-01-02T17:21:44.000Z","published_at":"2013-05-01T18:40:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the inverse problem to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1485\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 1485\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Problem 1485 illustrates the method of differences takes a sequence and takes successive differences till it hits a constant. The output was the initial values and the final common difference. This output can be used to regenerate the original sequence. Thus this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the initial value and difference vector in the form output in 1485 and generate first n values of the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEx: Consider the vector [1 3 2]. The last value '2' is the second order difference and the previous values are the initial values. This generates the sequence [1 4 9 16 25 36 ... ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 10) Prev:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1485\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1485\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Prev:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1496\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1496\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56260,"title":"Leonardo primes","description":"Leonardo numbers are defined by following recurrence relation:\r\n\r\n\r\n\r\nLeonard prime is Leonardo number which is also prime (see https://en.wikipedia.org/wiki/Leonardo_number). \r\n\r\nFor given n, find all Leonardo primes.\r\n\r\nExample:\r\nn=5;\r\nLeoNumbers=[1 1 3 5 9 15];\r\nPrimes=[2 3 5 7 11 13];\r\nLeoPrimes=[3 5];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.375px; transform-origin: 407px 196.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonardo numbers are defined by following recurrence relation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; 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\" width=\"273.5\" height=\"61\" style=\"width: 273.5px; height: 61px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonard prime is Leonardo number which is also prime (see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Leonardo_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find all Leonardo primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.75px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.875px; transform-origin: 404px 40.875px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoNumbers=[1 1 3 5 9 15];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ePrimes=[2 3 5 7 11 13];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoPrimes=[3 5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function LeoPrimes = LeonardoPrimes(n)\r\n LeoPrimes=n;\r\nend","test_suite":"%%\r\nn = 5;\r\nLeoPrimes_correct = [3,5];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n\r\n%%\r\nn = 0;\r\n%LeoPrimes_correct = [];\r\nassert(isempty(LeonardoPrimes(n)))\r\n\r\n%%\r\nn = 25;\r\nLeoPrimes_correct = [3,5,41,67,109,1973,5167];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":2663765,"edited_by":2663765,"edited_at":"2022-10-10T14:54:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2022-10-10T13:22:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:53:17.000Z","updated_at":"2026-01-13T16:14:23.000Z","published_at":"2022-10-10T12:53:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonardo numbers are defined by following recurrence relation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL(n) = \\n \\\\begin{cases}\\n 1 \u0026amp; \\\\mbox{if }~n = 0 \\\\\\\\\\n 1 \u0026amp; \\\\mbox{if }~n = 1 \\\\\\\\\\n L(n - 1) + L(n - 2) + 1 \u0026amp; \\\\mbox{if }~n \u0026gt; 1 \\\\\\\\\\n \\\\end{cases}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonard prime is Leonardo number which is also prime (see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Leonardo_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find all Leonardo primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n=5;\\nLeoNumbers=[1 1 3 5 9 15];\\nPrimes=[2 3 5 7 11 13];\\nLeoPrimes=[3 5];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42581,"title":"Create sequnce 1 4 9 16 25.........","description":"Create sequnce 1 4 9 16 25......... upto entered input value using matlab scripting commands. Let y be output and x be input","description_html":"\u003cp\u003eCreate sequnce 1 4 9 16 25......... upto entered input value using matlab scripting commands. Let y be output and x be input\u003c/p\u003e","function_template":"function y = prntseq(x)\r\n% Enter code\r\nend","test_suite":"%%\r\nx = 25;\r\ny_correct = [1 4 9 16 25];\r\nassert(isequal(prntseq(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = [1 4 9 16 25 36 49 64 81 100];\r\nassert(isequal(prntseq(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = [1 4 9];\r\nassert(isequal(prntseq(x),y_correct))\r\n%%\r\nx = 36;\r\ny_correct = [1 4 9 16 25 36];\r\nassert(isequal(prntseq(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46868,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":414,"test_suite_updated_at":"2015-08-28T11:26:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-28T11:17:32.000Z","updated_at":"2026-02-08T06:17:39.000Z","published_at":"2015-08-28T11:26:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate sequnce 1 4 9 16 25......... upto entered input value using matlab scripting commands. Let y be output and x be input\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1132,"title":"Create a recurrence matrix for a vector of data","description":"In \u003chttps://en.wikipedia.org/wiki/Conversation_analysis conversation analysis\u003e, it's often useful to track the contributions from each speaker to see who talks when. One measurement of engagement between a pair of conversants is to see if they talk to each other more than they talk to other people; for example, at a double date, two old friends might talk to each other more than they talk to their spouses.\r\n\r\nAssuming we've coded up the conversation data (e.g. using Gail Jefferson's \u003chttp://mis.ucd.ie/wiki/JeffersonianTranscription transcription methods\u003e) and assigned a unique number to each participant, MATLAB makes an excellent tool to quickly gather some of these statistics.\r\n\r\nGiven a vector of speaker observations V, where element _V(i)_ indicates who spoke sentence _i_ in the data, find how many times each element occurs directly after each other element. Note that since we may only be analyzing a part of a larger transcripts, not all speaker numbers may appear in the vector.\r\n\r\nReturn a matrix containing this data, as well as the list of (ordered) unique elements.\r\n\r\nE.g., if V = [1 3 5 3 5 5], then\r\n\r\n [R, U] = recurrence(V)\r\n R =\r\n 0 1 0\r\n 0 0 2\r\n 0 1 1\r\n U =\r\n 1 3 5\r\n \r\nSuch a tool will have other uses, of course.","description_html":"\u003cp\u003eIn \u003ca href=\"https://en.wikipedia.org/wiki/Conversation_analysis\"\u003econversation analysis\u003c/a\u003e, it's often useful to track the contributions from each speaker to see who talks when. One measurement of engagement between a pair of conversants is to see if they talk to each other more than they talk to other people; for example, at a double date, two old friends might talk to each other more than they talk to their spouses.\u003c/p\u003e\u003cp\u003eAssuming we've coded up the conversation data (e.g. using Gail Jefferson's \u003ca href=\"http://mis.ucd.ie/wiki/JeffersonianTranscription\"\u003etranscription methods\u003c/a\u003e) and assigned a unique number to each participant, MATLAB makes an excellent tool to quickly gather some of these statistics.\u003c/p\u003e\u003cp\u003eGiven a vector of speaker observations V, where element \u003ci\u003eV(i)\u003c/i\u003e indicates who spoke sentence \u003ci\u003ei\u003c/i\u003e in the data, find how many times each element occurs directly after each other element. Note that since we may only be analyzing a part of a larger transcripts, not all speaker numbers may appear in the vector.\u003c/p\u003e\u003cp\u003eReturn a matrix containing this data, as well as the list of (ordered) unique elements.\u003c/p\u003e\u003cp\u003eE.g., if V = [1 3 5 3 5 5], then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[R, U] = recurrence(V)\r\nR =\r\n 0 1 0\r\n 0 0 2\r\n 0 1 1\r\nU =\r\n 1 3 5\r\n\u003c/pre\u003e\u003cp\u003eSuch a tool will have other uses, of course.\u003c/p\u003e","function_template":"function [A, V] = recurrence(DATA)\r\n A = [];\r\n V = [];\r\nend\r\n","test_suite":"%%\r\nv = [4 2 3 1 1 3 4 5 1 3];\r\nreal_r = [1 0 2 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 1 0 0 1; 1 0 0 0 0];\r\nreal_u = 1:5;\r\n[r,u] = recurrence(v);\r\nassert(and(isequal(r,real_r), isequal(u,real_u)));\r\n%%\r\nv = [1:6,1];\r\nreal_r = circshift(eye(6),[0 1]);\r\nreal_u = 1:6;\r\n[r,u] = recurrence(v);\r\nassert(and(isequal(r,real_r), isequal(u,real_u)));\r\n%%\r\nv = [0 0 0 0 0 0];\r\nreal_r = 5;\r\nreal_u = 0;\r\n[r,u] = recurrence(v);\r\nassert(and(isequal(r,real_r), isequal(u,real_u)));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":78,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-21T15:19:46.000Z","updated_at":"2025-12-08T02:41:57.000Z","published_at":"2012-12-21T15:20:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Conversation_analysis\\\"\u003e\u003cw:r\u003e\u003cw:t\u003econversation analysis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, it's often useful to track the contributions from each speaker to see who talks when. One measurement of engagement between a pair of conversants is to see if they talk to each other more than they talk to other people; for example, at a double date, two old friends might talk to each other more than they talk to their spouses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming we've coded up the conversation data (e.g. using Gail Jefferson's\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://mis.ucd.ie/wiki/JeffersonianTranscription\\\"\u003e\u003cw:r\u003e\u003cw:t\u003etranscription methods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) and assigned a unique number to each participant, MATLAB makes an excellent tool to quickly gather some of these statistics.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector of speaker observations V, where element\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV(i)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e indicates who spoke sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the data, find how many times each element occurs directly after each other element. Note that since we may only be analyzing a part of a larger transcripts, not all speaker numbers may appear in the vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn a matrix containing this data, as well as the list of (ordered) unique elements.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g., if V = [1 3 5 3 5 5], then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[R, U] = recurrence(V)\\nR =\\n 0 1 0\\n 0 0 2\\n 0 1 1\\nU =\\n 1 3 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuch a tool will have other uses, of course.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1894,"title":"GJam 2014 China Rd A: Library Sorting (Large)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2924486/dashboard#s=p2 GJam 2014 China Sorting\u003e. Subset of cases.\r\n\r\nThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations. \r\n\r\n*Input:* V a vector\r\n\r\n*Output:* Vout a sorted vector Odds Increasing/Evens Increasing\r\n\r\n*Example:*\r\n\r\nV= [-5 -12 87 2 88 20 11]\r\n\r\nVout=[-5 88 11 20 2 -12 87]\r\n\r\n\r\n*Contest Performance:* Best Time to Complete: \u003c 10 minutes","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\"\u003eGJam 2014 China Sorting\u003c/a\u003e. Subset of cases.\u003c/p\u003e\u003cp\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e V a vector\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eV= [-5 -12 87 2 88 20 11]\u003c/p\u003e\u003cp\u003eVout=[-5 88 11 20 2 -12 87]\u003c/p\u003e\u003cp\u003e\u003cb\u003eContest Performance:\u003c/b\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/p\u003e","function_template":"function vout=Sort_CH(v)\r\n vout=v;\r\nend","test_suite":"%%\r\ntic\r\nv=[1 ];\r\nvexp=[1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[2 1 ];\r\nvexp=[2 1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 ];\r\nvexp=[1 2 3 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 4 5 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[5 2 3 4 1 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[994 994 -981 -975 -971 980 -971 976 -969 -969 968 968 958 -963 -957 948 -955 932 926 -935 924 -931 -923 -917 922 -917 -909 -899 916 914 -899 -877 -871 -871 -867 -847 912 -829 912 -825 -819 -817 910 -811 -805 -803 -801 904 -791 -783 -745 -731 902 -725 -725 -715 900 896 -707 896 -705 -705 -693 -691 882 -687 -685 -683 -671 -663 882 -663 880 880 -651 -651 -637 876 -637 -623 -613 -605 -601 -577 -577 862 -571 -565 856 848 -559 -559 -555 -553 844 -551 840 828 -547 -539 -527 812 -525 806 802 -505 -503 -497 -497 -495 798 -493 -491 -483 -481 798 770 770 -481 770 762 758 -477 -469 -463 -457 756 -455 -451 -441 -439 -431 -429 752 -427 -413 -409 742 -403 726 -391 722 -389 -385 718 -379 -365 -363 -359 712 702 -355 -351 682 -347 682 674 672 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];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-891 962 792 -851 784 730 -789 -781 662 662 -765 -737 -713 644 -567 -525 -465 534 -451 526 454 -427 -399 -173 -15 454 -1 77 378 175 202 185 170 275 313 367 82 407 459 473 507 621 691 707 731 805 825 935 981 52 48 46 -10 -66 -162 -168 -192 -196 -218 -232 -262 -280 -288 -332 -358 -402 -438 -448 -490 -502 -516 -572 -590 -598 -832 -834 ];\r\nvexp=[-891 962 792 -851 784 730 -789 -781 662 662 -765 -737 -713 644 -567 -525 -465 534 -451 526 454 -427 -399 -173 -15 454 -1 77 378 175 202 185 170 275 313 367 82 407 459 473 507 621 691 707 731 805 825 935 981 52 48 46 -10 -66 -162 -168 -192 -196 -218 -232 -262 -280 -288 -332 -358 -402 -438 -448 -490 -502 -516 -572 -590 -598 -832 -834 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[990 988 -999 -995 -993 -993 -991 976 970 958 -989 -973 946 -965 -963 -957 -957 -941 938 -939 -937 -937 -913 -907 -901 938 938 924 -901 -893 924 -891 -889 918 -869 912 910 -869 -869 -845 -827 -811 -793 -741 906 868 -715 -715 844 836 -711 -709 812 -693 -693 -687 -665 808 786 774 -665 -663 -663 -615 -603 -593 -589 770 762 -587 756 -585 -581 -565 -565 -561 -555 -555 -553 -541 706 704 -539 -505 694 -503 -493 -455 -451 672 -427 -399 670 -385 658 -373 -359 656 -339 -335 654 -333 -327 636 -325 -313 -297 -297 -273 616 -263 -253 614 -251 604 590 -219 -209 550 -207 -203 -187 -185 -181 -177 -167 -159 546 -157 -145 -137 544 -135 -105 -77 -71 -67 -65 -41 540 -39 532 528 -37 526 -33 -31 -23 -21 -13 524 11 15 19 520 506 27 37 41 43 494 77 488 89 101 105 127 486 129 131 472 468 458 133 133 139 450 139 171 171 428 175 428 189 203 219 410 237 251 396 255 265 271 273 273 273 293 392 297 376 299 301 315 315 351 373 374 377 377 379 385 387 389 397 407 374 368 409 411 425 433 439 449 451 481 507 535 342 537 553 338 338 575 322 312 577 577 581 583 585 308 306 603 292 264 619 248 242 228 224 623 637 645 220 661 663 208 671 681 204 186 693 693 701 719 721 178 170 737 749 154 763 154 767 154 769 789 154 144 142 130 793 793 795 803 803 805 815 817 819 821 120 823 120 825 86 86 78 74 72 825 62 839 841 861 861 861 873 875 56 875 42 897 935 935 949 12 949 955 955 8 975 979 0 0 0 0 0 -52 -56 -60 -70 -70 -72 -94 -96 -98 -110 -110 -114 -116 -126 -126 -136 -158 -160 -176 -178 -182 -188 -196 -200 -206 -208 -208 -222 -224 -228 -276 -278 -296 -302 -316 -318 -324 -334 -346 -350 -350 -358 -364 -368 -370 -378 -378 -378 -386 -404 -416 -416 -418 -420 -432 -448 -462 -480 -482 -490 -502 -514 -516 -520 -546 -546 -546 -550 -564 -570 -570 -572 -574 -580 -600 -602 -624 -626 -626 -634 -650 -658 -658 -662 -686 -712 -716 -720 -726 -730 -732 -756 -756 -770 -780 -790 -798 -802 -824 -836 -882 -894 -906 -914 -914 -932 -950 -952 -966 -968 -978 -978 -990 -990 ];\r\nvexp=[990 988 -999 -995 -993 -993 -991 976 970 958 -989 -973 946 -965 -963 -957 -957 -941 938 -939 -937 -937 -913 -907 -901 938 938 924 -901 -893 924 -891 -889 918 -869 912 910 -869 -869 -845 -827 -811 -793 -741 906 868 -715 -715 844 836 -711 -709 812 -693 -693 -687 -665 808 786 774 -665 -663 -663 -615 -603 -593 -589 770 762 -587 756 -585 -581 -565 -565 -561 -555 -555 -553 -541 706 704 -539 -505 694 -503 -493 -455 -451 672 -427 -399 670 -385 658 -373 -359 656 -339 -335 654 -333 -327 636 -325 -313 -297 -297 -273 616 -263 -253 614 -251 604 590 -219 -209 550 -207 -203 -187 -185 -181 -177 -167 -159 546 -157 -145 -137 544 -135 -105 -77 -71 -67 -65 -41 540 -39 532 528 -37 526 -33 -31 -23 -21 -13 524 11 15 19 520 506 27 37 41 43 494 77 488 89 101 105 127 486 129 131 472 468 458 133 133 139 450 139 171 171 428 175 428 189 203 219 410 237 251 396 255 265 271 273 273 273 293 392 297 376 299 301 315 315 351 373 374 377 377 379 385 387 389 397 407 374 368 409 411 425 433 439 449 451 481 507 535 342 537 553 338 338 575 322 312 577 577 581 583 585 308 306 603 292 264 619 248 242 228 224 623 637 645 220 661 663 208 671 681 204 186 693 693 701 719 721 178 170 737 749 154 763 154 767 154 769 789 154 144 142 130 793 793 795 803 803 805 815 817 819 821 120 823 120 825 86 86 78 74 72 825 62 839 841 861 861 861 873 875 56 875 42 897 935 935 949 12 949 955 955 8 975 979 0 0 0 0 0 -52 -56 -60 -70 -70 -72 -94 -96 -98 -110 -110 -114 -116 -126 -126 -136 -158 -160 -176 -178 -182 -188 -196 -200 -206 -208 -208 -222 -224 -228 -276 -278 -296 -302 -316 -318 -324 -334 -346 -350 -350 -358 -364 -368 -370 -378 -378 -378 -386 -404 -416 -416 -418 -420 -432 -448 -462 -480 -482 -490 -502 -514 -516 -520 -546 -546 -546 -550 -564 -570 -570 -572 -574 -580 -600 -602 -624 -626 -626 -634 -650 -658 -658 -662 -686 -712 -716 -720 -726 -730 -732 -756 -756 -770 -780 -790 -798 -802 -824 -836 -882 -894 -906 -914 -914 -932 -950 -952 -966 -968 -978 -978 -990 -990 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-997 -995 994 -981 -977 -975 -971 988 -969 -931 -929 986 968 -903 -903 956 -897 -895 -887 -883 948 -879 -871 -871 -865 -863 946 -863 -861 -861 944 -853 934 924 -853 914 914 -847 -845 910 -829 898 -819 890 -807 -807 888 880 -803 -797 880 874 868 -793 860 842 -791 -783 840 -771 838 -767 -765 832 826 -763 826 -759 814 -759 -753 -733 812 -733 -729 -727 -727 -723 804 -715 802 -715 -707 798 -693 -671 -669 -669 -665 792 -663 -663 -663 -663 790 -653 -643 -635 -615 778 774 770 752 -611 -587 -579 746 -569 -569 -561 740 -555 -555 -553 -539 740 -537 -523 728 -517 -513 -509 -505 -497 -497 -493 -483 728 -479 -479 -475 -475 -467 722 722 -439 -431 -429 -425 706 -413 -407 704 702 690 678 676 -407 674 -393 -385 -385 672 670 -385 664 -383 -377 -371 -367 -355 -353 -353 -351 -347 658 -345 656 -327 652 -325 -323 650 616 -319 -315 616 604 602 602 -315 596 594 -313 572 572 566 -311 562 -295 -287 -285 -285 -275 -273 -273 -271 -261 -259 -259 -253 -249 550 -239 542 538 530 -233 -231 -231 -231 526 -217 520 -203 518 -189 518 -187 -183 516 -177 510 508 506 -173 -171 -145 506 504 504 -143 -143 494 492 482 -133 -129 478 474 -129 -125 -113 -111 -99 -93 -91 -81 472 -81 -77 -75 -63 -53 -45 -39 468 462 -39 -39 -13 7 9 13 21 23 35 43 452 43 450 49 49 51 55 67 71 448 73 77 77 81 91 446 93 97 101 105 115 119 121 125 428 151 422 151 171 173 181 187 420 189 195 410 400 392 197 207 211 211 392 221 221 376 376 223 225 364 229 231 231 342 235 241 340 241 336 332 245 326 247 253 322 253 312 255 308 261 269 306 279 291 286 309 286 315 323 266 258 323 329 341 343 256 347 357 379 381 385 397 401 403 403 407 421 427 244 427 429 242 429 433 433 238 433 437 441 234 220 208 443 208 196 451 455 459 467 469 186 182 178 469 475 483 483 505 511 513 539 539 557 559 561 565 168 168 567 166 156 575 156 585 593 154 150 593 148 144 136 130 595 597 597 609 613 617 120 633 637 639 647 661 671 118 114 112 679 110 679 679 110 681 683 687 106 98 98 693 693 695 98 76 699 72 699 713 715 721 64 727 62 731 733 62 56 735 739 741 745 52 749 749 52 28 22 20 759 14 759 763 8 763 765 767 8 6 4 0 0 0 0 0 0 767 767 785 791 801 -2 803 805 -8 -22 819 -24 825 833 -40 839 845 -44 847 847 847 -60 847 865 -64 865 871 909 -84 913 913 915 -84 919 -108 923 -110 929 933 933 -112 939 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898 -819 890 -807 -807 888 880 -803 -797 880 874 868 -793 860 842 -791 -783 840 -771 838 -767 -765 832 826 -763 826 -759 814 -759 -753 -733 812 -733 -729 -727 -727 -723 804 -715 802 -715 -707 798 -693 -671 -669 -669 -665 792 -663 -663 -663 -663 790 -653 -643 -635 -615 778 774 770 752 -611 -587 -579 746 -569 -569 -561 740 -555 -555 -553 -539 740 -537 -523 728 -517 -513 -509 -505 -497 -497 -493 -483 728 -479 -479 -475 -475 -467 722 722 -439 -431 -429 -425 706 -413 -407 704 702 690 678 676 -407 674 -393 -385 -385 672 670 -385 664 -383 -377 -371 -367 -355 -353 -353 -351 -347 658 -345 656 -327 652 -325 -323 650 616 -319 -315 616 604 602 602 -315 596 594 -313 572 572 566 -311 562 -295 -287 -285 -285 -275 -273 -273 -271 -261 -259 -259 -253 -249 550 -239 542 538 530 -233 -231 -231 -231 526 -217 520 -203 518 -189 518 -187 -183 516 -177 510 508 506 -173 -171 -145 506 504 504 -143 -143 494 492 482 -133 -129 478 474 -129 -125 -113 -111 -99 -93 -91 -81 472 -81 -77 -75 -63 -53 -45 -39 468 462 -39 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649 649 651 651 226 653 675 679 224 685 689 220 689 689 697 214 705 705 206 707 709 711 715 725 200 735 735 198 737 741 196 196 749 753 196 753 759 194 771 777 777 787 789 178 799 803 811 813 176 174 815 815 158 154 819 827 827 833 841 845 847 847 154 851 851 859 154 861 861 863 867 154 875 154 885 887 891 154 895 154 895 907 909 913 915 154 917 148 921 923 136 931 130 937 130 118 949 957 957 961 112 963 110 110 971 979 102 979 98 98 92 88 985 987 84 84 76 66 56 46 42 42 42 40 28 24 14 0 0 0 0 -2 -6 -26 -26 -26 -34 -34 -42 -42 -42 -44 -52 -58 -92 -94 -98 -100 -108 -110 -120 -126 -126 -134 -142 -144 -146 -150 -154 -154 -154 -154 -156 -156 -158 -174 -176 -182 -196 -228 -252 -252 -260 -264 -266 -266 -278 -278 -282 -286 -290 -296 -304 -310 -312 -316 -320 -326 -330 -334 -340 -342 -346 -348 -352 -362 -364 -374 -378 -382 -386 -388 -390 -392 -396 -404 -406 -406 -412 -414 -418 -426 -428 -432 -438 -442 -450 -462 -464 -468 -468 -472 -476 -486 -490 -492 -518 -520 -526 -526 -532 -532 -534 -546 -546 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];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[994 -969 988 986 -957 -931 966 -889 -889 -883 -881 -877 -877 960 -873 914 -861 912 -847 -845 -841 -835 900 -805 -803 -793 -793 886 864 -785 -765 -765 -737 -713 -713 -701 -661 -655 -621 840 -619 -615 -599 832 -595 -567 -553 828 -541 -497 -467 -455 -429 -419 -415 -387 794 -377 792 -375 -371 -365 -337 -333 -331 -321 -285 780 -285 762 -271 -263 758 -259 -257 732 728 -249 -235 -231 -231 -189 726 -189 -181 -175 698 -153 -149 696 684 -127 672 -119 -115 652 -115 -113 644 -93 -91 608 -91 602 -77 -49 -45 594 -35 -5 562 -3 11 540 538 518 506 41 43 506 57 111 121 474 123 161 177 191 203 207 217 217 247 259 269 273 468 464 442 297 303 319 321 333 343 349 420 418 353 410 397 406 427 384 427 429 384 455 455 467 378 370 493 505 364 525 364 533 348 336 539 541 583 589 611 330 316 619 627 647 651 681 717 719 308 725 739 757 767 282 777 274 779 797 847 264 262 252 853 873 242 933 947 969 971 979 232 208 182 999 999 174 170 138 132 126 110 108 98 98 70 44 44 22 4 0 0 0 -2 -22 -58 -66 -74 -94 -116 -148 -158 -182 -210 -214 -222 -226 -238 -248 -252 -256 -286 -310 -320 -336 -342 -370 -388 -402 -402 -416 -440 -440 -458 -460 -460 -490 -504 -514 -528 -560 -572 -588 -596 -600 -616 -638 -642 -654 -660 -676 -684 -702 -706 -708 -720 -726 -742 -746 -766 -786 -812 -832 -840 -846 -864 -910 -912 -916 -948 -966 -982 -986 -992 ];\r\nvexp=[994 -969 988 986 -957 -931 966 -889 -889 -883 -881 -877 -877 960 -873 914 -861 912 -847 -845 -841 -835 900 -805 -803 -793 -793 886 864 -785 -765 -765 -737 -713 -713 -701 -661 -655 -621 840 -619 -615 -599 832 -595 -567 -553 828 -541 -497 -467 -455 -429 -419 -415 -387 794 -377 792 -375 -371 -365 -337 -333 -331 -321 -285 780 -285 762 -271 -263 758 -259 -257 732 728 -249 -235 -231 -231 -189 726 -189 -181 -175 698 -153 -149 696 684 -127 672 -119 -115 652 -115 -113 644 -93 -91 608 -91 602 -77 -49 -45 594 -35 -5 562 -3 11 540 538 518 506 41 43 506 57 111 121 474 123 161 177 191 203 207 217 217 247 259 269 273 468 464 442 297 303 319 321 333 343 349 420 418 353 410 397 406 427 384 427 429 384 455 455 467 378 370 493 505 364 525 364 533 348 336 539 541 583 589 611 330 316 619 627 647 651 681 717 719 308 725 739 757 767 282 777 274 779 797 847 264 262 252 853 873 242 933 947 969 971 979 232 208 182 999 999 174 170 138 132 126 110 108 98 98 70 44 44 22 4 0 0 0 -2 -22 -58 -66 -74 -94 -116 -148 -158 -182 -210 -214 -222 -226 -238 -248 -252 -256 -286 -310 -320 -336 -342 -370 -388 -402 -402 -416 -440 -440 -458 -460 -460 -490 -504 -514 -528 -560 -572 -588 -596 -600 -616 -638 -642 -654 -660 -676 -684 -702 -706 -708 -720 -726 -742 -746 -766 -786 -812 -832 -840 -846 -864 -910 -912 -916 -948 -966 -982 -986 -992 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-991 -989 998 -987 -983 -973 996 982 980 -971 978 -965 -959 974 -957 -951 -947 966 -941 966 966 962 -931 -931 -909 -903 -895 -893 -889 -885 -883 944 -883 936 -869 912 -845 896 894 -845 -837 -833 -829 886 882 -817 880 -803 872 -791 -791 -777 -769 -765 -759 -753 870 -743 -729 864 -717 864 854 -711 -707 850 -695 -689 -683 840 826 -665 -661 -659 812 798 -659 766 -657 760 -653 -637 756 -631 -627 -621 -611 748 -609 -605 -605 -601 -597 -589 -573 -567 -541 -539 -539 740 730 -539 -535 -507 -483 728 -475 -469 714 -455 -453 710 704 -451 -447 -433 -433 -431 -421 -417 -417 686 -405 682 -403 680 -399 678 -391 672 -387 670 668 -385 660 -381 -381 636 -377 -367 -363 -353 -331 626 618 -325 -303 616 -299 -297 -291 584 -281 -277 578 578 572 570 -245 -243 -239 -231 -223 -221 -209 570 -205 -201 -185 -183 -175 -165 -163 -159 -157 568 -147 564 -139 562 -125 548 -117 544 542 -103 -101 528 -95 524 -95 -79 -71 -71 -61 -49 520 -41 -37 520 518 -33 -27 502 -25 490 -21 482 474 -17 474 -17 -9 -7 -7 7 13 15 446 17 23 446 31 35 440 35 39 45 49 49 426 59 418 406 67 91 404 93 103 388 105 107 113 388 117 119 121 123 131 141 143 143 161 173 173 179 378 195 358 197 203 231 257 356 263 271 273 275 277 287 297 338 301 303 338 305 323 325 336 330 369 381 399 322 308 407 308 413 308 296 419 419 296 425 439 292 445 280 451 451 260 451 453 246 469 469 469 483 246 495 242 501 242 511 517 232 212 529 539 206 180 178 539 178 549 549 553 559 561 561 565 567 573 585 585 595 607 623 633 641 657 683 689 719 727 733 735 741 759 168 779 783 166 164 791 807 817 819 823 861 865 869 869 162 903 907 138 907 913 913 917 923 132 132 941 130 953 957 126 122 965 971 981 985 993 995 104 98 98 94 88 88 86 80 78 76 68 66 66 60 58 52 36 36 22 16 0 0 0 -14 -20 -22 -26 -28 -52 -54 -56 -58 -70 -70 -72 -76 -118 -126 -126 -140 -140 -142 -154 -154 -168 -172 -174 -182 -188 -196 -196 -206 -208 -220 -220 -222 -226 -236 -262 -286 -300 -308 -308 -322 -322 -336 -342 -346 -366 -396 -396 -404 -444 -446 -450 -462 -462 -466 -468 -468 -486 -486 -490 -498 -498 -506 -520 -532 -546 -548 -588 -594 -594 -596 -596 -604 -608 -612 -616 -616 -616 -622 -622 -626 -626 -656 -656 -656 -664 -672 -680 -682 -682 -714 -718 -744 -750 -750 -756 -770 -788 -800 -806 -814 -816 -850 -858 -858 -864 -868 -868 -870 -882 -884 -910 -924 -928 -932 -942 -946 -950 -952 -980 -986 -988 ];\r\nvexp=[-991 -989 998 -987 -983 -973 996 982 980 -971 978 -965 -959 974 -957 -951 -947 966 -941 966 966 962 -931 -931 -909 -903 -895 -893 -889 -885 -883 944 -883 936 -869 912 -845 896 894 -845 -837 -833 -829 886 882 -817 880 -803 872 -791 -791 -777 -769 -765 -759 -753 870 -743 -729 864 -717 864 854 -711 -707 850 -695 -689 -683 840 826 -665 -661 -659 812 798 -659 766 -657 760 -653 -637 756 -631 -627 -621 -611 748 -609 -605 -605 -601 -597 -589 -573 -567 -541 -539 -539 740 730 -539 -535 -507 -483 728 -475 -469 714 -455 -453 710 704 -451 -447 -433 -433 -431 -421 -417 -417 686 -405 682 -403 680 -399 678 -391 672 -387 670 668 -385 660 -381 -381 636 -377 -367 -363 -353 -331 626 618 -325 -303 616 -299 -297 -291 584 -281 -277 578 578 572 570 -245 -243 -239 -231 -223 -221 -209 570 -205 -201 -185 -183 -175 -165 -163 -159 -157 568 -147 564 -139 562 -125 548 -117 544 542 -103 -101 528 -95 524 -95 -79 -71 -71 -61 -49 520 -41 -37 520 518 -33 -27 502 -25 490 -21 482 474 -17 474 -17 -9 -7 -7 7 13 15 446 17 23 446 31 35 440 35 39 45 49 49 426 59 418 406 67 91 404 93 103 388 105 107 113 388 117 119 121 123 131 141 143 143 161 173 173 179 378 195 358 197 203 231 257 356 263 271 273 275 277 287 297 338 301 303 338 305 323 325 336 330 369 381 399 322 308 407 308 413 308 296 419 419 296 425 439 292 445 280 451 451 260 451 453 246 469 469 469 483 246 495 242 501 242 511 517 232 212 529 539 206 180 178 539 178 549 549 553 559 561 561 565 567 573 585 585 595 607 623 633 641 657 683 689 719 727 733 735 741 759 168 779 783 166 164 791 807 817 819 823 861 865 869 869 162 903 907 138 907 913 913 917 923 132 132 941 130 953 957 126 122 965 971 981 985 993 995 104 98 98 94 88 88 86 80 78 76 68 66 66 60 58 52 36 36 22 16 0 0 0 -14 -20 -22 -26 -28 -52 -54 -56 -58 -70 -70 -72 -76 -118 -126 -126 -140 -140 -142 -154 -154 -168 -172 -174 -182 -188 -196 -196 -206 -208 -220 -220 -222 -226 -236 -262 -286 -300 -308 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315 966 999 -138 -449 -869 636 951 -266 -417 -127 -429 385 -406 -395 -75 -802 -929 -377 -290 882 -554 -529 233 -979 830 330 -737 845 309 670 -415 341 339 479 -550 -139 -47 -357 627 351 320 39 -291 182 -956 882 455 -308 781 -151 -349 33 -506 149 -325 315 -895 273 943 143 -357 -968 -923 163 526 446 -505 -497 59 -580 -89 -161 -39 777 671 832 -939 -185 263 -473 -321 514 -351 -276 294 231 699 -429 899 29 -678 -402 -958 -88 938 -80 285 -553 203 925 -790 471 -684 271 420 -559 -15 -582 -81 22 600 -903 455 -285 914 -382 -692 319 -986 363 -23 795 253 -257 -467 211 -908 -559 845 -478 687 -515 387 134 931 203 -7 303 572 737 669 945 -547 379 911 -117 882 704 454 -269 -488 756 -567 -125 -59 715 265 147 429 243 574 -197 -523 -462 -987 937 -305 347 394 462 373 517 -673 640 532 -720 32 185 -821 -749 -727 106 308 -572 721 -34 -803 -613 537 836 -489 -658 168 331 -368 871 -602 399 992 729 -325 -173 -765 -793 -901 -728 -109 -705 -40 -825 972 -46 884 76 471 -814 -753 -169 837 -499 381 178 -363 509 -847 -855 359 65 149 -481 -468 89 417 814 -358 -357 5 91 -924 -738 765 -15 -881 -634 -303 -769 -105 225 -245 -109 -437 -165 625 704 964 539 659 -357 -373 889 173 825 -963 -627 -529 -700 537 851 6 273 -637 -840 -576 -343 -992 9 145 551 -447 870 286 88 -850 440 661 -729 -279 556 588 870 -110 -723 429 -759 -616 361 815 60 861 -522 -29 455 -91 -917 -781 -469 -89 406 -231 -569 289 -84 -847 -199 912 64 748 389 781 -224 -525 -504 287 -605 559 722 -775 -879 991 689 721 -504 -362 988 99 949 202 -931 -920 -284 -213 616 581 847 495 363 -418 608 49 -832 157 763 -203 -581 -689 -632 -231 -91 376 -309 -352 672 253 -301 418 885 85 321 812 501 -79 366 -249 -175 65 737 -849 -453 871 -468 868 919 952 425 351 -935 -301 -595 372 -155 -21 913 50 597 548 825 299 465 -501 249 -583 734 -983 -224 19 -218 476 -364 392 211 580 717 557 942 255 972 -88 -420 -763 -438 -721 351 -289 661 -741 904 -949 -954 -103 858 155 -251 -245 429 -149 -752 657 -781 -583 -224 -202 -771 525 442 978 -13 681 430 198 -623 937 -897 -910 -155 708 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974 972 -913 -903 972 -901 972 968 -897 -895 -883 966 -881 -879 -871 966 964 960 -869 952 -857 -855 -855 -853 946 -849 -847 -847 -845 942 938 -845 938 -839 -825 932 -825 926 920 -821 -803 -793 -781 -781 918 914 912 912 -775 912 -775 910 -775 910 -773 -771 -769 -765 -763 904 898 -759 890 -753 -751 888 -749 -741 -739 -737 884 -737 -729 -727 -723 882 -721 -715 882 882 -705 -703 -689 882 872 -689 870 -689 870 -681 868 -673 -673 868 -663 -637 -631 -627 858 -627 852 -623 -613 848 -605 846 -595 -589 -589 -585 836 -583 -583 834 -581 -569 832 830 820 -569 -567 -559 814 812 -559 -553 -547 806 -537 -529 -529 -525 800 -523 -515 -509 -507 -505 796 -503 -501 786 782 774 -499 760 -499 -497 -495 -489 756 -481 -473 -469 -467 -463 -459 -453 -451 752 -449 -447 748 734 -445 -437 -429 728 -429 -429 -429 -421 -417 724 -415 -411 -403 -395 -385 722 -383 712 708 -383 -377 -377 -373 -373 704 704 704 704 702 700 -367 -363 -357 -357 698 -357 692 -357 686 -357 -351 676 -349 676 672 -343 -341 -335 670 668 650 -335 642 -327 -325 -325 -325 -321 -313 -313 640 -309 -307 636 -305 -305 -303 634 -303 -301 -301 -295 630 -291 -289 -285 -285 -279 -279 -269 630 624 622 -257 616 616 -255 -251 -249 -247 -245 -245 -243 -235 616 -231 -231 608 -231 -231 -217 -213 602 600 -203 -203 -199 592 588 584 580 -199 -197 -197 -187 580 580 574 -185 572 -181 -181 -179 570 -175 564 560 -175 556 -173 552 -169 548 -165 -161 -159 -155 -155 -151 546 -149 -139 546 -139 542 536 532 530 -127 528 -125 -117 -109 -109 -109 526 -105 -103 -91 -91 -91 -89 -89 -81 520 -79 -77 514 510 -75 -59 -47 504 504 -39 -29 -23 500 -23 -21 -19 -15 -15 -13 -9 -7 3 490 482 5 5 7 9 11 15 19 19 29 29 476 33 37 470 39 49 468 468 59 462 65 65 65 71 462 462 460 456 454 85 89 89 446 442 442 442 91 99 99 440 107 119 436 119 434 123 143 145 147 149 149 153 430 155 157 163 430 169 171 428 426 422 173 181 420 185 420 187 203 203 418 211 211 211 217 225 406 402 394 227 231 394 233 392 376 233 374 243 249 251 253 374 372 253 370 255 259 259 263 265 368 271 273 366 273 352 346 273 273 346 277 283 285 344 287 289 330 295 299 303 309 315 315 317 326 320 319 316 321 325 331 335 339 314 341 347 347 312 351 308 351 351 359 361 363 363 308 373 302 379 298 294 286 280 381 276 385 387 252 389 252 252 252 393 242 399 403 403 415 417 242 425 240 429 238 429 429 437 439 443 234 449 455 455 224 224 455 459 216 216 461 465 214 210 471 471 473 202 479 198 487 198 495 501 190 507 188 188 509 186 517 182 180 178 523 525 533 178 537 537 168 539 158 539 543 150 136 134 112 545 551 553 106 104 555 557 102 559 559 567 581 597 607 98 98 623 96 625 627 631 633 651 651 96 92 88 86 657 659 84 661 661 84 80 669 76 671 66 64 671 673 60 679 681 687 689 693 699 60 715 717 56 56 50 717 721 721 46 38 721 729 735 737 737 741 32 741 747 755 759 763 32 765 24 777 22 22 781 781 14 795 801 809 813 14 815 821 825 12 825 6 0 837 845 0 -2 -24 845 847 851 -26 857 861 -28 871 -28 -34 871 -40 885 889 889 897 897 899 905 911 -40 -44 -46 -70 913 913 919 -72 -74 923 -80 -82 925 -82 927 931 937 937 943 -84 945 945 -84 949 951 955 955 955 965 975 981 -86 983 -88 991 993 999 -88 -90 -104 -104 -110 -112 -132 -138 -138 -138 -146 -154 -156 -160 -178 -180 -182 -196 -202 -206 -210 -218 -220 -224 -224 -224 -224 -224 -234 -242 -246 -248 -252 -254 -256 -256 -266 -266 -270 -274 -276 -280 -282 -284 -284 -286 -288 -290 -290 -294 -294 -294 -300 -308 -308 -344 -346 -350 -350 -352 -352 -358 -362 -364 -364 -366 -368 -374 -376 -380 -382 -386 -394 -402 -406 -412 -416 -418 -418 -418 -420 -428 -438 -438 -438 -440 -444 -448 -450 -462 -462 -466 -468 -468 -472 -476 -478 -488 -504 -504 -504 -504 -506 -506 -512 -514 -514 -518 -522 -522 -528 -540 -544 -546 -550 -554 -554 -568 -572 -572 -574 -576 -580 -580 -582 -594 -598 -602 -602 -608 -610 -616 -616 -616 -618 -628 -628 -628 -630 -632 -634 -634 -636 -638 -640 -658 -660 -664 -668 -672 -672 -676 -678 -682 -682 -684 -684 -688 -690 -690 -692 -696 -700 -700 -702 -704 -716 -720 -724 -726 -728 -728 -728 -728 -730 -738 -740 -744 -746 -752 -754 -766 -768 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];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2013-09-26T04:17:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-26T04:12:00.000Z","updated_at":"2026-01-22T14:04:54.000Z","published_at":"2013-09-26T04:14:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2014 China Sorting\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Subset of cases.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e V a vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV= [-5 -12 87 2 88 20 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVout=[-5 88 11 20 2 -12 87]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContest Performance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2736,"title":"Pernicious Anniversary Problem","description":"Since Cody is 5 years old, it's pernicious. A \u003chttp://rosettacode.org/wiki/Pernicious_numbers Pernicious number\u003e is an integer whose population count is a prime. Check if the given number is pernicious.","description_html":"\u003cp\u003eSince Cody is 5 years old, it's pernicious. A \u003ca href = \"http://rosettacode.org/wiki/Pernicious_numbers\"\u003ePernicious number\u003c/a\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/p\u003e","function_template":"function y = isPernicious(x)\r\n y = false;\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2^randi(16);\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 17;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 18;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 61;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2115;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2114;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2017;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":1,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":837,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":34,"created_at":"2014-12-08T08:48:45.000Z","updated_at":"2026-03-18T13:27:13.000Z","published_at":"2017-10-16T01:45:06.000Z","restored_at":"2017-10-25T14:37:50.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince Cody is 5 years old, it's pernicious. A\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://rosettacode.org/wiki/Pernicious_numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePernicious number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42837,"title":"Increasing sub-sequence (Level 1)","description":"Given a vector, v, of real numbers, return a positive integer, n, representing the longest contiguous increasing sub-sequence contained in v.\r\n\r\nExample:\r\n\r\nv = [2 18 9 *6 11 20 25* 3]\r\n\r\nn = 4","description_html":"\u003cp\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest contiguous increasing sub-sequence contained in v.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ev = [2 18 9 \u003cb\u003e6 11 20 25\u003c/b\u003e 3]\u003c/p\u003e\u003cp\u003en = 4\u003c/p\u003e","function_template":"function n = subseq(v)\r\n n = numel(v);\r\nend","test_suite":"%%\r\nv = [2 18 9 6 11 20 25 3];\r\nn_correct = 4;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [-6 -18 -9 -4 -11 -20 -25 -3];\r\nn_correct = 3;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = zeros(1,30);\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [exp(-1) sqrt(2) sqrt(3) exp(1) pi exp(2)];\r\nn_correct = 6;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = 100:-10:-100;\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [0:5 1:7 3:9 2:8];\r\nn_correct = 7;\r\nassert(isequal(subseq(v),n_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-28T09:13:07.000Z","updated_at":"2025-10-06T19:31:12.000Z","published_at":"2016-04-28T09:13:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest contiguous increasing sub-sequence contained in v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = [2 18 9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6 11 20 25\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1893,"title":"GJam 2014 China Rd A: Library Sorting (Small)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2924486/dashboard#s=p2 GJam 2014 China Sorting\u003e. \r\n\r\nThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations. \r\n\r\n*Input:* V a vector\r\n\r\n*Output:* Vout a sorted vector Odds Increasing/Evens Increasing\r\n\r\n*Example:*\r\n\r\nV= [-5 -12 87 2 88 20 11]\r\n\r\nVout=[-5 88 11 20 2 -12 87]\r\n\r\n\r\n*Contest Performance:* Best Time to Complete: \u003c 10 minutes\r\n","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\"\u003eGJam 2014 China Sorting\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e V a vector\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eV= [-5 -12 87 2 88 20 11]\u003c/p\u003e\u003cp\u003eVout=[-5 88 11 20 2 -12 87]\u003c/p\u003e\u003cp\u003e\u003cb\u003eContest Performance:\u003c/b\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/p\u003e","function_template":"function vout=Sort_CH(v)\r\n vout=v;\r\nend","test_suite":"%%\r\ntic\r\nv=[1 ];\r\nvexp=[1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[2 1 ];\r\nvexp=[2 1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 ];\r\nvexp=[1 2 3 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 4 5 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[5 2 3 4 1 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 -87 -85 -83 -71 -71 98 96 -67 -63 -59 -53 -47 -41 96 -41 82 -37 -29 82 -25 -25 80 -21 -13 -11 5 76 72 72 66 66 66 9 60 15 31 35 56 52 52 46 42 39 45 42 40 36 45 30 24 18 51 18 12 53 0 63 -6 65 -10 -12 67 69 79 85 85 -14 89 -16 -22 89 -24 91 -24 -26 -30 -38 -38 -38 -42 -44 -58 -58 -60 -62 -66 -68 -70 -70 -82 -82 -86 -86 -86 -94 -100 ];\r\nvexp=[-87 -87 -85 -83 -71 -71 98 96 -67 -63 -59 -53 -47 -41 96 -41 82 -37 -29 82 -25 -25 80 -21 -13 -11 5 76 72 72 66 66 66 9 60 15 31 35 56 52 52 46 42 39 45 42 40 36 45 30 24 18 51 18 12 53 0 63 -6 65 -10 -12 67 69 79 85 85 -14 89 -16 -22 89 -24 91 -24 -26 -30 -38 -38 -38 -42 -44 -58 -58 -60 -62 -66 -68 -70 -70 -82 -82 -86 -86 -86 -94 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-95 98 -81 -55 90 -29 -19 35 37 75 79 85 93 97 56 54 14 14 0 -14 -22 -34 -38 -46 -62 -90 -98 ];\r\nvexp=[-95 98 -81 -55 90 -29 -19 35 37 75 79 85 93 97 56 54 14 14 0 -14 -22 -34 -38 -46 -62 -90 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-89 -75 -73 -65 86 86 68 66 -41 -37 -25 56 5 21 25 52 36 26 14 27 29 35 45 6 51 63 87 93 -22 95 -26 -48 -54 -70 95 -86 -92 -96 ];\r\nvexp=[-89 -75 -73 -65 86 86 68 66 -41 -37 -25 56 5 21 25 52 36 26 14 27 29 35 45 6 51 63 87 93 -22 95 -26 -48 -54 -70 95 -86 -92 -96 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[76 -7 ];\r\nvexp=[76 -7 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-93 96 -91 86 -87 -87 -67 -53 68 30 -33 0 -33 -13 1 0 3 -10 3 -10 -16 19 23 45 51 -18 53 -30 -36 -72 79 -82 -96 83 91 ];\r\nvexp=[-93 96 -91 86 -87 -87 -67 -53 68 30 -33 0 -33 -13 1 0 3 -10 3 -10 -16 19 23 45 51 -18 53 -30 -36 -72 79 -82 -96 83 91 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 100 96 -81 86 -79 -79 -77 -73 -69 -69 -65 82 -59 -59 70 70 -57 -49 -47 70 -43 -41 54 -35 -31 -31 -29 -25 -17 -13 -5 50 -5 -3 7 21 25 46 27 27 44 31 33 35 37 44 49 42 38 49 51 34 69 34 75 83 20 85 87 91 91 14 12 10 6 0 0 0 -8 -8 -20 -24 -26 -34 -36 -40 -52 -56 -60 -66 -68 -68 -72 -72 -80 -84 -84 -90 -90 ];\r\nvexp=[-87 100 96 -81 86 -79 -79 -77 -73 -69 -69 -65 82 -59 -59 70 70 -57 -49 -47 70 -43 -41 54 -35 -31 -31 -29 -25 -17 -13 -5 50 -5 -3 7 21 25 46 27 27 44 31 33 35 37 44 49 42 38 49 51 34 69 34 75 83 20 85 87 91 91 14 12 10 6 0 0 0 -8 -8 -20 -24 -26 -34 -36 -40 -52 -56 -60 -66 -68 -68 -72 -72 -80 -84 -84 -90 -90 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 100 -81 -75 96 86 -71 -71 86 -33 -27 -25 82 -21 76 -11 68 5 7 9 13 68 15 25 41 41 51 61 56 61 56 67 54 67 48 83 89 91 99 34 30 28 16 16 10 10 4 0 0 0 0 -24 -26 -26 -34 -48 -50 -62 -66 -92 -100 ];\r\nvexp=[-87 100 -81 -75 96 86 -71 -71 86 -33 -27 -25 82 -21 76 -11 68 5 7 9 13 68 15 25 41 41 51 61 56 61 56 67 54 67 48 83 89 91 99 34 30 28 16 16 10 10 4 0 0 0 0 -24 -26 -26 -34 -48 -50 -62 -66 -92 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-93 -89 -87 88 -85 -75 -65 -63 -61 -59 -49 84 -39 -37 80 80 -37 -25 -11 -7 78 -5 78 72 3 5 9 58 11 50 46 23 29 29 31 35 44 37 49 67 71 44 40 30 71 30 28 24 75 75 79 83 18 97 99 6 6 2 0 -4 -8 -10 -16 -18 -30 -32 -34 -36 -38 -46 -46 -48 -48 -52 -54 -56 -66 -68 -88 -90 -100 -100 -100 ];\r\nvexp=[-93 -89 -87 88 -85 -75 -65 -63 -61 -59 -49 84 -39 -37 80 80 -37 -25 -11 -7 78 -5 78 72 3 5 9 58 11 50 46 23 29 29 31 35 44 37 49 67 71 44 40 30 71 30 28 24 75 75 79 83 18 97 99 6 6 2 0 -4 -8 -10 -16 -18 -30 -32 -34 -36 -38 -46 -46 -48 -48 -52 -54 -56 -66 -68 -88 -90 -100 -100 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[90 -89 90 74 -87 62 -83 -79 58 -77 -75 -75 -63 52 52 -59 46 42 -49 -39 -31 36 12 -25 6 -13 -11 5 9 17 23 29 39 -2 -8 -10 47 63 -28 -54 -70 -74 -78 63 65 83 -82 -84 91 97 97 ];\r\nvexp=[90 -89 90 74 -87 62 -83 -79 58 -77 -75 -75 -63 52 52 -59 46 42 -49 -39 -31 36 12 -25 6 -13 -11 5 9 17 23 29 39 -2 -8 -10 47 63 -28 -54 -70 -74 -78 63 65 83 -82 -84 91 97 97 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-97 88 -93 74 70 46 38 36 -91 -85 -83 -77 -67 -63 -55 34 -45 32 -37 16 0 0 -23 -21 -2 -4 5 13 27 -10 -32 -38 -38 -50 39 -56 45 49 -56 77 -56 87 95 97 -62 -62 -68 -68 -72 -80 -94 ];\r\nvexp=[-97 88 -93 74 70 46 38 36 -91 -85 -83 -77 -67 -63 -55 34 -45 32 -37 16 0 0 -23 -21 -2 -4 5 13 27 -10 -32 -38 -38 -50 39 -56 45 49 -56 77 -56 87 95 97 -62 -62 -68 -68 -72 -80 -94 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[81 29 29 -71 -70 16 -70 -93 25 97 51 3 -8 39 -83 97 98 -86 -53 69 58 86 19 75 9 87 -84 66 75 82 85 -87 53 7 65 99 -93 59 -74 4 1 -15 -22 59 -35 -15 51 -10 -27 -98 60 -17 37 29 -98 69 83 9 51 13 -12 -13 50 -39 45 5 -34 75 -84 15 -91 18 -97 -8 0 -44 34 79 -13 -74 -92 80 -84 -92 -32 -46 -26 46 -16 -32 -72 16 84 -46 22 -32 84 58 28 -60 ];\r\nvexp=[-97 -93 -93 -91 98 86 84 -87 -83 -71 -53 -39 84 -35 -27 -17 82 80 -15 -15 66 60 -13 -13 1 3 58 58 5 50 7 9 9 13 15 19 25 29 46 34 29 29 28 37 39 45 51 22 51 18 16 51 53 59 16 59 65 69 69 75 4 75 0 75 79 81 -8 83 -8 85 87 -10 97 -12 -16 -22 -26 97 99 -32 -32 -32 -34 -44 -46 -46 -60 -70 -70 -72 -74 -74 -84 -84 -84 -86 -92 -92 -98 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[10 50 52 3 -29 51 29 -89 55 -34 -77 -41 65 7 -89 0 -44 -98 61 -21 11 -57 -10 95 -12 -25 91 28 90 -49 -57 97 57 -47 33 -59 7 -39 55 91 -89 -41 -7 -18 -61 -93 78 -57 97 45 44 -59 5 38 9 28 -38 11 -36 -92 15 -70 44 -84 18 -24 38 20 -54 0 2 44 28 12 42 -22 74 6 -72 -52 34 -50 30 -44 -6 -42 98 -96 42 38 64 92 -36 92 -90 2 -6 -44 -98 -2 ];\r\nvexp=[98 92 92 -93 -89 -89 -89 -77 -61 90 -59 -59 -57 -57 -57 78 74 64 -49 -47 -41 -41 52 -39 50 -29 -25 44 44 -21 -7 3 5 7 7 9 11 11 15 29 33 45 51 44 55 55 42 57 61 65 42 91 91 38 95 38 38 97 34 30 97 28 28 28 20 18 12 10 6 2 2 0 0 -2 -6 -6 -10 -12 -18 -22 -24 -34 -36 -36 -38 -42 -44 -44 -44 -50 -52 -54 -70 -72 -84 -90 -92 -96 -98 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[34 46 -93 78 -26 11 77 26 47 73 75 53 -89 -52 71 19 -52 -47 16 -19 74 49 21 1 -33 -89 5 -74 67 -55 88 -85 1 -41 93 53 -97 61 -71 -85 77 -45 -1 0 74 95 67 -65 -27 -2 -44 -8 -37 27 36 -58 71 -8 -95 43 17 -19 25 -5 -10 42 10 -64 27 94 41 -69 37 81 -97 -50 -54 66 -22 40 -62 90 -70 40 48 48 52 48 20 98 -42 92 88 40 36 -28 -10 -44 -52 96 ];\r\nvexp=[98 96 -97 94 92 -97 -95 90 -93 -89 -89 -85 -85 88 -71 -69 88 -65 78 -55 74 -47 -45 -41 -37 -33 -27 74 -19 -19 66 -5 -1 1 1 5 11 17 19 21 25 27 27 52 48 37 41 43 47 48 48 46 49 53 42 40 53 40 61 67 67 71 71 73 40 36 36 34 75 26 77 77 81 93 95 20 16 10 0 -2 -8 -8 -10 -10 -22 -26 -28 -42 -44 -44 -50 -52 -52 -52 -54 -58 -62 -64 -70 -74 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-27 ];\r\nvexp=[-27 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[53 75 55 -92 23 -19 83 -70 95 43 -57 1 -11 -9 42 -98 -30 -35 -35 94 -95 -43 -11 -44 96 53 23 -80 -77 -32 -34 45 -16 -2 -77 56 -92 0 -15 38 36 4 -18 72 -84 88 48 58 82 -4 88 -62 -10 -30 10 -100 22 0 -12 -40 -48 -74 ];\r\nvexp=[-95 -77 -77 96 -57 -43 -35 94 -35 -19 -15 -11 -11 -9 88 88 82 1 23 72 23 43 45 58 56 53 53 48 55 42 38 75 36 22 83 10 4 0 95 0 -2 -4 -10 -12 -16 -18 -30 -30 -32 -34 -40 -44 -48 -62 -70 -74 -80 -84 -92 -92 -98 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 63 -79 74 66 5 -51 -9 69 -58 -23 77 -75 -71 91 0 -40 41 -79 32 27 90 66 -56 100 -48 -80 14 -24 ];\r\nvexp=[-87 -79 -79 100 90 -75 -71 -51 -23 74 -9 5 27 41 63 66 66 69 77 32 91 14 0 -24 -40 -48 -56 -58 -80 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[91 34 34 -92 -34 42 99 51 0 54 17 -51 -31 -45 35 -33 92 7 -33 -45 0 -15 76 58 58 100 85 -68 5 -20 -13 83 -39 89 55 89 -90 84 -40 20 90 54 -84 -90 38 -100 60 64 54 32 -30 86 -60 90 -46 -58 -50 ];\r\nvexp=[-51 100 92 90 90 86 -45 -45 84 76 -39 -33 -33 -31 -15 -13 64 5 7 17 60 35 58 58 54 54 51 54 55 42 83 85 89 89 91 99 38 34 34 32 20 0 0 -20 -30 -34 -40 -46 -50 -58 -60 -68 -84 -90 -90 -92 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-41 25 30 -41 20 51 -75 -72 45 -73 75 -77 60 -79 -45 80 19 49 -25 -99 -16 71 55 -79 -35 31 -66 61 -19 -45 -55 -34 73 -55 17 -29 -41 65 -93 51 -58 62 99 73 59 -66 83 -95 -23 62 -82 -81 -31 -33 -9 -41 1 83 36 92 82 80 0 10 78 38 70 0 -52 4 -56 88 -92 -14 56 -6 -74 -90 92 96 86 96 -88 ];\r\nvexp=[-99 -95 96 -93 96 -81 -79 92 -79 -77 -75 -73 92 -55 -55 88 -45 -45 -41 -41 86 -41 -41 -35 -33 -31 82 -29 -25 -23 -19 80 -9 1 17 19 25 31 45 49 80 78 51 51 55 70 59 61 65 62 62 71 73 73 75 83 83 99 60 56 38 36 30 20 10 4 0 0 -6 -14 -16 -34 -52 -56 -58 -66 -66 -72 -74 -82 -88 -90 -92 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-55 93 -57 -68 25 48 -100 75 11 -82 -60 64 74 19 11 -87 -56 -10 45 74 -21 -5 1 12 55 66 -72 73 37 85 -97 -80 51 44 55 -54 -15 -79 32 -93 1 23 -77 -86 90 -71 82 4 14 -100 55 -51 33 -60 65 -30 -34 -37 -75 75 90 33 -35 38 -97 -72 49 4 24 42 88 -60 -78 -68 0 48 -44 -56 24 -12 -48 -78 100 68 -32 -58 24 -44 94 ];\r\nvexp=[-97 -97 -93 100 -87 94 90 -79 -77 90 88 82 74 -75 -71 -57 74 68 -55 66 -51 -37 -35 64 -21 48 48 -15 -5 1 1 44 11 42 11 38 19 23 32 25 33 33 37 24 24 45 24 14 12 4 49 51 55 4 55 0 -10 55 65 73 -12 75 75 -30 85 -32 93 -34 -44 -44 -48 -54 -56 -56 -58 -60 -60 -60 -68 -68 -72 -72 -78 -78 -80 -82 -86 -100 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-41 97 83 0 -33 87 29 18 21 30 90 4 -10 -56 -66 79 -25 55 -40 -55 1 1 0 85 -66 -15 36 -68 -100 65 -8 -77 64 -47 -60 -96 83 -67 12 -85 11 24 -63 -50 17 -60 ];\r\nvexp=[-85 -77 -67 90 -63 -55 -47 64 -41 36 30 24 18 12 4 -33 -25 -15 0 1 1 11 0 17 -8 21 -10 -40 -50 29 -56 55 -60 65 -60 -66 79 83 -66 83 85 -68 87 -96 97 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-75 77 13 57 62 43 -9 13 -61 -37 -19 49 -1 65 -53 -87 -40 -73 -33 80 -11 15 73 -42 -58 -20 85 -97 -57 22 -46 -60 8 62 30 -84 66 40 58 -44 -100 ];\r\nvexp=[-97 -87 -75 -73 80 -61 -57 -53 -37 -33 -19 -11 -9 -1 13 13 66 15 43 62 49 57 65 62 58 40 73 77 85 30 22 8 -20 -40 -42 -44 -46 -58 -60 -84 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[80 30 85 -54 -87 -32 47 33 57 -57 -64 50 67 -84 58 -79 37 -39 77 65 55 26 -58 47 -24 50 -34 72 65 30 38 -57 -49 13 -81 -3 -90 73 -69 91 -38 -49 -52 87 81 -70 51 -98 82 80 0 96 -68 -34 -54 -96 ];\r\nvexp=[96 82 -87 80 -81 80 -79 -69 -57 -57 72 58 -49 50 50 -49 -39 -3 13 33 37 38 30 47 30 26 0 -24 47 -32 -34 51 55 57 65 65 -34 67 73 77 -38 81 -52 85 87 -54 91 -54 -58 -64 -68 -70 -84 -90 -96 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[45 7 -49 57 7 -11 -7 53 -83 99 -90 9 87 100 16 -58 45 33 -98 30 -58 -50 -29 15 -66 76 -86 58 4 -82 ];\r\nvexp=[-83 -49 -29 -11 -7 7 7 9 15 33 100 45 45 76 58 30 53 57 16 4 -50 -58 87 99 -58 -66 -82 -86 -90 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-13 20 -29 34 47 -38 -55 -25 37 41 -87 47 31 -63 -27 -68 -35 32 77 11 -7 -91 -67 -32 59 41 -11 -81 10 96 -50 -11 74 0 -42 -22 92 -72 46 0 0 -80 78 -32 58 4 24 -22 -56 -34 60 ];\r\nvexp=[-91 96 -87 92 -81 78 -67 -63 -55 -35 -29 -27 -25 -13 -11 74 -11 60 -7 11 31 37 41 58 41 47 47 59 46 34 32 77 24 20 10 4 0 0 0 -22 -22 -32 -32 -34 -38 -42 -50 -56 -68 -72 -80 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[35 69 33 35 -7 -54 -89 95 -95 -72 2 42 -89 -10 17 -65 -99 -43 27 95 71 61 -5 -95 -82 21 47 79 -59 52 -44 -10 -19 53 35 -92 -35 -61 -95 -43 35 -98 95 -2 -19 66 89 -54 32 -18 36 72 -64 -10 -88 -50 -8 38 88 -50 ];\r\nvexp=[-99 -95 -95 -95 -89 88 -89 -65 -61 72 66 52 -59 42 -43 -43 -35 -19 -19 -7 -5 17 21 27 38 33 35 35 35 36 32 2 35 47 53 -2 61 69 71 79 89 -8 95 -10 95 -10 95 -10 -18 -44 -50 -50 -54 -54 -64 -72 -82 -88 -92 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-26T03:58:52.000Z","updated_at":"2026-03-11T15:29:23.000Z","published_at":"2013-09-26T04:09:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2014 China Sorting\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e V a vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV= [-5 -12 87 2 88 20 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVout=[-5 88 11 20 2 -12 87]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContest Performance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":566,"title":"Sum of first n terms of a harmonic progression","description":"Given inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 21px; vertical-align: baseline; perspective-origin: 332px 21px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = harmonicSum(a,d,n)\r\n s=0;\r\nend","test_suite":"%%\r\na=1;d=1;n=1;\r\ny_correct = 1;\r\nassert(isequal(harmonicSum(a,d,n),y_correct));\r\n\r\n%%\r\na=2;d=2;n=5;\r\ny_correct = round(3.5746,4);\r\nassert(isequal(round(harmonicSum(a,d,n),4),y_correct));\r\n\r\n%%\r\na=4;d=5;n=2;\r\ny_correct = round(4.6667,4);\r\nassert(isequal(round(harmonicSum(a,d,n),4),y_correct));","published":true,"deleted":false,"likes_count":3,"comments_count":14,"created_by":2974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":501,"test_suite_updated_at":"2020-09-29T02:43:20.000Z","rescore_all_solutions":false,"group_id":27,"created_at":"2012-04-08T16:38:19.000Z","updated_at":"2026-04-01T16:06:03.000Z","published_at":"2012-04-08T18:58:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44523,"title":"Pattern Sum","description":"Write a function which receives two single digit positive integers, (k and m) as parameters and calculates the total sum as: \r\nk + kk + kkk + .... (the last number in the sequence should have m digits) \r\nFor example, if the two integers are:\r\n(4, 5).\r\nYour function should return the total sum of: \r\n4 + 44 + 444 + 4444 + 44444.\r\nNotice the last number in this sequence has 5 digits. The return value should be 49380.","description_html":"\u003cp\u003eWrite a function which receives two single digit positive integers, (k and m) as parameters and calculates the total sum as: \r\nk + kk + kkk + .... (the last number in the sequence should have m digits) \r\nFor example, if the two integers are:\r\n(4, 5).\r\nYour function should return the total sum of: \r\n4 + 44 + 444 + 4444 + 44444.\r\nNotice the last number in this sequence has 5 digits. The return value should be 49380.\u003c/p\u003e","function_template":"function y = pattern_sum(a,b)\r\n \r\nend","test_suite":"%%\r\na = 4;\r\nb = 5;\r\ny_correct = 49380;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 7;\r\nb = 4;\r\ny_correct = 8638;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 5;\r\nb = 3;\r\ny_correct = 615;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 1;\r\ny_correct = 1;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 2;\r\ny_correct = 24;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 9;\r\nb = 9;\r\ny_correct = 1111111101;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 0;\r\nb = 0;\r\ny_correct = 0;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 3;\r\nb = 8;\r\ny_correct = 37037034;\r\nassert(isequal(pattern_sum(a,b),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":181342,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":237,"test_suite_updated_at":"2018-07-13T17:24:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-02-15T01:05:11.000Z","updated_at":"2026-03-24T20:17:24.000Z","published_at":"2018-02-15T01:18:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function which receives two single digit positive integers, (k and m) as parameters and calculates the total sum as: k + kk + kkk + .... (the last number in the sequence should have m digits) For example, if the two integers are: (4, 5). Your function should return the total sum of: 4 + 44 + 444 + 4444 + 44444. Notice the last number in this sequence has 5 digits. The return value should be 49380.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42839,"title":"Identify the sequence","description":"Given a row vector, x, return 1 if it is an arithmetic series, or 2 if it is a geometric series. If it is neither, return 0.\r\n\r\nExample 1:\r\n\r\nx = 1:8\r\n\r\ny = 1\r\n\r\nExample 2:\r\n\r\nx = 2^(1:8)\r\n\r\ny = 2\r\n\r\nExample 3:\r\n\r\nx = [1 1 2 3 5 8 13 21 34]\r\n\r\ny = 0","description_html":"\u003cp\u003eGiven a row vector, x, return 1 if it is an arithmetic series, or 2 if it is a geometric series. If it is neither, return 0.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003ex = 1:8\u003c/p\u003e\u003cp\u003ey = 1\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003ex = 2^(1:8)\u003c/p\u003e\u003cp\u003ey = 2\u003c/p\u003e\u003cp\u003eExample 3:\u003c/p\u003e\u003cp\u003ex = [1 1 2 3 5 8 13 21 34]\u003c/p\u003e\u003cp\u003ey = 0\u003c/p\u003e","function_template":"function y = stype(x)\r\n y = -1;\r\nend","test_suite":"%%\r\nx = 1:8;\r\ny_correct = 1;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = 2.^(1:8);\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [1 1 2 3 5 8 13 21 34];\r\ny_correct = 0;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = ones(1,80);\r\ny_correct1 = 1;\r\ny_correct2 = 2;\r\nassert(isequal(stype(x),y_correct1)|isequal(stype(x),y_correct2))\r\n\r\n%%\r\nx = [ones(1,40) 0 ones(1,40)];\r\ny_correct = 0;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [exp(1) exp(3) exp(5) exp(7) exp(9)];\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n\r\n%%\r\nx = [-64 32 -16 8 -4 2 -1 0.5 -0.25];\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [-9.6 -9.7 -9.8 -9.9 -10 -10.1 -10.2 -10.3 -10.4];\r\ny_correct = 1;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [1 1 -1 -1];\r\ny_correct = 0;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [i 3i 5i 7i];\r\ny_correct = 1;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [i -2 -4i 8 16i];\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2016-05-27T18:43:30.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-28T17:52:25.000Z","updated_at":"2025-12-30T12:59:47.000Z","published_at":"2016-04-28T17:52:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a row vector, x, return 1 if it is an arithmetic series, or 2 if it is a geometric series. If it is neither, return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 1:8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 2^(1:8)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 3:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = [1 1 2 3 5 8 13 21 34]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2329,"title":"Finding the next number in a number list, are you able to crack it!","description":"So it goes like this, I give a number list and you find the next value!\r\n\r\nI found a way to do it, just wondering how many others can to! \r\n\r\nThis could be a fun test of skill! Please try and see if you can get it!\r\n\r\nExample:\r\n\r\n x = [ ...\r\n 11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3];\r\n NextValue = 3;\r\n\r\n %% Next value after x(1), so your finding the ? in sequence x = [?; 11; 4; 16; 3; ... 3];\r\n\r\nGood luck, just saying, it is tricky! Many have solved this, but the key is to find the pattern...","description_html":"\u003cp\u003eSo it goes like this, I give a number list and you find the next value!\u003c/p\u003e\u003cp\u003eI found a way to do it, just wondering how many others can to!\u003c/p\u003e\u003cp\u003eThis could be a fun test of skill! Please try and see if you can get it!\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e x = [ ...\r\n 11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3];\r\n NextValue = 3;\u003c/pre\u003e\u003cpre\u003e %% Next value after x(1), so your finding the ? in sequence x = [?; 11; 4; 16; 3; ... 3];\u003c/pre\u003e\u003cp\u003eGood luck, just saying, it is tricky! Many have solved this, but the key is to find the pattern...\u003c/p\u003e","function_template":"function NextNumber = FindNextNumber(x)\r\n NextNumber = x;\r\nend","test_suite":"%%\r\nx = [11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3];\r\nNextNumber= 3;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [9;\r\n 1;\r\n 7;\r\n 1;\r\n 7;\r\n 9;\r\n 2;\r\n 8;\r\n 4;\r\n 8;\r\n 16;\r\n 21;\r\n 13;\r\n 15;\r\n 1;\r\n 13;\r\n 10];\r\nNextNumber= 8;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [6;\r\n 20;\r\n 9;\r\n 3;\r\n 25;\r\n 4;\r\n 1;\r\n 4;\r\n 8;\r\n 9;\r\n 1;\r\n 7];\r\nNextNumber= 1;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [17;\r\n 5;\r\n 12;\r\n 33;\r\n 5;\r\n 7;\r\n 4];\r\nNextNumber= 4;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [8;\r\n 6;\r\n 11;\r\n 4;\r\n 1;\r\n 6;\r\n 2;\r\n 1;\r\n 3;\r\n 11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3;\r\n 1;\r\n 2;\r\n 5;\r\n 16;\r\n 1;\r\n 2;\r\n 17;\r\n 9;\r\n 8;\r\n 5;\r\n 12;\r\n 16;\r\n 11;\r\n 8;\r\n 5;\r\n 10;\r\n 11;\r\n 10;\r\n 10;\r\n 2;\r\n 4;\r\n 17;\r\n 5;\r\n 12;\r\n 33;\r\n 5;\r\n 7;\r\n 4;\r\n 11;\r\n 16;\r\n 5;\r\n 1;\r\n 6;\r\n 20;\r\n 9;\r\n 3;\r\n 25;\r\n 4;\r\n 1];\r\nNextNumber= 5;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [4;\r\n 4;\r\n 18;\r\n 12;\r\n 27;\r\n 20;\r\n 24;\r\n 25;\r\n 14;\r\n 29;\r\n 16;\r\n 25;\r\n 15;\r\n 6;\r\n 6;\r\n 3;\r\n 20;\r\n 9;\r\n 20;\r\n 5;\r\n 12;\r\n 24;\r\n 16;\r\n 27];\r\nNextNumber= 20;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [14;\r\n 22;\r\n 27;\r\n 15;\r\n 8;\r\n 30;\r\n 24;\r\n 33;\r\n 28;\r\n 27;\r\n 31;\r\n 31;\r\n 38;\r\n 29;\r\n 30;\r\n 35;\r\n 12;\r\n 7;\r\n 15;\r\n 22;\r\n 10;\r\n 26;\r\n 35;\r\n 15;\r\n 25;\r\n 18;\r\n 32;\r\n 30;\r\n 31;\r\n 35;\r\n 22;\r\n 15;\r\n 21;\r\n 13;\r\n 19;\r\n 24;\r\n 32;\r\n 18;\r\n 30;\r\n 31;\r\n 28;\r\n 32;\r\n 40;\r\n 17;\r\n 15;\r\n 28;\r\n 41;\r\n 42;\r\n 35;\r\n 30;\r\n 35;\r\n 39;\r\n 33;\r\n 17;\r\n 34;\r\n 26;\r\n 13;\r\n 14;\r\n 19;\r\n 40;\r\n 13;\r\n 27;\r\n 16;\r\n 23;\r\n 22;\r\n 29;\r\n 42;\r\n 33;\r\n 37;\r\n 28;\r\n 36;\r\n 30;\r\n 26;\r\n 6;\r\n 25;\r\n 39;\r\n 26;\r\n 23;\r\n 39;\r\n 27;\r\n 28;\r\n 14;\r\n 25;\r\n 29;\r\n 7;\r\n 16];\r\nNextNumber= 35;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%% \r\nx = [27;\r\n 31;\r\n 31;\r\n 38;\r\n 29;\r\n 30;\r\n 35;\r\n 12;\r\n 7;\r\n 15;\r\n 22;\r\n 10;\r\n 26;\r\n 35;\r\n 15;\r\n 25;\r\n 18;\r\n 32;\r\n 30;\r\n 31;\r\n 35;\r\n 22;\r\n 15;\r\n 21;\r\n 13;\r\n 19;\r\n 24;\r\n 32;\r\n 18;\r\n 30;\r\n 31;\r\n 28;\r\n 32;\r\n 40;\r\n 17;\r\n 15;\r\n 28;\r\n 41;\r\n 42;\r\n 35;\r\n 30;\r\n 35;\r\n 39;\r\n 33;\r\n 17;\r\n 34;\r\n 26;\r\n 13;\r\n 14;\r\n 19;\r\n 40;\r\n 13;\r\n 27;\r\n 16;\r\n 23;\r\n 22;\r\n 29;\r\n 42;\r\n 33;\r\n 37;\r\n 28;\r\n 36;\r\n 30;\r\n 26;\r\n 6;\r\n 25;\r\n 39;\r\n 26;\r\n 23;\r\n 39;\r\n 27;\r\n 28;\r\n 14;\r\n 25;\r\n 29;\r\n 7;\r\n 16;\r\n 28;\r\n 11;\r\n 14];\r\nNextNumber= 28;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [39;\r\n 46;\r\n 39;\r\n 21;\r\n 46;\r\n 46;\r\n 45;\r\n 31;\r\n 47;\r\n 45;\r\n 39;\r\n 44;\r\n 47];\r\nNextNumber= 45;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [7;\r\n 8;\r\n 18;\r\n 7;\r\n 9;\r\n 2;\r\n 11;\r\n 2;\r\n 2;\r\n 2;\r\n 13;\r\n 4;\r\n 4;\r\n 13;\r\n 11;\r\n 6;\r\n 3;\r\n 15;\r\n 16;\r\n 17;\r\n 4;\r\n 7;\r\n 17;\r\n 12;\r\n 3;\r\n 12;\r\n 9;\r\n 3;\r\n 17;\r\n 2;\r\n 4;\r\n 17;\r\n 5;\r\n 18;\r\n 1;\r\n 4;\r\n 15;\r\n 2;\r\n 11;\r\n 6;\r\n 19;\r\n 4;\r\n 2;\r\n 1;\r\n 18;\r\n 15;\r\n 12;\r\n 17;\r\n 11;\r\n 2;\r\n 1;\r\n 3;\r\n 17;\r\n 15;\r\n 4;\r\n 12;\r\n 10;\r\n 11;\r\n 16;\r\n 4;\r\n 2;\r\n 13;\r\n 13;\r\n 8;\r\n 16;\r\n 2;\r\n 9;\r\n 19;\r\n 7;\r\n 15;\r\n 12;\r\n 5;\r\n 17;\r\n 6;\r\n 9;\r\n 16;\r\n 9;\r\n 11;\r\n 4;\r\n 12;\r\n 7;\r\n 12;\r\n 9;\r\n 18;\r\n 2;\r\n 8;\r\n 14];\r\nNextNumber= 4;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-16T23:24:44.000Z","updated_at":"2014-05-19T14:19:51.000Z","published_at":"2014-05-16T23:24:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo it goes like this, I give a number list and you find the next value!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI found a way to do it, just wondering how many others can to!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis could be a fun test of skill! Please try and see if you can get it!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ ...\\n 11;\\n 4;\\n 16;\\n 3;\\n 3;\\n 15;\\n 6;\\n 17;\\n 10;\\n 18;\\n 7;\\n 13;\\n 15;\\n 5;\\n 24;\\n 5;\\n 3;\\n 3];\\n NextValue = 3;\\n\\n %%Next value after x(1), so your finding the ? in sequence x = [?; 11; 4; 16; 3; ... 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck, just saying, it is tricky! Many have solved this, but the key is to find the pattern...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43649,"title":"4 Digit Sequence Repetitions","description":"Given a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.\r\n\r\nFor example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:\r\n\r\n2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...\r\n\r\nGiven a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.\r\n\r\nFor example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.\r\n\r\nTaken from L-S Hahn's New Year's Puzzle for 2009","description_html":"\u003cp\u003eGiven a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.\u003c/p\u003e\u003cp\u003eFor example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:\u003c/p\u003e\u003cp\u003e2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...\u003c/p\u003e\u003cp\u003eGiven a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.\u003c/p\u003e\u003cp\u003eFor example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.\u003c/p\u003e\u003cp\u003eTaken from L-S Hahn's New Year's Puzzle for 2009\u003c/p\u003e","function_template":"function i = seq_appears(yr, tst)\r\n i=0;\r\nend","test_suite":"%%\r\nyr = [2 0 0 9];\r\ntst = [2 0 1 0];\r\nia = 0;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 2 3 4];\r\ntst = [5 6 7 8];\r\nia = 621;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 2 3 4];\r\ntst = [4 5 6 7];\r\nia = 1125;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 1 1 1];\r\ntst = [4 7 3 5];\r\nia = 5;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 1 1 1];\r\ntst = [2 2 2 2];\r\nia = 0;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 1 1 1];\r\ntst = [7 7 7 7];\r\nia = 1171;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [0 0 0 1];\r\ntst = [9 0 0 0];\r\nia = 780;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2016-11-01T17:01:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-11-01T16:59:37.000Z","updated_at":"2026-01-18T13:14:50.000Z","published_at":"2016-11-01T16:59:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTaken from L-S Hahn's New Year's Puzzle for 2009\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46615,"title":"Find terms in the Connell sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.742px 7.79167px; transform-origin: 375.742px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Connell sequence starts with the first odd number and continues with the next two even numbers, the next three odd numbers, the next four even numbers, and so on. Therefore, the first ten terms are 1, 2, 4, 5, 7, 9, 10, 12, 14, and 16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 7.79167px; transform-origin: 373.275px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the terms at the specified positions in the Connell sequence. FOR and WHILE loops are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Connell(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nfiletext = fileread('Connell.m');\r\nnoloops = isempty(strfind(filetext, 'for')) \u0026\u0026 isempty(strfind(filetext, 'while'));\r\nassert(noloops, 'No loops allowed')\r\n\r\n%%\r\nn = 1:10;\r\ny_correct = [1 2 4 5 7 9 10 12 14 16];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 35:40;\r\ny_correct = [62 64 65 67 69 71];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 628:633;\r\ny_correct = [1221 1223 1225 1226 1228 1230];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 1620:1625;\r\ny_correct = 3183:2:3193;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 11111:11111:66666;\r\ny_correct = [22073 44233 66408 88590 110777 132967];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 12457910;\r\ny_correct = 24910828;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 12457910121416;\r\ny_correct = 24915815251257;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 15053\r\ny_correct = 59619;\r\nassert(isequal(Connell(Connell(n)),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2020-12-31T19:26:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-25T12:18:07.000Z","updated_at":"2025-12-09T15:00:13.000Z","published_at":"2020-09-25T13:32:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Connell sequence starts with the first odd number and continues with the next two even numbers, the next three odd numbers, the next four even numbers, and so on. Therefore, the first ten terms are 1, 2, 4, 5, 7, 9, 10, 12, 14, and 16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the terms at the specified positions in the Connell sequence. FOR and WHILE loops are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53004,"title":"Collect a set of candy wrappers","description":"This past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) their many neighbors with their costumes inspired by “mundane Halloween”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\r\n“This wrapper has a proof of the infinitude of primes!”, said Matilda.\r\n“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\r\n“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\r\nThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the Handbook of Mathematical Functions by Abramowitz and Stegun. \r\nMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\r\nWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 369px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.5px; transform-origin: 407px 184.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276.975px 8.05px; transform-origin: 276.975px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51251\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003etheir many neighbors\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8917px 8.05px; transform-origin: 31.8917px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with their costumes inspired by “\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003emundane Halloween\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.658px 8.05px; transform-origin: 244.658px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.317px 8.05px; transform-origin: 207.317px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“This wrapper has a proof of the infinitude of primes!”, said Matilda.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.475px 8.05px; transform-origin: 253.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242.983px 8.05px; transform-origin: 242.983px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.025px 8.05px; transform-origin: 359.025px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.475px 8.05px; transform-origin: 117.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e Handbook of Mathematical Functions\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4583px 8.05px; transform-origin: 89.4583px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by Abramowitz and Stegun. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.15px 8.05px; transform-origin: 383.15px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8.05px; transform-origin: 383px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = collectWrappers(n)\r\n y = factorial(factorial(n));","test_suite":"%%\r\nn = 5;\r\ny_correct = 12;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 25;\r\ny_correct = 96;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 40;\r\ny_correct = 172;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 1526;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 500;\r\ny_correct = 3397;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 1000:25:1125;\r\ny_correct = [7486 7698 7911 8125 8339 8554];\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2500;\r\ny_correct = 21004;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny_correct = 97877;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250000;\r\ny_correct = 3251609;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e6;\r\ny_correct = 80010822;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e7;\r\ny_correct = 440290052;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e8;\r\ny_correct = 10303667162;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e9;\r\ny_correct = 55541930585;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%% Anti-lookup\r\nn = [7 17 71 77 117 171 177 711 717 771 777];\r\nyy_correct = [68 276 2216 2478 4393 7308 7647 46281 46777 51268 51779];\r\nindx = randi(11,[1 randi(11)]);\r\nassert(isequal(collectWrappers(collectWrappers(n(indx))),yy_correct(indx)))\r\n\r\n%%\r\nfiletext = fileread('collectWrappers.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2021-11-06T13:42:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-06T13:09:20.000Z","updated_at":"2026-01-02T17:08:42.000Z","published_at":"2021-11-06T13:12:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51251\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etheir many neighbors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e with their costumes inspired by “\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emundane Halloween\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e“This wrapper has a proof of the infinitude of primes!”, said Matilda.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Handbook of Mathematical Functions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by Abramowitz and Stegun. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52462,"title":"Easy Sequences 1: Find the index of an element","description":"The nth element of a series is defined by: . Obviously, the first element . Given the nth element , find the value of the corresponding index .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 66px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 33px; transform-origin: 407px 33px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe nth element of a series \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined by: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 155.5px; height: 45px;\" width=\"155.5\" height=\"45\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Obviously, the first element \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5px 8px; transform-origin: 36.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Given the nth element \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18.5px;\" width=\"33\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the value of the corresponding index \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = index(a)\r\n n = a;\r\nend","test_suite":"%%\r\na = 1;\r\nn = index(a);\r\nassert(isequal(1,n))\r\n%%\r\na = 25;\r\nn = index(a);\r\nbs = arrayfun(@(x) sum(arrayfun(@(k) k*(-1)^(k^3+1),1:x)),1:n);\r\nb = bs(end);\r\nassert(isequal(a,b))\r\n%%\r\na = 100;\r\nn = index(a);\r\nbs = arrayfun(@(x) sum(arrayfun(@(k) k*(-1)^(k^3+1),1:x)),1:n);\r\nb = bs(end);\r\nassert(isequal(a,b))\r\n%%\r\na = randi([1000,ceil(exp(log(double(intmax)/2)))]);\r\nn = index(a);\r\nassert(isequal(index(-a+(1-(-1)^(n+1))/2),n+1))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":"2021-08-11T04:47:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-10T10:31:40.000Z","updated_at":"2026-04-01T20:40:04.000Z","published_at":"2021-08-10T10:34:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe nth element of a series \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined by: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(n) = \\\\displaystyle\\\\sum\\\\limits_{k=1}^n (k\\\\cdot(-1)^{k^3+1})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, the first element \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Given the nth element \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the value of the corresponding index \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46676,"title":"List the erauqs","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.825px 8.16667px; transform-origin: 33.825px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter I told \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/players/8608872-jessicar\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eJessicaR\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3917px 8.16667px; transform-origin: 21.3917px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e about \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46624\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.558px 8.16667px; transform-origin: 230.558px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involves the emirps, she asked, \"What about the erauqs?\" As I will do with you, she let me deduce what they are.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.742px 8.16667px; transform-origin: 222.742px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the erauqs less than or equal to the input number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = erauqs(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 99;\r\nassert(isempty(erauqs(n)))\r\n \t\r\n%%\r\nn = 1000;\r\ny_correct = [100 144 169 400 441 900 961];\r\nassert(isequal(erauqs(n),y_correct))\r\n \t\r\n%%\r\nn = 10000;\r\ny_correct = [100 144 169 400 441 900 961 1089 9801 10000];\r\nassert(isequal(erauqs(n),y_correct))\r\n \t\r\n%%\r\nn = 100000;\r\ny = erauqs(n);\r\nlen_correct = 29;\r\nyp_correct = [10404 10609 12100 12544 12769 14400 14884 16900 40000 40401 44100 44521 48400 48841 67600 90000 90601 96100 96721];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(11:29),yp_correct))\r\n\t\r\n%%\r\nn = 1000000;\r\ny = erauqs(n);\r\nlen_correct = 32;\r\nyp_correct = [108900 980100 1000000];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(end-2:end),yp_correct))\r\n \t\r\n%%\r\nn = 1e8;\r\ny = erauqs(n);\r\nlen_correct = 100;\r\nyp_correct = [4456321 4498641 4888521 9678321];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y([76 78 83 94]),yp_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T01:35:23.000Z","updated_at":"2026-02-27T09:58:31.000Z","published_at":"2020-10-06T02:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter I told \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/8608872-jessicar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJessicaR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e about \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46624\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involves the emirps, she asked, \\\"What about the erauqs?\\\" As I will do with you, she let me deduce what they are.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the erauqs less than or equal to the input number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44628,"title":"The other half of the Fibonacci sequence","description":"The \u003chttp://mathworld.wolfram.com/FibonacciNumber.html \"Fibonacci sequence\"\u003e — \r\nF = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from _circa_ 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \"Fibonacci\") _circa_ 1202 CE. \r\n\r\nThis sequence can be defined by \r\n\r\n*F(n+2) = F(n+1) + F(n)*\r\n\r\nin which F(1) = 1, F(2) = 1, F(3) = 2, ....\r\n\r\nLater in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0). \r\n\r\nYour job in this Cody Problem is to 'create history'(?) by extending this sequence to _negative values of n_, to discover the missing half of this sequence!\r\n\r\nEXAMPLE:\r\n\r\nIf n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.\r\n\r\nYou are only required to provide outputs for n \u003c 3 that can be represented by an \u003chttps://au.mathworks.com/help/matlab/ref/int64.html |int64|\u003e \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e. To enforce this, your output needs to be of this data type. ","description_html":"\u003cp\u003eThe \u003ca href = \"http://mathworld.wolfram.com/FibonacciNumber.html\"\u003e\"Fibonacci sequence\"\u003c/a\u003e — \r\nF = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from \u003ci\u003ecirca\u003c/i\u003e 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \"Fibonacci\") \u003ci\u003ecirca\u003c/i\u003e 1202 CE.\u003c/p\u003e\u003cp\u003eThis sequence can be defined by\u003c/p\u003e\u003cp\u003e\u003cb\u003eF(n+2) = F(n+1) + F(n)\u003c/b\u003e\u003c/p\u003e\u003cp\u003ein which F(1) = 1, F(2) = 1, F(3) = 2, ....\u003c/p\u003e\u003cp\u003eLater in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0).\u003c/p\u003e\u003cp\u003eYour job in this Cody Problem is to 'create history'(?) by extending this sequence to \u003ci\u003enegative values of n\u003c/i\u003e, to discover the missing half of this sequence!\u003c/p\u003e\u003cp\u003eEXAMPLE:\u003c/p\u003e\u003cp\u003eIf n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.\u003c/p\u003e\u003cp\u003eYou are only required to provide outputs for n \u0026lt; 3 that can be represented by an \u003ca href = \"https://au.mathworks.com/help/matlab/ref/int64.html\"\u003e\u003ctt\u003eint64\u003c/tt\u003e\u003c/a\u003e \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e. To enforce this, your output needs to be of this data type.\u003c/p\u003e","function_template":"% This was my logic: ...\r\nfunction F = negativeRabbits(n)\r\n % Here's how I implemented that conceptual logic in code:\r\n n = F\r\nend","test_suite":"%% Ban str2num \u0026 str2double; regexp \u0026 regexpi\r\n% Banning these to discourage hard-coded answers and silly 'scoring cheats'. Sorry if it disrupts some legitimate usage. \r\n% Please don't try any other hacks or workarounds. \r\nassessFunctionAbsence({'str2num','str2double','regexp', 'regexpi'}, 'FileName','negativeRabbits.m');\r\nFR = fileread('negativeRabbits.m');\r\nmsg = 'Don''t hard-code your ''solution''.';\r\nassert( ~any( cellfun( @(z) contains(FR, z) , {'54800875592', '716768017756', '9845401187926'} ) ) , msg )\r\n\r\n%% Ban \"ans\" and a few hard-coded values (digits stripped)\r\n% I don't think it's very good style to be using \"ans\". \r\nRE = regexp(fileread('negativeRabbits.m'), '\\w+', 'match');\r\ntabooWords = {'ans'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not include the following banned strings in your code!' char([10 13]) ...\r\n strjoin(RE(testResult)) char([10 13])];\r\nassert(~any( cellfun( @(z) ismember(z, tabooWords), RE ) ), msg)\r\n\r\n%% Check data type\r\n% This is important.\r\nassert( isequal( class(negativeRabbits(0)) , 'int64' ) , 'Wrong data type.')\r\n\r\n%% Initial conditions and other such key values. \r\n% Test Suite shall ensure it only ever checks n \u003c 3. \r\nassert( isequal(negativeRabbits(+2), 1) , 'Failed at n =+2.' )\r\nassert( isequal(negativeRabbits(+1), 1) , 'Failed at n =+1.' )\r\nassert( isequal(negativeRabbits( 0), 0) , 'Failed at n = 0.' )\r\nassert( isequal(negativeRabbits(-1), 1) , 'Failed at n =-1.' )\r\n\r\n%% Terms from 0 down to -10\r\nfor n = 0 : -1 : -10\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -10 down to -20\r\nfor n = -10 : -1 : -20\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -20 down to -40\r\nfor n = -20 : -1 : -40\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -40 down to -77\r\nfor n = -40 : -1 : -77\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -77 down to -92\r\n% This is difficult, but feasible within the parameters of the problem. \r\nfor n = -77 : -1 : -92\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2018-05-03T02:41:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-04-28T14:33:34.000Z","updated_at":"2026-02-21T13:17:20.000Z","published_at":"2018-04-28T16:25:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://mathworld.wolfram.com/FibonacciNumber.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"Fibonacci sequence\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e — F = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecirca\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \\\"Fibonacci\\\")\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecirca\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1202 CE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence can be defined by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF(n+2) = F(n+1) + F(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein which F(1) = 1, F(2) = 1, F(3) = 2, ....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLater in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour job in this Cody Problem is to 'create history'(?) by extending this sequence to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enegative values of n\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to discover the missing half of this sequence!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are only required to provide outputs for n \u0026lt; 3 that can be represented by an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/ref/int64.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eint64\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. To enforce this, your output needs to be of this data type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61018,"title":"Find the logic and return the nth number","description":"given a sequence of numbers arranged in the following order:\r\nA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\r\nWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\r\neg:\r\nn=5\r\n--\u003e output=9","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 85.5px; transform-origin: 408px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003egiven a sequence of numbers arranged in the following order:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeg:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en=5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--\u0026gt; output=9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(n)\r\n y=n;\r\nend","test_suite":"%%\r\nn = 15;\r\ny_correct = 39;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 325;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 100;\r\ny_correct = 976;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 150;\r\ny_correct = 2278;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 200;\r\ny_correct = 2929;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 3268;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4946338,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-20T06:08:57.000Z","updated_at":"2026-03-23T12:09:51.000Z","published_at":"2025-10-20T06:08:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a sequence of numbers arranged in the following order:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeg:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--\u0026gt; output=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52594,"title":"Easy Sequences 10: Sum of Cumsums of Fibonacci Sequence","description":"The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:\r\n \u003e\u003e Fn = [1 1 2 3 5 8 13 21 34 55];\r\n \u003e\u003e Sn = sum(cumsum(Fn))\r\n \u003e\u003e Sn =\r\n 364\r\nIt has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation. \r\nGiven a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. In the example above we have, 'n = 10' for 's = 364' . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 236.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 118.367px; transform-origin: 407px 118.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.5px 8px; transform-origin: 130.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function F(n) is defined as the set of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFibonacci numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.5px 8px; transform-origin: 188.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 144px 8.5px; tab-size: 4; transform-origin: 144px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; Fn = [1 1 2 3 5 8 13 21 34 55];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100px 8.5px; tab-size: 4; transform-origin: 100px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; Sn = sum(cumsum(Fn))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; Sn =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 32px 8.5px; tab-size: 4; transform-origin: 32px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 364\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327px 8px; transform-origin: 327px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.5px 8px; transform-origin: 47.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the example above we have,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'n = 10' for 's = 364' . \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = N(s)\r\n n = inv_cumsum(inv_sum(s));\r\nend","test_suite":"%%\r\ns = 364;\r\nn_correct = 10;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = 2000;\r\nn_correct = 13;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = 5000:100:10000;\r\nn_correct = 798;\r\nn_answer = sum(arrayfun(@(i) N(i),s));\r\nassert(isequal(n_answer,n_correct))\r\n%%\r\ns = intmax;\r\nn_correct = 42;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = 10^10;\r\nn_correct = 45;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = intmax('uint64');\r\nn_correct = 89;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = realmax/10;\r\nn_correct = 1467;\r\nassert(isequal(N(s),n_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-23T07:31:32.000Z","updated_at":"2025-12-16T04:43:30.000Z","published_at":"2021-08-23T12:03:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function F(n) is defined as the set of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFibonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e Fn = [1 1 2 3 5 8 13 21 34 55];\\n \u003e\u003e Sn = sum(cumsum(Fn))\\n \u003e\u003e Sn =\\n 364]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIn the example above we have,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'n = 10' for 's = 364' . \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52654,"title":"Easy Sequences 13: Average Speed of Spaceship","description":"A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around. \r\nGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops. Please round-off your answer to the nearest integer.\r\nNOTE: Use clasical physics only. Ignore any relativistic effects.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e Please round-off your answer to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = mean_velocity(s,v)\r\n y = x;\r\nend","test_suite":"%%\r\ns = 10000;\r\nv = 10000;\r\nv_correct = 1022;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1234567;\r\nv = 1234567;\r\nv_correct = 84539;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = '1234567891011121314151617181920';\r\nv = 123456789;\r\nv_correct = 6427156;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1e100;\r\nvs = 1:1000;\r\nv_correct = 72076;\r\nassert(isequal(sum(arrayfun(@(v) mean_velocity(s,v),vs)),v_correct))\r\n%%\r\ns = intmax;\r\nv = double(intmax);\r\nv_correct = 97326319;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = intmax('int64')/100;\r\nv = double(intmax('int64'))/100;\r\nv_correct = 2326765408587627;\r\nassert(isequal(mean_velocity(s,v),v_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-09-05T14:22:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T08:20:36.000Z","updated_at":"2025-12-22T16:16:27.000Z","published_at":"2021-09-05T08:20:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \\\"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Please round-off your answer to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52584,"title":"Easy Sequences 9: Faithful Pairs","description":"A \"faithful number\" is a non-prime number that is one less or one more than some prime number but not both. For example, for numbers up to 20, the numbers 1 8, 10, 14, 16 and 20 are faithful. The number 4 does not qualify because it is equal to \"3 + 1\" and \"5 - 1\". \r\nIf both 'x' and 'x+2' are faithful but not to the same prime, the pair (x, x+2) is called a faithful pair. So, from 1 to 20 the faithful pairs are (8, 10) and (14, 16). Faithful pairs are scarse and rarer than primes themselves. We can only find 1 faithful pair for numbers 1 to 10, 5 pairs for numbers up to 50 and 8 pairs up to 100.\r\nLet \"P\" be the set of all faithful pairs from 1 to a given number \"n\". We define \"F\" as the set of all p1, p1 \u003c p2 ∀pairs (p1,p2) ∈ P. Write a function \"S(n)\", that sums all the elements of F. \r\nFor 1 to 20, P(20) = [8 10; 14 16], F(20) = [8 14] and S(20) = 22. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 237px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA \"faithful number\" is a non-prime number that is one less or one more than some prime number but not both. For example, for numbers up to 20, the numbers 1 8, 10, 14, 16 and 20 are faithful. The number 4 does not qualify because it is equal to \"3 + 1\" and \"5 - 1\". \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIf both 'x' and 'x+2' are faithful but not to the same prime, the pair (x, x+2) is called a faithful pair. So, from 1 to 20 the faithful pairs are (8, 10) and (14, 16). Faithful pairs are scarse and rarer than primes themselves. We can only find 1 faithful pair for numbers 1 to 10, 5 pairs for numbers up to 50 and 8 pairs up to 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eLet \"P\" be the set of all faithful pairs from 1 to a given number \"n\". We define \"F\" as the set of all p1, p1 \u0026lt; p2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e∀\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003epairs (p1,p2) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e∈\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e P. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite a function \"S(n)\", that sums all the elements of F.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor 1 to 20, P(20) = [8 10; 14 16], F(20) = [8 14] and S(20) = 22. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n n = 20;\r\n p = [8 10; 14 16];\r\n f = [8 14];\r\n s = 22;\r\nend\r\n","test_suite":"%%\r\nn = 20;\r\ns_correct = 22;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 9;\r\ns_correct = 0;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 5:5:100;\r\ns_correct = [0 8 8 22 42 42 42 80 80 124 124 124 124 192 192 192 272 272 272 370];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 17216;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 2^20;\r\ns_correct = 4054100250;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = intmax;\r\ns_correct = 6921757389660954;\r\nassert(isequal(S(n),s_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-22T10:45:18.000Z","updated_at":"2025-11-30T19:31:23.000Z","published_at":"2021-08-22T11:03:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \\\"faithful number\\\" is a non-prime number that is one less or one more than some prime number but not both. For example, for numbers up to 20, the numbers 1 8, 10, 14, 16 and 20 are faithful. The number 4 does not qualify because it is equal to \\\"3 + 1\\\" and \\\"5 - 1\\\". \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf both 'x' and 'x+2' are faithful but not to the same prime, the pair (x, x+2) is called a faithful pair. So, from 1 to 20 the faithful pairs are (8, 10) and (14, 16). Faithful pairs are scarse and rarer than primes themselves. We can only find 1 faithful pair for numbers 1 to 10, 5 pairs for numbers up to 50 and 8 pairs up to 100.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \\\"P\\\" be the set of all faithful pairs from 1 to a given number \\\"n\\\". We define \\\"F\\\" as the set of all p1, p1 \u0026lt; p2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e∀\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epairs (p1,p2) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e∈\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e P. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function \\\"S(n)\\\", that sums all the elements of F.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor 1 to 20, P(20) = [8 10; 14 16], F(20) = [8 14] and S(20) = 22. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46624,"title":"List the emirps","description":"An emirp is a prime number that becomes a different prime when reversed. The numbers 13, 17, and 149 are emirps, but 11, 19, and 101 are not. \r\nList the emirps less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 36px; transform-origin: 407.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.5px 7.66667px; transform-origin: 10.5px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/Emirp.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eemirp\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 348.383px 7.66667px; transform-origin: 348.383px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a prime number that becomes a different prime when reversed. The numbers 13, 17, and 149 are emirps, but 11, 19, and 101 are not. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.417px 7.66667px; transform-origin: 168.417px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eList the emirps less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = emirps(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 10;\r\nassert(isempty(emirps(n)))\r\n\r\n%%\r\nn = 100;\r\ny_correct = [13 17 31 37 71 73 79 97];\r\nassert(isequal(emirps(n),y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny_correct = [13 17 31 37 71 73 79 97 107 113 149 157 167 179 199 311 337 347 359 389 701 709 733 739 743 751 761 769 907 937 941 953 967 971 983 991];\r\nassert(isequal(emirps(n),y_correct))\r\n\r\n%%\r\nn = 10007;\r\ny = emirps(n);\r\nlen_correct = 241;\r\nyp_correct = [3049 3371 3803 7321 7717 9173 9551 9967];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(100:20:end),yp_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = emirps(n);\r\nlen_correct = 1646;\r\nyp_correct = [17417 33287 39827 76607 92993 99401];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(530:220:end),yp_correct))\r\n\r\n%%\r\nn = 1e6;\r\ny = emirps(n);\r\nsum_correct = 5129429596;\r\nlen_correct = 11184;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('emirps.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'webread') || contains(filetext, 'urlread'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":142,"test_suite_updated_at":"2022-01-30T17:10:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-30T05:34:18.000Z","updated_at":"2026-01-06T08:07:22.000Z","published_at":"2020-09-30T05:52:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/Emirp.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eemirp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a prime number that becomes a different prime when reversed. The numbers 13, 17, and 149 are emirps, but 11, 19, and 101 are not. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eList the emirps less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":12,"title":"Fibonacci sequence","description":"Calculate the nth Fibonacci number.\r\nGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\r\nExamples:\r\n Input n = 5\r\n Output f is 5\r\n\r\n Input n = 7\r\n Output f is 13","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 181px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 90.5px; transform-origin: 468.5px 90.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the nth Fibonacci number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.117px 8px; transform-origin: 199.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 45px; transform-origin: 464.5px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Input \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 19.25px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 19.25px 8.5px; \"\u003en = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 23.1px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 23.1px 8.5px; \"\u003ef is 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Input \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 19.25px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 19.25px 8.5px; \"\u003en = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 26.95px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 26.95px 8.5px; \"\u003ef is 13\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = fib(n)\r\n f = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('fib.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n contains(filetext, '610') || contains(filetext, '1597');\r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\nf = 1;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 6;\r\nf = 8;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 7;\r\nf = 13;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 10;\r\nf = 55;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 12;\r\nf = 144;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 15;\r\nf = 610;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 17;\r\nf = 1597;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 20;\r\nf = 6765;\r\nassert(isequal(fib(n),f))","published":true,"deleted":false,"likes_count":108,"comments_count":25,"created_by":1,"edited_by":223089,"edited_at":"2026-02-05T13:22:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14133,"test_suite_updated_at":"2026-02-05T13:22:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:18.000Z","updated_at":"2026-04-03T07:15:44.000Z","published_at":"2012-01-18T01:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the nth Fibonacci number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input n = 5\\n Output f is 5\\n\\n Input n = 7\\n Output f is 13]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44466,"title":"The twelve days of Christmas","description":"Traditionally there are twelve days of Christmas to celebrate (\"Twelvetide\"), typically starting with Christmas Day (25 December) as the \"First Day of Christmas\" and finishing on the 5th of January. \r\n\r\nIn the traditional Christmas carol, helpfully entitled \u003chttp://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/ _The Twelve Days of Christmas_\u003e, the singer recounts receiving gifts on each day, sent to them by their True Love. \r\n\r\nOn the *first* day, they receive *one* gift (1 × \"partridge in a pear tree\"). \r\n\r\nOn the *second* day they receive *two* _new_ gifts (2 × \"turtle doves\") *plus* a repeat of each gift corresponding to the previous days — in this case meaning plus *one* _repeat_ gift (1 × \"partridge in a pear tree\"). Therefore they have _accumulated_ a total of four gifts: one from the first day, and three from the second day. \r\n\r\nOn the *third* day they receive *three* _new_ gifts (3 × \"French hens\") *plus* a repeat of each gift corresponding to the previous days — in this case meaning plus *three* _repeat_ gifts (1 × \"partridge in a pear tree\" and 2 × \"turtle doves\"). By now they have _accumulated_ a total of ten gifts: one from the first day, three from the second day, and six from the third day. \r\n\r\nThis continues until the twelfth day (the _last_ day of Christmas). \r\n\r\nFor this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)\r\n\r\nEXAMPLE\r\n\r\n day = 2\r\n accumulatedGifts = 4\r\n","description_html":"\u003cp\u003eTraditionally there are twelve days of Christmas to celebrate (\"Twelvetide\"), typically starting with Christmas Day (25 December) as the \"First Day of Christmas\" and finishing on the 5th of January.\u003c/p\u003e\u003cp\u003eIn the traditional Christmas carol, helpfully entitled \u003ca href = \"http://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/\"\u003e\u003ci\u003eThe Twelve Days of Christmas\u003c/i\u003e\u003c/a\u003e, the singer recounts receiving gifts on each day, sent to them by their True Love.\u003c/p\u003e\u003cp\u003eOn the \u003cb\u003efirst\u003c/b\u003e day, they receive \u003cb\u003eone\u003c/b\u003e gift (1 × \"partridge in a pear tree\").\u003c/p\u003e\u003cp\u003eOn the \u003cb\u003esecond\u003c/b\u003e day they receive \u003cb\u003etwo\u003c/b\u003e \u003ci\u003enew\u003c/i\u003e gifts (2 × \"turtle doves\") \u003cb\u003eplus\u003c/b\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus \u003cb\u003eone\u003c/b\u003e \u003ci\u003erepeat\u003c/i\u003e gift (1 × \"partridge in a pear tree\"). Therefore they have \u003ci\u003eaccumulated\u003c/i\u003e a total of four gifts: one from the first day, and three from the second day.\u003c/p\u003e\u003cp\u003eOn the \u003cb\u003ethird\u003c/b\u003e day they receive \u003cb\u003ethree\u003c/b\u003e \u003ci\u003enew\u003c/i\u003e gifts (3 × \"French hens\") \u003cb\u003eplus\u003c/b\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus \u003cb\u003ethree\u003c/b\u003e \u003ci\u003erepeat\u003c/i\u003e gifts (1 × \"partridge in a pear tree\" and 2 × \"turtle doves\"). By now they have \u003ci\u003eaccumulated\u003c/i\u003e a total of ten gifts: one from the first day, three from the second day, and six from the third day.\u003c/p\u003e\u003cp\u003eThis continues until the twelfth day (the \u003ci\u003elast\u003c/i\u003e day of Christmas).\u003c/p\u003e\u003cp\u003eFor this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)\u003c/p\u003e\u003cp\u003eEXAMPLE\u003c/p\u003e\u003cpre\u003e day = 2\r\n accumulatedGifts = 4\u003c/pre\u003e","function_template":"% Comments...\r\nfunction accumulatedGifts = twelvetide(day)\r\n accumulatedGifts = 12\r\nend","test_suite":"%% Please do not try to hack the Test Suite. \r\n% The Test Suite will be updated if inappropriate submissions are received. \r\n% This includes hard-coded (pre-calculated, externally calculated, manually calculated) 'solutions'.\r\n\r\n% EDIT (2019-06-24). Anti-hacking provision\r\n% Ensure builtin function will be called. (Probably only the second of these will work.) \r\n! del fileread.m\r\n! rm -v fileread.m\r\n% Probably only the second of these will work. \r\nRE = regexp(fileread('twelvetide.m'), '\\w+', 'match');\r\n%tabooWords = {'ans', 'assert', 'freepass', 'tic'};\r\ntabooWords = {'assert', 'freepass'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not do that in your code!' char([10 13]) ...\r\n 'Found: ' strjoin(RE(testResult)) '.' char([10 13]) ...\r\n 'Banned word.' char([10 13])];\r\nassert(~any( cellfun( @(z) ismember(z, tabooWords), RE ) ), msg)\r\n% END EDIT (2019-06-24)\r\n\r\n\r\n%% Anti-hardcoding test\r\n% Adapted from the code of Alfonso Nieto-Castanon in a comment at \r\n% https://www.mathworks.com/matlabcentral/cody/problems/44343 .\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[120,165,220,286]),regexp(fileread('twelvetide.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))), 'Please do not hard-code your ''solution''.') \r\n%assert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[120,165,220,286,364]),regexp(fileread('twelvetide.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))), 'Please do not hard-code your ''solution''.') \u003c-- prior to 2018-01-02.\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[55,66,78]),regexp(fileread('twelvetide.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))), 'No, really: please do not hard-code your ''solution''.') % Added on 2018-01-06.\r\n\r\n%% Before Christmas\r\nday = 0 - randi(50);\r\naccumulatedGifts = 0;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%% Before Christmas\r\nday = 0;\r\naccumulatedGifts = 0;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%% First day of Christmas\r\nday = 1;\r\naccumulatedGifts = 1;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 2;\r\naccumulatedGifts = 4;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 3;\r\naccumulatedGifts = 10;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 4;\r\naccumulatedGifts = 20;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 5;\r\naccumulatedGifts = 35;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 6;\r\naccumulatedGifts = 56;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 7;\r\naccumulatedGifts = 84;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 8;\r\naccumulatedGifts = 120;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 9;\r\naccumulatedGifts = 165;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 10;\r\naccumulatedGifts = 220;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 11;\r\naccumulatedGifts = 286;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%% Last day of Christmas\r\nday = 12;\r\naccumulatedGifts = 364;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 13;\r\naccumulatedGifts = 364;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 100;\r\naccumulatedGifts = 364;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nfor i = 1 : 10\r\n day = 12 + randi(300);\r\n accumulatedGifts = 364;\r\n assert( isequal(twelvetide(day), accumulatedGifts) )\r\nend;","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":158,"test_suite_updated_at":"2019-06-24T08:48:56.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2017-12-23T07:03:22.000Z","updated_at":"2026-02-02T10:48:27.000Z","published_at":"2017-12-23T07:42:59.000Z","restored_at":"2018-02-06T15:11:41.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTraditionally there are twelve days of Christmas to celebrate (\\\"Twelvetide\\\"), typically starting with Christmas Day (25 December) as the \\\"First Day of Christmas\\\" and finishing on the 5th of January.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the traditional Christmas carol, helpfully entitled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Twelve Days of Christmas\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the singer recounts receiving gifts on each day, sent to them by their True Love.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efirst\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day, they receive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gift (1 × \\\"partridge in a pear tree\\\").\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esecond\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day they receive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enew\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gifts (2 × \\\"turtle doves\\\")\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erepeat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gift (1 × \\\"partridge in a pear tree\\\"). Therefore they have\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaccumulated\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a total of four gifts: one from the first day, and three from the second day.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethird\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day they receive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enew\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gifts (3 × \\\"French hens\\\")\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erepeat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gifts (1 × \\\"partridge in a pear tree\\\" and 2 × \\\"turtle doves\\\"). By now they have\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaccumulated\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a total of ten gifts: one from the first day, three from the second day, and six from the third day.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis continues until the twelfth day (the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elast\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day of Christmas).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ day = 2\\n accumulatedGifts = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52689,"title":"Easy Sequences 18: Set Bits of Triple Summations","description":"The function S(n) is defined by the following triple summations:\r\n \r\nThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. Write the function 'bitS(n)', which is the number of bits set in the binary representation of S(n).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 127px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function S(n) is defined by the following triple summations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"186\" height=\"46\" style=\"width: 186px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite the function 'bitS(n)', which is the number of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.quora.com/What-do-we-mean-by-a-set-bit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ebits set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e in the binary representation of S(n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bitS(n)\r\n y = x;\r\nend","test_suite":"%%\r\nn = 100;\r\ny_correct = 7;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 10000;\r\ny_correct = 17;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 1000000;\r\ny_correct = 19;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 100000000;\r\ny_correct = 25;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 12345678910;\r\ny_correct = 30;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nns = 1000:2000;\r\ny = sum(arrayfun(@(n) bitS(n),ns))\r\ny_correct = 10663;\r\nassert(isequal(y,y_correct))\r\n%%\r\nn = intmax-123;\r\ny_correct = 33;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = intmax('int64')-123456;\r\ny_correct = 74;\r\nassert(isequal(bitS(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-12T09:14:05.000Z","updated_at":"2025-12-22T16:36:34.000Z","published_at":"2021-09-12T10:34:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function S(n) is defined by the following triple summations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)=\\\\left [\\\\sum_{k=2}^{n}\\\\sum_{j=2}^{k} \\\\sum_{i=2}^{j}\\\\frac{1}{\\\\log {_{i}}{\\\\left ( j! \\\\right )}} \\\\right ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite the function 'bitS(n)', which is the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.quora.com/What-do-we-mean-by-a-set-bit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebits set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in the binary representation of S(n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57720,"title":"The Yellowstone Permutation","description":"The Yellowstone Permutation is a sequence of positive integers, defined by the following rules:\r\nNo term is repeated.\r\nGiven n terms, the next term, a(n+1), is always the smallest possible integer.\r\nEvery term, a(n), must be relatively prime to the previous term, a(n-1).\r\nEvery term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).\r\nThe first three terms of the sequence, after which we start applying the rules, are [1 2 3]. \r\nGiven a positive integer, n, return the n-th term of the sequence, a(n).\r\nExample:\r\nn = 4;\r\na = 4","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 264.659px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 132.33px; transform-origin: 406.996px 132.33px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe Yellowstone Permutation is a sequence of positive integers, defined by the following rules:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7614px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.994px 40.8807px; transform-origin: 390.994px 40.8807px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eNo term is repeated.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven n terms, the next term, a(n+1), is always the smallest possible integer.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEvery term, a(n), must be relatively prime to the previous term, a(n-1).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEvery term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe first three terms of the sequence, after which we start applying the rules, are [1 2 3]. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a positive integer, n, return the n-th term of the sequence, a(n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8807px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.991px 20.4403px; transform-origin: 403.999px 20.4403px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en = 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ea = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = yellowstone(n)\r\n a = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('yellowstone.m');\r\nassert(isempty(strfind(filetext,'regexp')))\r\nassert(isempty(strfind(filetext,'assign')))\r\nassert(isempty(strfind(filetext,'eval')))\r\nassert(isempty(strfind(filetext,'echo')))\r\nassert(isempty(strfind(filetext,'!')))\r\n\r\n%%\r\nn = 1;\r\nassert(isequal(yellowstone(n),1))\r\n\r\n%%\r\nn = 2;\r\nassert(isequal(yellowstone(n),2))\r\n\r\n%%\r\nn = 3;\r\nassert(isequal(yellowstone(n),3))\r\n\r\n%%\r\nn = 11;\r\nassert(isequal(yellowstone(n),25))\r\n\r\n%%\r\nn = 13;\r\nassert(isequal(yellowstone(n),35))\r\n\r\n%%\r\nn = 15;\r\nassert(isequal(yellowstone(n),7))\r\n\r\n%%\r\nn = 21;\r\nassert(isequal(yellowstone(n),39))\r\n\r\n%%\r\nn = 28;\r\nassert(isequal(yellowstone(n),51))\r\n\r\n%%\r\nn = 32;\r\nassert(isequal(yellowstone(n),85))\r\n\r\n%%\r\nn = 38;\r\nassert(isequal(yellowstone(n),91))\r\n\r\n%%\r\nn = 45;\r\nassert(isequal(yellowstone(n),95))\r\n\r\n%%\r\nn = 53;\r\nassert(isequal(yellowstone(n),115))\r\n\r\n%%\r\nn = 70;\r\nassert(isequal(yellowstone(n),119))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-18T10:49:57.000Z","updated_at":"2023-02-18T10:49:57.000Z","published_at":"2023-02-18T10:49:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Yellowstone Permutation is a sequence of positive integers, defined by the following rules:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNo term is repeated.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n terms, the next term, a(n+1), is always the smallest possible integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery term, a(n), must be relatively prime to the previous term, a(n-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first three terms of the sequence, after which we start applying the rules, are [1 2 3]. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return the n-th term of the sequence, a(n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n = 4;\\na = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":594,"title":"\"Look and say\" sequence","description":"What's the next number in this sequence?\r\n\r\n* [0]\r\n* [1 0]\r\n* [1 1 1 0]\r\n* [3 1 1 0]\r\n* [1 3 2 1 1 0]\r\n\r\nThis a variant on the well-known \u003chttp://en.wikipedia.org/wiki/Look-and-say_sequence \"look and say\" or Morris sequence\u003e, where each new iteration is made up by 'saying' the number of numbers you see. That last line is \"one 3; then two 1s; then one 0\".\r\n\r\nCreate a function that returns the next element of this sequence, given a vector as a starting seed..","description_html":"\u003cp\u003eWhat's the next number in this sequence?\u003c/p\u003e\u003cul\u003e\u003cli\u003e[0]\u003c/li\u003e\u003cli\u003e[1 0]\u003c/li\u003e\u003cli\u003e[1 1 1 0]\u003c/li\u003e\u003cli\u003e[3 1 1 0]\u003c/li\u003e\u003cli\u003e[1 3 2 1 1 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThis a variant on the well-known \u003ca href = \"http://en.wikipedia.org/wiki/Look-and-say_sequence\"\u003e\"look and say\" or Morris sequence\u003c/a\u003e, where each new iteration is made up by 'saying' the number of numbers you see. That last line is \"one 3; then two 1s; then one 0\".\u003c/p\u003e\u003cp\u003eCreate a function that returns the next element of this sequence, given a vector as a starting seed..\u003c/p\u003e","function_template":"function NEXT = look_and_say(SEED)\r\n NEXT = SEED;\r\nend","test_suite":"%%\r\nassert(isequal(look_and_say([1]),[1 1]))\r\n%%\r\nassert(isequal(look_and_say([1 1 1 1 1]),[5 1]))\r\n%%\r\nassert(isequal(look_and_say([1 3 3 1 5 2 2]),[1 1 2 3 1 1 1 5 2 2]))\r\n%%\r\nassert(isequal(look_and_say([8 6 7 5 3 0 9]),[1 8 1 6 1 7 1 5 1 3 1 0 1 9]))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":78,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":238,"test_suite_updated_at":"2012-04-17T19:20:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-04-17T15:20:45.000Z","updated_at":"2026-03-25T05:08:20.000Z","published_at":"2012-04-17T15:21:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat's the next number in this sequence?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1 1 1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[3 1 1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1 3 2 1 1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis a variant on the well-known\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Look-and-say_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"look and say\\\" or Morris sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, where each new iteration is made up by 'saying' the number of numbers you see. That last line is \\\"one 3; then two 1s; then one 0\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function that returns the next element of this sequence, given a vector as a starting seed..\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47833,"title":"List the delete-a-digit primes","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.267px 7.91667px; transform-origin: 331.267px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence starting 23, 37, 53, 73, 113, 131, 137, 173, 179, 197… is interesting because each term is a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.4083px 7.91667px; transform-origin: 42.4083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003edelete-a-digit prime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361.342px 7.91667px; transform-origin: 361.342px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, a prime number of two or more digits such that deleting any one digit leaves a prime number. For example, deleting the 1 from 137 leaves 37, deleting the 3 leaves 17, and deleting the 7 leaves 13. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 268.258px 7.91667px; transform-origin: 268.258px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that lists the delete-a-digit primes less than or equal the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = deleteADigitPrimes(n)\r\n y = primes(n);\r\nend","test_suite":"%%\r\nn = 20;\r\ny_correct = [];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 100;\r\ny_correct = [23 37 53 73];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 400;\r\ny_correct = [23 37 53 73 113 131 137 173 179 197 311 317];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny_correct = [23 37 53 73 113 131 137 173 179 197 311 317 431 617 719 1013 1031 1097 1499 1997 2239 2293 3137 4019 4919 6173 7019 7433 9677];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = deleteADigitPrimes(n);\r\nyp_correct = [30011 37019 40013 47933 73331 74177 90011 91733 93491 94397];\r\nlen_correct = 45;\r\nassert(isequal(y(end-9:end),yp_correct) \u0026\u0026 isequal(length(y),len_correct))\r\n\r\n%%\r\nn = 2e6;\r\ny = deleteADigitPrimes(n);\r\nyp_correct = [746099 779699 901499 901997 944777 962233 991733 1367777 1440731 1799999];\r\nlen_correct = 66;\r\nsum_correct = 16944054;\r\nassert(isequal(y(end-9:end),yp_correct) \u0026\u0026 isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('deleteADigitPrimes.m');\r\ncheating = ~isempty(strfind(filetext, 'urlread')) || ~isempty(strfind(filetext, 'oeis')); \r\nassert(~cheating)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-06T02:18:24.000Z","updated_at":"2025-11-29T22:19:33.000Z","published_at":"2020-12-06T02:49:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence starting 23, 37, 53, 73, 113, 131, 137, 173, 179, 197… is interesting because each term is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edelete-a-digit prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, a prime number of two or more digits such that deleting any one digit leaves a prime number. For example, deleting the 1 from 137 leaves 37, deleting the 3 leaves 17, and deleting the 7 leaves 13. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that lists the delete-a-digit primes less than or equal the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1696,"title":"Morse Code Generator! Try it!","description":" .... . .-.. .-.. --- . ...- . .-. -.-- --- -. . -.-.-- \r\n .-.. . - ... -.. --- ... --- -- . -- --- .-. ... . -.-. --- -.. . -.-.-- .-- . .-.. .-.. - .... .. ... -- --- .-. ... . -.-. --- -.. . --. . -. . .-. .- - --- .-. ..- ... . ... - .... . .. -. - . .-. -. .- - .. --- -. .- .-.. ... - -.-- .-.. . -- --- .-. ... . -.-. --- -.. . .-.-.- - .... . .-.-.- .- -. -.. -- .- -.- . ..- .--. .- .-.. .-.. - .... . -.-. --- -.. . --..-- - .... . .-. . .. ... --- -. . ... .--. .- -.-. . - .... .- - ... . .--. .- .-. .- - . ... .-.. . - - . .-. ... .- -. -.. ..... ... .--. .- -.-. . ... - .... .- - ... . .--. .- .-. .- - . .-- --- .-. -.. ... .-.-.- ... --- -- . .--. ..- -. -.-. - ..- .- - .. --- -. .. ... ..- ... . -.. .-.-.- .-.-.- .-.-.- --- - .... . .-. - .... . -. - .... .- - --..-- .- .-.. .-.. -.-- --- ..- -. . . -.. - --- -.. --- .. ... - .- -.- . .. -. ... --- -- . - -.-- .--. . --- ..-. - . -..- - .. -. - .... . ..-. --- .-. -- --- ..-. .- ... - .-. .. -. --. .- -. -.. - ..- .-. -. .. - .. -. - --- .- -- --- .-. ... . -.-. --- -.. . .-.. .. -. . -.-. .... .- .-. -.-. .-.. .- ... ... --..-- .- ... - .... . . -..- .- -- .--. .-.. . -... . .-.. --- .-- ... .... --- .-- ... \r\n \r\n\r\n\r\n \r\n\r\n text = 'Morse code is FUN!'\r\n Morse_code_out = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--'\r\n\r\n\r\nJust a note: this uses international style Morse code found in:\r\n\r\nhttp://en.wikipedia.org/wiki/American_Morse_code\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003e.... . .-.. .-.. --- . ...- . .-. -.-- --- -. . -.-.-- \r\n .-.. . - ... -.. --- ... --- -- . -- --- .-. ... . -.-. --- -.. . -.-.-- .-- . .-.. .-.. - .... .. ... -- --- .-. ... . -.-. --- -.. . --. . -. . .-. .- - --- .-. ..- ... . ... - .... . .. -. - . .-. -. .- - .. --- -. .- .-.. ... - -.-- .-.. . -- --- .-. ... . -.-. --- -.. . .-.-.- - .... . .-.-.- .- -. -.. -- .- -.- . ..- .--. .- .-.. .-.. - .... . -.-. --- -.. . --..-- - .... . .-. . .. ... --- -. . ... .--. .- -.-. . - .... .- - ... . .--. .- .-. .- - . ... .-.. . - - . .-. ... .- -. -.. ..... ... .--. .- -.-. . ... - .... .- - ... . .--. .- .-. .- - . .-- --- .-. -.. ... .-.-.- ... --- -- . .--. ..- -. -.-. - ..- .- - .. --- -. .. ... ..- ... . -.. .-.-.- .-.-.- .-.-.- --- - .... . .-. - .... . -. - .... .- - --..-- .- .-.. .-.. -.-- --- ..- -. . . -.. - --- -.. --- .. ... - .- -.- . .. -. ... --- -- . - -.-- .--. . --- ..-. - . -..- - .. -. - .... . ..-. --- .-. -- --- ..-. .- ... - .-. .. -. --. .- -. -.. - ..- .-. -. .. - .. -. - --- .- -- --- .-. ... . -.-. --- -.. . .-.. .. -. . -.-. .... .- .-. -.-. .-.. .- ... ... --..-- .- ... - .... . . -..- .- -- .--. .-.. . -... . .-.. --- .-- ... .... --- .-- ... \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003etext = 'Morse code is FUN!'\r\nMorse_code_out = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--'\r\n\u003c/pre\u003e\u003cp\u003eJust a note: this uses international style Morse code found in:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://en.wikipedia.org/wiki/American_Morse_code\"\u003ehttp://en.wikipedia.org/wiki/American_Morse_code\u003c/a\u003e\u003c/p\u003e","function_template":"function Morse_code_out = MorseCodeGenerator(text)\r\n Morse_code_out = text_in;\r\nend","test_suite":"%%\r\nx = 'Morse code is FUN!';\r\ny_correct = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n%%\r\nx = 'Am I 20, (who knows?)';\r\ny_correct = '.- -- .. ..--- ----- --..-- -.--. .-- .... --- -.- -. --- .-- ... ..--.. -.--.-';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n%%\r\nx = 'THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG: or does he...';\r\ny_correct = '- .... . --.- ..- .. -.-. -.- -... .-. --- .-- -. ..-. --- -..- .--- ..- -- .--. ... --- ...- . .-. - .... . .-.. .- --.. -.-- -.. --- --. ---... --- .-. -.. --- . ... .... . .-.-.- .-.-.- .-.-.-';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n%%\r\nx = '1234567890';\r\ny_correct = '.---- ..--- ...-- ....- ..... -.... --... ---.. ----. -----';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":"2019-09-16T11:37:52.000Z","rescore_all_solutions":false,"group_id":28,"created_at":"2013-07-05T18:50:09.000Z","updated_at":"2025-12-29T01:11:58.000Z","published_at":"2013-07-09T15:55:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[.... . .-.. .-.. --- . ...- . .-. -.-- --- -. . -.-.-- \\n .-.. . - ... -.. --- ... --- -- . -- --- .-. ... . -.-. --- -.. . -.-.-- .-- . .-.. .-.. - .... .. ... -- --- .-. ... . -.-. --- -.. . --. . -. . .-. .- - --- .-. ..- ... . ... - .... . .. -. - . .-. -. .- - .. --- -. .- .-.. ... - -.-- .-.. . -- --- .-. ... . -.-. --- -.. . .-.-.- - .... . .-.-.- .- -. -.. -- .- -.- . ..- .--. .- .-.. .-.. - .... . -.-. --- -.. . --..-- - .... . .-. . .. ... --- -. . ... .--. .- -.-. . - .... .- - ... . .--. .- .-. .- - . ... .-.. . - - . .-. ... .- -. -.. ..... ... .--. .- -.-. . ... - .... .- - ... . .--. .- .-. .- - . .-- --- .-. -.. ... .-.-.- ... --- -- . .--. ..- -. -.-. - ..- .- - .. --- -. .. ... ..- ... . -.. .-.-.- .-.-.- .-.-.- --- - .... . .-. - .... . -. - .... .- - --..-- .- .-.. .-.. -.-- --- ..- -. . . -.. - --- -.. --- .. ... - .- -.- . .. -. ... --- -- . - -.-- .--. . --- ..-. - . -..- - .. -. - .... . ..-. --- .-. -- --- ..-. .- ... - .-. .. -. --. .- -. -.. - ..- .-. -. .. - .. -. - --- .- -- --- .-. ... . -.-. --- -.. . .-.. .. -. . -.-. .... .- .-. -.-. .-.. .- ... ... --..-- .- ... - .... . . -..- .- -- .--. .-.. . -... . .-.. --- .-- ... .... --- .-- ... \\n\\ntext = 'Morse code is FUN!'\\nMorse_code_out = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJust a note: this uses international style Morse code found in:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/American_Morse_code\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/American_Morse_code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52497,"title":"Easy Sequences 3: Prime 44-number Squares","description":"The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a \"44-number\".\r\nIf 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. Write a function that returns P(n), given that P(3) = 2 and P(10) = 5.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 156px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 78px; transform-origin: 407px 78px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a \"44-number\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that returns P(n),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given that P(3) = 2 and P(10) = 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function prime_count = P(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 3 10 15 20];\r\ny_correct = [0 2 5 8 11];\r\nassert(isequal(arrayfun(@(i) P(i),x),y_correct))\r\n%%\r\nx = 1:20;\r\ny_correct = 108;\r\nassert(isequal(sum(arrayfun(@(i) P(i),x)),y_correct))\r\n%%\r\nx = arrayfun(@(i) P(i),15:30);\r\ny_correct = 118;\r\nassert(isequal(sum(arrayfun(@(i) P(i),x)),y_correct))\r\n%%\r\nx = 25:100;\r\ny_correct = 3077;\r\nassert(isequal(sum(arrayfun(@(i) P(i),x)),y_correct))\r\n%%\r\nx = floor(sqrt(double(intmax)));\r\ny_correct = 17862;\r\nassert(isequal(P(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":"2021-08-12T04:00:36.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-08-11T10:45:05.000Z","updated_at":"2025-11-30T19:35:26.000Z","published_at":"2021-08-11T19:07:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a \\\"44-number\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that returns P(n),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e given that P(3) = 2 and P(10) = 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1779,"title":"Oh Zero Zero Zero!!!","description":"Hello all,\r\nSo you have to find the largest section of zeros in a vector and then find the length of those zeros and there starting position...\r\nFor example:\r\n \r\n x = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\r\n %then the output is:\r\n LP = [9 10] %[Length Position]\r\n \r\n %Or another example:\r\n \r\n x = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\r\n %then the output is:\r\n LP = [6 9]\r\n \r\n %Or another example:\r\n \r\n x = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\r\n %then the output is:\r\n LP = [7 3];\r\n\r\nHave Fun!\r\n","description_html":"\u003cp\u003eHello all,\r\nSo you have to find the largest section of zeros in a vector and then find the length of those zeros and there starting position...\r\nFor example:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\r\n%then the output is:\r\nLP = [9 10] %[Length Position]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e%Or another example:\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\r\n%then the output is:\r\nLP = [6 9]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e%Or another example:\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\r\n%then the output is:\r\nLP = [7 3];\r\n\u003c/pre\u003e\u003cp\u003eHave Fun!\u003c/p\u003e","function_template":"function y = LengthAndPosnZeros(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\r\nLP = [9 10] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\r\nLP = [6 9]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\r\nLP = [7 3];\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 2 0 0];\r\nLP = [2 3] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 2 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0];\r\nLP = [9 3] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 0 0 0 0 0 0 0 0 0 1];\r\nLP = [9 2] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [111 541 0 45 3 0 0 0 15 26 0 4 84 3 84 0 9];\r\nLP = [3 6] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 0 1];\r\nLP = [1 2] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n\r\n","published":true,"deleted":false,"likes_count":15,"comments_count":1,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":540,"test_suite_updated_at":"2013-08-08T19:35:25.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2013-08-08T18:54:26.000Z","updated_at":"2026-03-24T00:57:27.000Z","published_at":"2013-08-08T19:35:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHello all, So you have to find the largest section of zeros in a vector and then find the length of those zeros and there starting position... For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\\n%then the output is:\\nLP = [9 10] %[Length Position]\\n\\n%Or another example:\\n\\nx = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\\n%then the output is:\\nLP = [6 9]\\n\\n%Or another example:\\n\\nx = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\\n%then the output is:\\nLP = [7 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHave Fun!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":49803,"title":"Compute expulsions from the Kimberling shuffle","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 155.583px; transform-origin: 407px 155.583px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.983px 7.79167px; transform-origin: 368.983px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.8917px 7.79167px; transform-origin: 10.8917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.05px 7.79167px; transform-origin: 26.05px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.79167px; transform-origin: 20.6167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eexcept\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 235.725px 7.79167px; transform-origin: 235.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 2 3 4 5 6 7 8 9 10...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e2 3 4 5 6 7 8 9 10 11...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e4 2 5 6 7 8 9 10 11 12...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e6 2 7 4 8 9 10 11 12 13...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 157.85px 8.25px; transform-origin: 157.85px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 146.3px 8.25px; transform-origin: 146.3px 8.25px; \"\u003e8 7 9 2 10 6 11 12 13 14.\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.25px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.25px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.008px 7.79167px; transform-origin: 369.008px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the row after which the input number is expelled. For example, because 5 appears on the main diagonal of row 3, your function should return 3. An optional challenge is to determine whether all numbers are eventually expelled from the array.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = KimberlingExpulsion(m)\r\n n = f(m);\r\nend","test_suite":"%%\r\nm = 1;\r\nn_correct = 1;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 5;\r\nn_correct = 3;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 10;\r\nn_correct = 5;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 18;\r\nn_correct = 11;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 19;\r\nn_correct = 49595;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 23;\r\nn_correct = 24;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 27;\r\nn_correct = 7598;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 31;\r\nn_correct = 13;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n%%\r\nm = 37;\r\nn_correct = 58;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 40;\r\nn_correct = 93167;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 43;\r\nn_correct = 1523;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 46;\r\nn_correct = 20;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 50;\r\nn_correct = 123;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 89;\r\nn_correct = 15803;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 101;\r\nn_correct = 95;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 108;\r\nn_correct = 63;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 117;\r\nn_correct = 390;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 8899;\r\nn_correct = 76973;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 8979;\r\nn_correct = 3465;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 1691;\r\nn_correct = 32633;\r\nassert(isequal(KimberlingExpulsion(KimberlingExpulsion(KimberlingExpulsion(m))),n_correct));\r\n\r\n%%\r\nk = randi(14);\r\nm = 9*2^k-3*k-10;\r\nn_correct = 3*(2^k-1);\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nfiletext = fileread('KimberlingExpulsion.m');\r\ncheating = contains(filetext, 'urlread') || contains(filetext, 'oeis'); \r\nassert(~cheating)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-09T19:48:53.000Z","updated_at":"2025-12-16T21:01:56.000Z","published_at":"2021-01-09T19:57:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexcept\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 2 3 4 5 6 7 8 9 10...\\n2 3 4 5 6 7 8 9 10 11...\\n4 2 5 6 7 8 9 10 11 12...\\n6 2 7 4 8 9 10 11 12 13...\\n8 7 9 2 10 6 11 12 13 14....]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the row after which the input number is expelled. For example, because 5 appears on the main diagonal of row 3, your function should return 3. An optional challenge is to determine whether all numbers are eventually expelled from the array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57730,"title":"Easy Sequences 97: One-line Code Challenge - Sequence with Constant Difference","description":"While answering Problem #57725, I noticed a pattern that immediately led me to a solution, namely: the -th difference of the sequence is constant. In that problem's case the constant is 6:\r\n diff(A,4) == [6 6 6 6 ...]\r\nwhere is the sequence.\r\nGiven an integer and a vector that enumerates the first elements of , write a function that outputs the -th element of , such that the -th difference is a constant:\r\n diff(A,k-1) == [c c c c ...]\r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nTo encourage vectorization, for and while loops are not allowed\r\nRegular expressions, string manipulation and curve fitting are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 335px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 167.5px; transform-origin: 407px 167.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhile answering \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57725\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem #57725\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e diff(A,4) == [6 6 6 6 \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e that enumerates the first \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e elements of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that outputs the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, such that the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th difference is a constant:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e diff(A,k-1) == [c c c c \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 80px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40px; transform-origin: 391px 40px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTo encourage vectorization, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ewhile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eloops are not allowed\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = nthElement(V,n)\r\n x = A(n);\r\nend","test_suite":"format longg\r\n%%\r\nV = [1 2 3 4 5 6]; n = 10000;\r\nx_correct = n;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [790 1303 2033 3034 4366]; n = [10 100 1000];\r\nx_correct = [18511 32160346 256563524446];\r\nassert(isequal(arrayfun(@(i) nthElement(V,i),n),x_correct))\r\n%%\r\nV = [12 23 34 56 78]; n = 6:10;\r\nds = diff([V arrayfun(@(i) nthElement(V,i),n)],length(V)-1);\r\nd_correct = -22;\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = [123456 234567 345678 456789]; n = 10000;\r\nx_correct = 1111122346;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [123 456 789 101112 131415 161718 192021 222324 252627 282930]; n = 11:18;\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\ns_correct = sum(x)\r\nds = diff([V x],length(V)-1);\r\nd_correct = 2170350;\r\nassert(isequal(sum(x),s_correct))\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = sort(randi(100,1,10)); n = (length(V)+1):(length(V)+20);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(~any(diff([V x],length(V))))\r\n%%\r\nV = sort(randi(1000,1,10)); n = (length(V)+1):(length(V)+10);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(isequal(diff(V,length(V)-1),diff(x,length(V)-1)))\r\n%%\r\nfiletext = fileread('nthElement.m');\r\nnot_allowed = contains(filetext, 'str') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'fit');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n c = c + numel(find(s{1}==';'));\r\n if ~isequal(s{1}(end),';')\r\n c = c + 1;\r\n end\r\n end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-25T18:40:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-25T12:35:50.000Z","updated_at":"2023-02-25T18:40:33.000Z","published_at":"2023-02-25T18:35:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile answering \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57725\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem #57725\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ diff(A,4) == [6 6 6 6 ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e that enumerates the first \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e elements of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that outputs the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(k-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th difference is a constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ diff(A,k-1) == [c c c c ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo encourage vectorization, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eloops are not allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55325,"title":"increasing sequences","description":"Given a string of digits, insert commas to create a sequence of strictly increasing numbers so as to minimize the magnitude of the last number. For this problem, leading zeros are allowed in front of a number. The solution is not necessary unique, see test2.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a string of digits, insert commas to create a sequence of strictly increasing numbers so as to minimize the magnitude of the last number. For this problem, leading zeros are allowed in front of a number. The solution is not necessary unique, see test2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = incr(str)\r\n y = str;\r\nend","test_suite":"%%\r\nx = '3456';\r\ny_correct = [3,4,5,6];\r\nassert(isequal(incr(x),y_correct))\r\n\r\n%%\r\nx = '3546';\r\ny_correct1 = [3,5,46];\r\ny_correct2 = [35,46];\r\nassert(isequal(incr(x),y_correct1) || isequal(incr(x),y_correct2) )\r\n\r\n%%\r\nx = '100000000011';\r\ny_correct = [10,11];\r\ny_correct2 = [1,11];\r\nassert( isequal(incr(x),y_correct) || isequal(incr(x),y_correct2) )\r\n\r\n%%\r\nx = '570344446780361';\r\ny_correct = [5,7,34,44,46,78,361];\r\nassert(isequal(incr(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":2197980,"edited_by":2197980,"edited_at":"2023-02-20T09:27:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-02-20T09:27:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T03:55:48.000Z","updated_at":"2025-07-26T02:53:26.000Z","published_at":"2022-08-20T03:55:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string of digits, insert commas to create a sequence of strictly increasing numbers so as to minimize the magnitude of the last number. For this problem, leading zeros are allowed in front of a number. The solution is not necessary unique, see test2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42838,"title":"Increasing sub-sequence (Level 2)","description":"This is the next step up from \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42837-increasing-sub-sequence-level-1 Problem 42837\u003e.\r\n\r\nGiven a vector, v, of real numbers, return a positive integer, n, representing the longest non-contiguous increasing sub-sequence contained in v.\r\n\r\nExample:\r\n\r\nv = [ *2* 18 9 *6 11 20 25* 3]\r\n\r\nn = 5","description_html":"\u003cp\u003eThis is the next step up from \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42837-increasing-sub-sequence-level-1\"\u003eProblem 42837\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest non-contiguous increasing sub-sequence contained in v.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ev = [ \u003cb\u003e2\u003c/b\u003e 18 9 \u003cb\u003e6 11 20 25\u003c/b\u003e 3]\u003c/p\u003e\u003cp\u003en = 5\u003c/p\u003e","function_template":"function n = subseq(v)\r\n n = numel(v);\r\nend","test_suite":"%%\r\nv = [2 18 9 6 11 20 25 3];\r\nn_correct = 5;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [-2 -18 -9 -6 -11 -20 -25 -3];\r\nn_correct = 4;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = zeros(1,30);\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [exp(-1) sqrt(2) sqrt(3) exp(1) pi exp(2)];\r\nn_correct = 6;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = 100:-10:-100;\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [9 0:5 1:7 3:9 2:8];\r\nn_correct = 10;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [0 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15];\r\nn_correct = 6;\r\nassert(isequal(subseq(v),n_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2017-12-09T06:56:32.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-28T09:14:17.000Z","updated_at":"2017-12-09T06:56:32.000Z","published_at":"2016-04-28T09:14:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the next step up from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42837-increasing-sub-sequence-level-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42837\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest non-contiguous increasing sub-sequence contained in v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 18 9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6 11 20 25\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54,"title":"Maximum running product for a string of numbers","description":"Given a string s representing a list of numbers, find the five consecutive numbers that multiply to form the largest number. Specifically, given s return the index i to the first of those five numbers. You can assume the maximum product is unique.\r\n \r\nExample: \r\n\r\n Input s = '123454321'\r\n Output i = 3\r\n\r\nsince the product of [3 4 5 4 3] is larger than any of the alternatives.\r\n \r\n_Inspired by \u003chttp://projecteuler.net/index.php?section=problems\u0026id=8 Problem 8 from Project Euler\u003e_\r\n","description_html":"\u003cp\u003eGiven a string s representing a list of numbers, find the five consecutive numbers that multiply to form the largest number. Specifically, given s return the index i to the first of those five numbers. You can assume the maximum product is unique.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input s = '123454321'\r\n Output i = 3\u003c/pre\u003e\u003cp\u003esince the product of [3 4 5 4 3] is larger than any of the alternatives.\u003c/p\u003e\u003cp\u003e\u003ci\u003eInspired by \u003ca href=\"http://projecteuler.net/index.php?section=problems\u0026amp;id=8\"\u003eProblem 8 from Project Euler\u003c/a\u003e\u003c/i\u003e\u003c/p\u003e","function_template":"function i = running_product(s)\r\n i = 1;\r\nend","test_suite":"%%\r\n\r\ns = '123454321';\r\ni_correct = 3;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%%\r\n\r\ns = '5820974944592307816406286208998628034825342117067';\r\ni_correct = 28;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%%\r\n\r\ns = '141592653589793238462643383279502884197169399399999';\r\ni_correct = 47;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%% \r\n\r\ns = '7831652712019091456485669234603486104543266482133936072602';\r\ni_correct = 21;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%% \r\n\r\ns = '70066063155881748815209209628292540917153643678925903600113305305488';\r\ni_correct = 44;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%% \r\n\r\ns = '11111';\r\ni_correct = 1;\r\nassert(isequal(running_product(s),i_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2254,"test_suite_updated_at":"2012-01-18T19:50:09.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:24.000Z","updated_at":"2026-03-04T13:30:28.000Z","published_at":"2012-01-18T01:00:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string s representing a list of numbers, find the five consecutive numbers that multiply to form the largest number. Specifically, given s return the index i to the first of those five numbers. You can assume the maximum product is unique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input s = '123454321'\\n Output i = 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince the product of [3 4 5 4 3] is larger than any of the alternatives.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://projecteuler.net/index.php?section=problems\u0026amp;id=8\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 8 from Project Euler\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51282,"title":"Compute a row of the Kimberling shuffle","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 320.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.083px; transform-origin: 407px 160.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.2417px 7.91667px; transform-origin: 90.2417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem continues from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/18242/problems/49803\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 49803\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.983px 7.91667px; transform-origin: 368.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.8917px 7.91667px; transform-origin: 10.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.05px 7.91667px; transform-origin: 26.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eexcept\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 235.725px 7.91667px; transform-origin: 235.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 2 3 4 5 6 7 8 9 10...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e2 3 4 5 6 7 8 9 10 11...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e4 2 5 6 7 8 9 10 11 12...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e6 2 7 4 8 9 10 11 12 13...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 157.85px 7.91667px; transform-origin: 157.85px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; \"\u003e8 7 9 2 10 6 11 12 13 14.\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 7.91667px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.4333px 7.91667px; transform-origin: 99.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 277.208px 7.91667px; transform-origin: 277.208px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth row of this array, up to and including the first number beyond which the numbers are in order. For example, given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.7417px 7.91667px; transform-origin: 86.7417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e your function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[8 7 9 2 10 6 11]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = KimberlingShuffleRow(n)\r\n r = 1:n;\r\nend","test_suite":"%%\r\nn = 1;\r\nr_correct = 1;\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 2;\r\nr_correct = 2;\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 3;\r\nr_correct = [4 2 5];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 5;\r\nr_correct = [8 7 9 2 10 6 11];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 26;\r\nr_correct = [60 58 44 48 26 54 65 64 16 30 19 45 51 50 66 34 38 29 47 40 32 49 67 63 39 55 56 12 41 61 68 13 59 25 69 57 37 17 70 62 27 52 71 43 72 11 73 21 74];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 53;\r\nr_correct = [101 118 73 81 43 56 68 21 88 131 136 71 143 32 45 110 40 142 119 109 57 72 77 80 19 90 61 51 144 114 49 112 134 93 124 92 69 102 121 111 39 16 74 85 145 129 27 47 17 141 108 94 67 127 132 64 50 98 38 29 146 96 137 139 117 128 130 41 147 107 100 37 120 75 30 106 148 113 103 12 63 140 89 104 149 123 126 87 150 66 105 78 151 135 86 125 152 116 153 60 154 133 155];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 151;\r\nr_correct = [383 377 319 392 360 103 85 187 375 136 299 309 125 432 398 258 270 410 40 411 189 372 168 311 380 74 231 176 306 167 123 425 239 159 284 295 393 17 335 206 205 260 282 386 133 363 171 337 433 152 139 387 196 242 340 57 127 424 254 417 142 226 381 388 288 357 150 241 199 323 217 56 43 287 385 308 368 431 365 155 215 60 32 170 268 420 419 312 303 253 105 63 251 220 356 314 89 324 145 404 193 106 116 371 137 184 203 225 274 333 237 182 434 291 427 113 262 132 301 202 294 397 317 98 423 409 224 339 329 272 180 281 345 164 163 66 102 78 154 428 252 207 195 197 435 300 396 292 289 367 112 322 334 148 77 332 415 179 384 266 304 320 257 181 213 351 173 390 256 348 261 364 394 235 418 354 436 313 117 305 209 107 407 328 290 190 273 338 280 265 344 92 219 111 395 325 271 248 68 330 353 370 183 27 277 430 326 336 437 416 185 421 315 399 379 422 400 234 94 177 391 346 426 267 438 298 69 316 307 369 279 297 412 143 285 247 250 186 401 342 439 246 343 310 188 134 362 19 149 293 131 276 278 201 405 406 440 361 373 359 212 218 296 118 441 378 321 429 331 350 318 109 442 214 87 140 259 403 347 129 443 414 413 147 444 269 174 349 445 51 408 286 446 221 447 240 448 75 449];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nr1 = KimberlingShuffleRow(1776);\r\nr2 = KimberlingShuffleRow(r1(1));\r\nsum_correct = 9180392;\r\nassert(isequal(sum(r2),sum_correct))\r\n\r\n%%\r\nr1 = KimberlingShuffleRow(4881);\r\nr2 = KimberlingShuffleRow(r1(1));\r\nsump_correct = 11284849;\r\nassert(isequal(sum(r2(isprime(r2))),sump_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-04T13:38:50.000Z","updated_at":"2025-12-16T21:10:34.000Z","published_at":"2021-04-04T13:48:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem continues from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/18242/problems/49803\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 49803\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexcept\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 2 3 4 5 6 7 8 9 10...\\n2 3 4 5 6 7 8 9 10 11...\\n4 2 5 6 7 8 9 10 11 12...\\n6 2 7 4 8 9 10 11 12 13...\\n8 7 9 2 10 6 11 12 13 14....]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth row of this array, up to and including the first number beyond which the numbers are in order. For example, given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e your function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[8 7 9 2 10 6 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2640,"title":"Find similar sequences","description":"Another problem inspired by a question on the \u003chttp://www.mathworks.com/matlabcentral/answers answers\u003e forum.\r\n\r\nGiven a matrix of positive integer numbers, find all the rows that are similar to the first rows and return these rows as a new matrix.\r\n\r\nRows are considered similar if the numbers common to both rows are in the exact same order with no other numbers in between. 0s in a row are always ignored and only occur at the end of the row.\r\n\r\nFor example:\r\n\r\n [3 1 5 0 0] and [4 2 1 5 0] are similar (1 5 are the common numbers and occur in the same order)\r\n [3 1 5 0 0] and [3 4 1 5 0] are not similar (3 1 5 are the common numbers, there's a 4 in between)\r\n ","description_html":"\u003cp\u003eAnother problem inspired by a question on the \u003ca href = \"http://www.mathworks.com/matlabcentral/answers\"\u003eanswers\u003c/a\u003e forum.\u003c/p\u003e\u003cp\u003eGiven a matrix of positive integer numbers, find all the rows that are similar to the first rows and return these rows as a new matrix.\u003c/p\u003e\u003cp\u003eRows are considered similar if the numbers common to both rows are in the exact same order with no other numbers in between. 0s in a row are always ignored and only occur at the end of the row.\u003c/p\u003e\u003cp\u003eFor example:\u003c/p\u003e\u003cpre\u003e [3 1 5 0 0] and [4 2 1 5 0] are similar (1 5 are the common numbers and occur in the same order)\r\n [3 1 5 0 0] and [3 4 1 5 0] are not similar (3 1 5 are the common numbers, there's a 4 in between)\u003c/pre\u003e","function_template":"function rows = findsimilar(m)\r\n rows = [];\r\nend","test_suite":"%%\r\nm = [3 1 5 0 0\r\n 3 4 1 5 0\r\n 4 2 1 5 0];\r\nsrows = [3 1 5 0 0;4 2 1 5 0];\r\nassert(isequal(findsimilar(m),srows))\r\n\r\n%%\r\nm = [3 1 5 0 0\r\n 1 2 5 0 0\r\n 1 3 4 1 5\r\n 2 1 5 0 0];\r\nsrows = [3 1 5 0 0; 2 1 5 0 0];\r\nassert(isequal(findsimilar(m),srows))\r\n\r\n%%\r\nm = [3 1 5 7 0\r\n 3 2 5 7 0\r\n 3 5 7 2 0\r\n 1 5 7 2 0\r\n 4 6 7 8 9\r\n 4 5 7 8 0\r\n 4 5 6 7 8];\r\nsrows = [3 1 5 7 0;1 5 7 2 0;4 6 7 8 9;4 5 7 8 0];\r\nassert(isequal(findsimilar(m),srows))\r\n\r\n%%\r\nm = [3 1 5 0 0\r\n 3 1 6 0 0\r\n 3 2 6 0 0\r\n 2 1 5 6 0];\r\nsrows = m;\r\nassert(isequal(findsimilar(m), srows))","published":true,"deleted":false,"likes_count":1,"comments_count":8,"created_by":999,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":140,"test_suite_updated_at":"2014-10-24T06:14:05.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2014-10-23T08:06:10.000Z","updated_at":"2026-03-17T14:55:43.000Z","published_at":"2014-10-23T08:06:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother problem inspired by a question on the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/answers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eanswers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e forum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix of positive integer numbers, find all the rows that are similar to the first rows and return these rows as a new matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRows are considered similar if the numbers common to both rows are in the exact same order with no other numbers in between. 0s in a row are always ignored and only occur at the end of the row.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ [3 1 5 0 0] and [4 2 1 5 0] are similar (1 5 are the common numbers and occur in the same order)\\n [3 1 5 0 0] and [3 4 1 5 0] are not similar (3 1 5 are the common numbers, there's a 4 in between)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61019,"title":"Find the logic and return the nth number (plus)","description":"This problem is the harder version of Problem 61015\r\ngiven a sequence of numbers arranged in the following order:\r\nA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\r\nWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\r\nnote: with this plus version you have to find the Nth number with extremely large N. Because the result can be extremely large, we will take the modulus of the nth number by 1e9+7\r\neg:\r\nn=5\r\n--\u003e output=9","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 252px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 126px; transform-origin: 408px 126px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem is the harder version of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61015\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 61015\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003egiven a sequence of numbers arranged in the following order:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enote: with this plus version you have to find the Nth number with extremely large N. Because the result can be extremely large, we will take the modulus of the nth number by 1e9+7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeg:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en=5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--\u0026gt; output=9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1e6;\r\ny_correct = 726671849;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1e10;\r\ny_correct = 671604939;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e11;\r\ny_correct = 126443114;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e12;\r\ny_correct = 570892696;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e13;\r\ny_correct = 41690901;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e14;\r\ny_correct = 719068874;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e15;\r\ny_correct = 468399005;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4946338,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-20T06:24:55.000Z","updated_at":"2026-03-26T05:55:02.000Z","published_at":"2025-10-20T06:24:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is the harder version of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61015\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61015\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a sequence of numbers arranged in the following order:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003enote: with this plus version you have to find the Nth number with extremely large N. Because the result can be extremely large, we will take the modulus of the nth number by 1e9+7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeg:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--\u0026gt; output=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":24,"title":"Function Iterator","description":"Given a handle fh to a function which takes a scalar input and returns a scalar output and an integer n \u003e= 1, return a handle fh2 to a function which applies the given function n times.\n\nExamples:\n\n \u003e\u003e addOne = @(x)x+1;\n \u003e\u003e addTen = iterate_fcn(addOne, 10);\n \u003e\u003e addTen(3)\n ans =\n 13\n\n \u003e\u003e squarer = @(a) a^2;\n \u003e\u003e fh2 = iterate_fcn(squarer, 3);\n \u003e\u003e fh2(3)\n ans =\n 6561\n\n % Golden Ratio\n \u003e\u003e fh = @(y)sqrt(y+1);\n \u003e\u003e fh2 = iterate_fcn(fh,30);\n \u003e\u003e fh2(1)\n ans =\n 1.6180\n","description_html":"\u003cp\u003eGiven a handle fh to a function which takes a scalar input and returns a scalar output and an integer n \u003e= 1, return a handle fh2 to a function which applies the given function n times.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e \u003e\u003e addOne = @(x)x+1;\n \u003e\u003e addTen = iterate_fcn(addOne, 10);\n \u003e\u003e addTen(3)\n ans =\n 13\u003c/pre\u003e\u003cpre\u003e \u003e\u003e squarer = @(a) a^2;\n \u003e\u003e fh2 = iterate_fcn(squarer, 3);\n \u003e\u003e fh2(3)\n ans =\n 6561\u003c/pre\u003e\u003cpre\u003e % Golden Ratio\n \u003e\u003e fh = @(y)sqrt(y+1);\n \u003e\u003e fh2 = iterate_fcn(fh,30);\n \u003e\u003e fh2(1)\n ans =\n 1.6180\u003c/pre\u003e","function_template":"function fh2 = iterate_fcn(fh, n)\nfh2 = fh;\nend","test_suite":"%%\nnoOp = @(x)x;\nfh2 = iterate_fcn(noOp, 50);\nassert(isequal(fh2(pi),pi));\n\n\n%%\naddOne = @(x)x+1;\naddTen = iterate_fcn(addOne, 10);\nassert(isequal(addTen(3),13));\n\n%%\naddOne = @(x)x+1;\naddOne2 = iterate_fcn(addOne, 1);\nassert(isequal(addOne2(3),4));\n\n%%\nsquarer = @(a) a^2;\nfh2 = iterate_fcn(squarer, 3);\nassert(isequal(fh2(3),6561));\n\n%%\nfh = @(y)sqrt(y+1);\nfh2 = iterate_fcn(fh,30);\nassert(abs(fh2(1) - (1+sqrt(5))/2) \u003c 100*eps);","published":true,"deleted":false,"likes_count":61,"comments_count":27,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2244,"test_suite_updated_at":"2012-01-18T01:00:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:20.000Z","updated_at":"2026-03-15T20:56:03.000Z","published_at":"2012-01-18T01:00:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a handle fh to a function which takes a scalar input and returns a scalar output and an integer n \u0026gt;= 1, return a handle fh2 to a function which applies the given function n times.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e addOne = @(x)x+1;\\n \u003e\u003e addTen = iterate_fcn(addOne, 10);\\n \u003e\u003e addTen(3)\\n ans =\\n 13\\n\\n \u003e\u003e squarer = @(a) a^2;\\n \u003e\u003e fh2 = iterate_fcn(squarer, 3);\\n \u003e\u003e fh2(3)\\n ans =\\n 6561\\n\\n % Golden Ratio\\n \u003e\u003e fh = @(y)sqrt(y+1);\\n \u003e\u003e fh2 = iterate_fcn(fh,30);\\n \u003e\u003e fh2(1)\\n ans =\\n 1.6180]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52609,"title":"Easy Sequences 11: Factorial Digits without Trailing Zeros","description":"Here is an easy one...\r\nIt is not difficult to count the number of digits of the factorial of a given number. For example for 'n = 10', we have:\r\n \u003e\u003e length(num2str(factorial(10)))\r\n \u003e\u003e ans =\r\n 7\r\nBut 2 of those digits are just trailing zeros. So, for 10!, if we remove the trailing zeros, there would only be 5 digits left.\r\nWrite a function that outputs the number of digits of factorials excluding trailing zeros.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.65px; transform-origin: 407px 91.65px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere is an easy one...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354.5px 8px; transform-origin: 354.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is not difficult to count the number of digits of the factorial of a given number. For example for 'n = 10', we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 140px 8.5px; tab-size: 4; transform-origin: 140px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; length(num2str(factorial(10)))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut 2 of those digits are just trailing zeros. So, for 10!, if we remove the trailing zeros, there would only be 5 digits left.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 303px 8px; transform-origin: 303px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that outputs the number of digits of factorials excluding trailing zeros.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = numFacDigits(x)\r\n n = length_of(num2string(x!)) - '0';\r\nend\r\n","test_suite":"%%\r\nx = randi(3);\r\nn_correct = 1;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 10;\r\nn_correct = 5;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 100;\r\nn_correct = 134;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 5000;\r\nn_correct = 15077;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = intmax;\r\nn_correct = 18570655587;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = double(intmax)*10;\r\nn_correct = 207181392197;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 3:12;\r\nn_correct = uint64([2319 33161 431575 5315711 63157061 731570558 8315705525 93157055190 1031570551819 11315705518107]);\r\nassert(isequal(numFacDigits(10.^x),n_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":223089,"edited_at":"2023-06-03T06:48:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2023-06-03T06:48:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-24T11:46:25.000Z","updated_at":"2025-11-30T19:40:35.000Z","published_at":"2021-08-24T12:11:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere is an easy one...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is not difficult to count the number of digits of the factorial of a given number. For example for 'n = 10', we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e length(num2str(factorial(10)))\\n \u003e\u003e ans =\\n 7]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut 2 of those digits are just trailing zeros. So, for 10!, if we remove the trailing zeros, there would only be 5 digits left.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs the number of digits of factorials excluding trailing zeros.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56220,"title":"Easy Sequences 75: Easy as Pisano Pi","description":"Pisano period , of an integer , is the period in which the sequence of Fibonacci numbers modulo repeats. For example it is not hard to show that , and are , and , respectively:\r\n \r\nI have used Pisano period in the solutions of Problem 56050. Easy Sequences 73: Emergence of Fibonacci Insects and Problem 56065. Easy Sequences 74: Fibonacci Bank Account.\r\nIn this problem, we are asked to simply output the Pisano period of given integer .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.45px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 12.6px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 327.95px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 163.975px; transform-origin: 407px 163.975px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 37.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.9px; text-align: left; transform-origin: 384px 18.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pisano_period\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePisano period\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 28px; height: 16px;\" width=\"28\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 7px; transform-origin: 44.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e of an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 7px; transform-origin: 4px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123px 7px; transform-origin: 123px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eis the period in which the sequence of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFibonacci numbers \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26px 7px; transform-origin: 26px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emodulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 7px; transform-origin: 29.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e repeats. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 7px; transform-origin: 11.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example it is not hard to show that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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style=\"width: 28px; height: 16px;\" width=\"28\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 7px; transform-origin: 4px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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data-image-state=\"image-loaded\" width=\"649\" height=\"201\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.9px; text-align: left; transform-origin: 384px 18.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129px 7px; transform-origin: 129px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI have used Pisano period in the solutions of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56050-easy-sequences-73-emergence-of-fibonacci-insects\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 56050. Easy Sequences 73: Emergence of Fibonacci Insects\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56065-easy-sequences-74-fibonacci-bank-account\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 56065. Easy Sequences 74: Fibonacci Bank Account\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 18.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 9.45px; text-align: left; transform-origin: 384px 9.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.5px 7px; transform-origin: 258.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn this problem, we are asked to simply output the Pisano period of given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = pisanoPi(n)\r\n y = x;\r\nend","test_suite":"%%\r\nn = 1:10;\r\np_correct = [1 3 8 6 20 24 16 12 24 60];\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 1234;\r\np_correct = 1236;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = [1111 2222 3333 4444 5555 6666 7777 8888 9999];\r\np_correct = [50 150 200 150 100 600 400 300 600];\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 1000000;\r\np_correct = 1500000;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 19531250;\r\np_correct = 117187500;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 102334155;\r\np_correct = 80;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 123456789;\r\np_correct = 6862416;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 4807526976;\r\np_correct = 96;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 1000:2000;\r\np = pisanoPi(n);\r\ns = floor([mean(p) mode(p) median(p) std(p)]);\r\ns_correct = [1153 240 768 1124];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('pisanoPi.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-10-06T12:23:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2022-10-06T10:06:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-05T08:50:04.000Z","updated_at":"2026-03-22T12:27:15.000Z","published_at":"2022-10-05T14:00:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pisano_period\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePisano period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e of an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eis the period in which the sequence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFibonacci numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emodulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e repeats. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example it is not hard to show that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"201\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"649\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI have used Pisano period in the solutions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56050-easy-sequences-73-emergence-of-fibonacci-insects\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 56050. Easy Sequences 73: Emergence of Fibonacci Insects\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56065-easy-sequences-74-fibonacci-bank-account\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 56065. Easy Sequences 74: Fibonacci Bank Account\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn this problem, we are asked to simply output the Pisano period of given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" 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Recurrence Equations - Generalised Fibonacci-like sequences","description":"This problem is inspired by problems \u003chttp://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci 2187\u003e, \u003chttp://uk.mathworks.com/matlabcentral/cody/problems/3092-return-fibonacci-sequence-do-not-use-loop-and-condition 3092\u003e and \u003chttp://uk.mathworks.com/matlabcentral/cody/?term=tag%3A%22fibonacci%22 other problems\u003e based on Fibonacci sequence.\r\n\r\nI haven't seen here many problems based on other recursive sequences such as \u003chttp://oeis.org/A000032 Lucas numbers\u003e, \u003chttp://oeis.org/A000129 Pell numbers\u003e, \u003chttp://oeis.org/A000931 Padovan sequence\u003e or \u003chttp://oeis.org/A000073 Tribonacci numbers\u003e so this is a problem about them all.\r\n\r\nYour function input will be _N_, _Init_ and _Rules_. _Init_ and _Rules_ represent initial values of sequence and a kernel which denotes recurrence relation:\r\n\r\n Init : [ A1 A2 ... Ak]\r\n Rules : [ Ck ... C2 C1]\r\n \r\n function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)\r\n and f(1) = A1, f(2) = A2, ..., f(k) = Ak,\r\n\r\n_Init_ and _Rules_ have the same length, _N_ may be a single number or a vector. Your function should return values of _f(N)_. Example:\r\n\r\n % Fibonacci sequence: f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)\r\n \u003e\u003e Init = [1 1];\r\n \u003e\u003e Rules = [1 1];\r\n \u003e\u003e N = 1:10;\r\n \u003e\u003e fibonacci = recurrence_seq(N,Init,Rules),\r\n fibonacci = \r\n 1 1 2 3 5 8 13 21 34 55\r\n \r\n \r\n \r\n\r\nOther info:\r\n\r\n* Different approaches may lead to solutions which won't be able to compute _f(n)_ for _n_ being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for _n\u003c1_.\r\n* Please, try to avoid unnecessary things like strings, _ans_, etc. ","description_html":"\u003cp\u003eThis problem is inspired by problems \u003ca href = \"http://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci\"\u003e2187\u003c/a\u003e, \u003ca href = \"http://uk.mathworks.com/matlabcentral/cody/problems/3092-return-fibonacci-sequence-do-not-use-loop-and-condition\"\u003e3092\u003c/a\u003e and \u003ca href = \"http://uk.mathworks.com/matlabcentral/cody/?term=tag%3A%22fibonacci%22\"\u003eother problems\u003c/a\u003e based on Fibonacci sequence.\u003c/p\u003e\u003cp\u003eI haven't seen here many problems based on other recursive sequences such as \u003ca href = \"http://oeis.org/A000032\"\u003eLucas numbers\u003c/a\u003e, \u003ca href = \"http://oeis.org/A000129\"\u003ePell numbers\u003c/a\u003e, \u003ca href = \"http://oeis.org/A000931\"\u003ePadovan sequence\u003c/a\u003e or \u003ca href = \"http://oeis.org/A000073\"\u003eTribonacci numbers\u003c/a\u003e so this is a problem about them all.\u003c/p\u003e\u003cp\u003eYour function input will be \u003ci\u003eN\u003c/i\u003e, \u003ci\u003eInit\u003c/i\u003e and \u003ci\u003eRules\u003c/i\u003e. \u003ci\u003eInit\u003c/i\u003e and \u003ci\u003eRules\u003c/i\u003e represent initial values of sequence and a kernel which denotes recurrence relation:\u003c/p\u003e\u003cpre\u003e Init : [ A1 A2 ... Ak]\r\n Rules : [ Ck ... C2 C1]\u003c/pre\u003e\u003cpre\u003e function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)\r\n and f(1) = A1, f(2) = A2, ..., f(k) = Ak,\u003c/pre\u003e\u003cp\u003e\u003ci\u003eInit\u003c/i\u003e and \u003ci\u003eRules\u003c/i\u003e have the same length, \u003ci\u003eN\u003c/i\u003e may be a single number or a vector. Your function should return values of \u003ci\u003ef(N)\u003c/i\u003e. Example:\u003c/p\u003e\u003cpre\u003e % Fibonacci sequence: f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)\r\n \u0026gt;\u0026gt; Init = [1 1];\r\n \u0026gt;\u0026gt; Rules = [1 1];\r\n \u0026gt;\u0026gt; N = 1:10;\r\n \u0026gt;\u0026gt; fibonacci = recurrence_seq(N,Init,Rules),\r\n fibonacci = \r\n 1 1 2 3 5 8 13 21 34 55\u003c/pre\u003e\u003cp\u003eOther info:\u003c/p\u003e\u003cul\u003e\u003cli\u003eDifferent approaches may lead to solutions which won't be able to compute \u003ci\u003ef(n)\u003c/i\u003e for \u003ci\u003en\u003c/i\u003e being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for \u003ci\u003en\u0026lt;1\u003c/i\u003e.\u003c/li\u003e\u003cli\u003ePlease, try to avoid unnecessary things like strings, \u003ci\u003eans\u003c/i\u003e, etc.\u003c/li\u003e\u003c/ul\u003e","function_template":"function values = recurrence_seq(N, Init, Rules)\r\n values = N;\r\n values(N\u003c1) = NaN;\r\n\r\n\r\n\r\nend","test_suite":"%% Fibonacci\r\nInit = [1,1];\r\nRules = [1,1];\r\nN = 1:10;\r\nvalues_correct = [1 1 2 3 5 8 13 21 34 55];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Fibonacci - shifted\r\nInit = [2,3];\r\nRules = [1,1];\r\nN = 1:10;\r\nvalues_correct = [2, 3, 5, 8, 13, 21, 34, 55, 89, 144];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Fibonacci - negative n\r\nInit = [1,1];\r\nRules = [1,1];\r\nN = -5:5;\r\nvalues_correct = [5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5];\r\nvalues_accepted = [nan, nan, nan, nan, nan, nan, 1, 1, 2, 3, 5];\r\nvalues = recurrence_seq(N, Init, Rules);\r\nassert(isequal(values,values_correct)||isequaln(values,values_accepted))\r\n%% Lucas numbers\r\nInit = [1,3];\r\nRules = [1,1];\r\nN = 1:10;\r\nvalues_correct = [1, 3, 4, 7, 11, 18, 29, 47, 76, 123];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Padovan sequence\r\nInit = [1, 1, 1];\r\nRules = [1, 1, 0];\r\nN = 4:21;\r\nvalues_correct = [2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Pell numbers\r\nInit = [0, 1];\r\nRules = [1, 2];\r\nN = 4:3:19;\r\nvalues_correct = [5, 70, 985, 13860, 195025, 2744210];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% 3^n-2^n sequence\r\nInit = [3-2, 9-4];\r\nRules = [-6 5];\r\nN = 1:10;\r\nvalues_correct = [1, 5, 19, 65, 211, 665, 2059, 6305, 19171, 58025];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Perrin sequence\r\nInit = [3, 0, 2];\r\nRules = [1, 1, 0];\r\nN = [28:38, 10:-1:1];\r\nvalues_correct = [1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 12, 10, 7, 5, 5, 2, 3, 2, 0, 3];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% \r\nInit = [3, 0, 2]; % Perrin init\r\nRules = [1, 1, 1]; % Tribonacci rules\r\nN = [1:15];\r\nvalues_correct = [3, 0, 2, 5, 7, 14, 26, 47, 87, 160, 294, 541, 995, 1830, 3366];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Tribonacci\r\nInit = [0, 0, 1];\r\nRules = [1, 1, 1];\r\nN = [1:23];\r\nvalues_correct = [0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Tetranacci\r\nInit = [0, 0, 0, 1];\r\nRules = [1, 1, 1, 1];\r\nN = [20:23];\r\nvalues_correct = [20569, 39648, 76424, 147312];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Heptanacci\r\nInit = [0, 0, 0, 0, 0, 0, 1];\r\nRules = [1, 1, 1, 1, 1, 1, 1];\r\nN = [7:15, 19];\r\nvalues_correct = [1, 1, 2, 4, 8, 16, 32, 64, 127, 2000];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, -1];\r\nRules = [1, -1];\r\nN = 1:10;\r\nvalues_correct = [1, -1, 2, -3, 5, -8, 13, -21, 34, -55];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, -1];\r\nRules = [-1, 1];\r\nN = 1:10;\r\nvalues_correct = [1, -1, -2, -1, 1, 2, 1, -1, -2, -1];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, -1];\r\nRules = [1, 1];\r\nN = 1:10;\r\nvalues_correct = [1, -1, 0, -1, -1, -2, -3, -5, -8, -13];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, 1];\r\nRules = [2, -1];\r\nN = 1:10;\r\nvalues_correct = ones(1,10);\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, 2];\r\nRules = [2, -1];\r\nN = 1:10;\r\nvalues_correct = [1, 2, 0, 4, -4, 12, -20, 44, -84, 172];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Jacobsthal numbers\r\nInit = [0, 1];\r\nRules = [2, 1];\r\nN = 1:10;\r\nvalues_correct = [0, 1, 1, 3, 5, 11, 21, 43, 85, 171];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% A028242\r\nInit = [1, 0, 2];\r\nRules = [-1 1 1];\r\nN = 1:20;\r\nvalues_correct = [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\n\r\n","published":true,"deleted":false,"likes_count":18,"comments_count":3,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":414,"test_suite_updated_at":"2015-04-02T15:23:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-04-02T14:52:53.000Z","updated_at":"2026-03-26T04:58:55.000Z","published_at":"2015-04-02T14:54:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is inspired by problems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2187\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://uk.mathworks.com/matlabcentral/cody/problems/3092-return-fibonacci-sequence-do-not-use-loop-and-condition\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e3092\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://uk.mathworks.com/matlabcentral/cody/?term=tag%3A%22fibonacci%22\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eother problems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e based on Fibonacci sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI haven't seen here many problems based on other recursive sequences such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000032\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLucas numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000129\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePell numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000931\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePadovan sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000073\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTribonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e so this is a problem about them all.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function input will be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRules\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRules\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e represent initial values of sequence and a kernel which denotes recurrence relation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Init : [ A1 A2 ... Ak]\\n Rules : [ Ck ... C2 C1]\\n\\n function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)\\n and f(1) = A1, f(2) = A2, ..., f(k) = Ak,]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRules\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e have the same length,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e may be a single number or a vector. Your function should return values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(N)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % Fibonacci sequence: f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)\\n \u003e\u003e Init = [1 1];\\n \u003e\u003e Rules = [1 1];\\n \u003e\u003e N = 1:10;\\n \u003e\u003e fibonacci = recurrence_seq(N,Init,Rules),\\n fibonacci = \\n 1 1 2 3 5 8 13 21 34 55]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOther info:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDifferent approaches may lead to solutions which won't be able to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026lt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease, try to avoid unnecessary things like strings,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eans\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52562,"title":"Easy Sequences 6: Coefficient sums of derivatives","description":"Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: etc. The total sum of this sequence converge to .\r\nFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, . Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 98px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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YCAwEBgIDFSJgf8D3Giv49mFrO8AAAAASUVORK5CYII=\" width=\"163\" height=\"20\" style=\"width: 163px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and its first-order derivative \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"35\" style=\"width: 129.5px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The sums of the coefficients of P and P', are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"120\" height=\"18\" style=\"width: 120px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"108\" height=\"18\" style=\"width: 108px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"18\" style=\"width: 90px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e etc. The total sum of this sequence converge to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"19\" style=\"width: 98.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function totSum = tot_dCoefSum(coef)\r\n y = x;\r\nend","test_suite":"%%\r\ncs = [5 6 -7 -8];\r\nts = '88';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [3 15 -2 1];\r\nts = '120';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [-7 22 43 6 -75 3 1 0 -80 10 5];\r\nts = '-42698751';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = 1:25;\r\nts = '1836856501837772435875025';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([2,-1],1,15);\r\nts = '47298214022376392514505945712317';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [ones(1,20) zeros(1,10)];\r\nts = '24893912605687593731774059567276';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([-2,-25,1],1,10);\r\nts = '-68761759219969440143678420163128';\r\nassert(isequal(tot_dCoefSum(cs),ts))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2021-08-17T17:53:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-16T19:00:56.000Z","updated_at":"2025-11-30T19:39:34.000Z","published_at":"2021-08-17T12:43:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\\\\left(x\\\\right)=5x^3+6x^2-7x-8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and its first-order derivative \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dP}{dx}=15x^2+12x-7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The sums of the coefficients of P and P', are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 + 6 - 7 - 8 = -4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e15+12-7= 20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-4,\\\\ 20,\\\\ 42, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e etc. The total sum of this sequence converge to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e88\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 6\\\\ -7\\\\ -8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":55195,"title":"Sequence","description":"Let S be a sequence of numbers \r\n\r\nLet \r\n\r\nFind for some , where and .\r\n\r\nUpdate - test suite cleaned up on 2-9-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 204px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 102px; transform-origin: 407px 102px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet S be a sequence of numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 52px; height: 20px;\" width=\"52\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 102px; height: 20px;\" width=\"102\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAoCAYAAADpE0oSAAACLUlEQVRYR+1VPS9EQRTd7SWCToQEBYlOUOgpFRJEIVuIj1KEhB9A4qNQ+SgUGh+FRCNBLREaHQUSlQoRes7ZzN3cjJn3DG+txJvkZPbt3HfPvefeOy+bKdHKlog3kxL/mvKp1KnURVMgba6iSWs7/vNSdyHiSaAWeDHYxD4BdADdwHGIXHEZV8LZNkDiWWAdeALagHND9Ia9zvz/Ze4oYpKeAk2GdN7y+m6emSkzDlo+Yk26AY+jDq9CTCXsoGKD8BEfGXkfsLc4ZKT0tOFqBG5jmSwDF7F26suGtR4BroFOKzC+XwG0As8+NVzEZzBmp/qyZRnugTJgD+i3kpEJkIZ0lsEmboCTG+PI5ZRHC8CUsRnHvuaQWUrVjrMLVxls4jEYrUY4ZWCXJluaVVkyC8crfhCu/sjb2MQ6mwGc76popdN5gbAUUl8GU69sZcZ9ijmJdca6sYR0C28NAZxtOl4CDoAeJekMfs8BLANt+kxgd9hPgPwE2BnrxuE5Z5hr0Dhjo8j8svm4coC+LqW+MmZUsRxgQLz18ss3Tis4Y1a8Dg8BZiZNIo5JtmyR0icDY1DVABVkGaaFMIrYtgl5ljuAEnPtA7pPCr7iPhIhpLTVzcnnRVe2PEia+Ao+a4BhYEdJ/imBJInZmI8Ax6wZkBtQLhmOXeFOT5KYVyezlK+Z1JuNlgN6gcJXLkli+XDoi0f+Y7Mx88hxCm2ob9knmXFQAClxkFw/Mf5/Un8AkB1yKXEBRiAAAAAASUVORK5CYII=\" style=\"width: 15px; height: 20px;\" width=\"15\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.5px 8px; transform-origin: 127.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - test suite cleaned up on 2-9-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summation(n)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(isequal(summation(1),1))\r\n%%\r\nassert(isequal(summation(2),2))\r\n%%\r\nassert(isequal(summation(3),1))\r\n%%\r\nassert(isequal(summation(4),-1))\r\n%%\r\nassert(isequal(summation(5),-2))\r\n%%\r\nassert(isequal(summation(6),-1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2457030,"edited_by":223089,"edited_at":"2022-09-02T13:52:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2022-09-02T13:49:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T21:23:39.000Z","updated_at":"2026-03-04T13:46:29.000Z","published_at":"2022-07-13T21:23:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S be a sequence of numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1, a_2, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = a_{n-1} -a_{n-2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for some \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUpdate - test suite cleaned up on 2-9-22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57422,"title":"Harmonic series counting","description":"The function takes a positive limit as input,\r\nAnd counts how many terms must be summed in the harmonic series:\r\n1/1, 1/2, 1/3, 1/4, ..., 1/N\r\nuntil the sum of the terms in the series is greater than the given limit.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 55.5px; transform-origin: 332px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function takes a positive limit as input,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAnd counts how many terms must be summed in the harmonic series:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1/1, 1/2, 1/3, 1/4, ..., 1/N\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003euntil the sum of the terms in the series is greater than the given limit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = count_of_harmonic_series(limit)\r\n sum_s = 1/1;\r\n n = 1;\r\nend","test_suite":"%%\r\nlimit = 2.0;\r\ny_correct = 4;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 10;\r\ny_correct = 12367;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 1.4;\r\ny_correct = 2;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 15;\r\ny_correct = 1835421;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n\r\n%%\r\nlimit = 13.6;\r\ny_correct = 452609;\r\nassert(isequal(count_of_harmonic_series(limit),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2710538,"edited_by":2710538,"edited_at":"2022-12-16T11:45:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-16T11:24:36.000Z","updated_at":"2026-02-19T15:16:16.000Z","published_at":"2022-12-16T11:40:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function takes a positive limit as input,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd counts how many terms must be summed in the harmonic series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1/1, 1/2, 1/3, 1/4, ..., 1/N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003euntil the sum of the terms in the series is greater than the given limit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44225,"title":"Sum of self power series","description":"The series, 1^1,2^2,3^3,4^4,....\r\n\r\nFind the sum of such series when x terms are given.","description_html":"\u003cp\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/p\u003e\u003cp\u003eFind the sum of such series when x terms are given.\u003c/p\u003e","function_template":"function y = sumofseries(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 5;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 288;\r\nassert(isequal(sumofseries(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":134801,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-05-25T05:40:41.000Z","updated_at":"2026-03-10T15:08:41.000Z","published_at":"2017-05-25T05:40:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of such series when x terms are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1485,"title":"Method of Common Differences part-1","description":"\r\nUse the method of common differences to output a vector containing the initial values and the nth order difference.\r\n\r\nex \r\n [ 1 4 9 16 25 36 ] has 1st differences [ 3 5 7 9 11 ] and second differences [2 2 2 2] . Therefore output [1 3 2] which is the 1st element of the above three vectors. \r\n\r\nThe use of this is that the sequence can be continued by using these differences. \r\n\r\nProblem 9) \r\nPrev: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1484 1484\u003e\r\nNext: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1486 1486\u003e\r\n\r\n","description_html":"\u003cp\u003eUse the method of common differences to output a vector containing the initial values and the nth order difference.\u003c/p\u003e\u003cp\u003eex \r\n [ 1 4 9 16 25 36 ] has 1st differences [ 3 5 7 9 11 ] and second differences [2 2 2 2] . Therefore output [1 3 2] which is the 1st element of the above three vectors.\u003c/p\u003e\u003cp\u003eThe use of this is that the sequence can be continued by using these differences.\u003c/p\u003e\u003cp\u003eProblem 9) \r\nPrev: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1484\"\u003e1484\u003c/a\u003e\r\nNext: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1486\"\u003e1486\u003c/a\u003e\u003c/p\u003e","function_template":"function y = seq2commondiff(x)\r\nt=[1];\r\nend","test_suite":"%%\r\nx = [1 4 9 16 25];\r\ny_correct = [1 3 2];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [1 9 29 67 129 221];\r\ny_correct = [1 8 12 6];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [3 4 9 23 51 98 169 269 403 576];\r\ny_correct = [3 1 4 5];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [1 8 27 64 125 216];\r\ny_correct = [1 7 12 6];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx = [2 0 2 9 22 42];\r\ny_correct = [2 -2 4 1];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n%%\r\nx=[1 8 28 67 131 226]\r\ny_correct = [1 7 13 6];\r\nassert(isequal(seq2commondiff(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":11275,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":"2013-05-01T18:21:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-01T17:52:16.000Z","updated_at":"2025-07-04T10:38:00.000Z","published_at":"2013-05-01T18:21:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the method of common differences to output a vector containing the initial values and the nth order difference.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eex [ 1 4 9 16 25 36 ] has 1st differences [ 3 5 7 9 11 ] and second differences [2 2 2 2] . Therefore output [1 3 2] which is the 1st element of the above three vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe use of this is that the sequence can be continued by using these differences.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 9) Prev:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1484\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1484\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Next:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1486\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1486\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54675,"title":"Define an arithmetic sequence","description":"Given three numbers n, a, and d, define an arithmetic sequence of n terms with a being the initial term of the sequence and d being the common difference of the sequence. If n = 0, then return an empty array since there would be no terms in the sequence.\r\nExamples:\r\nInput [n,a,d] = deal(10,5,2)\r\nOutput seq = [5 7 9 11 13 15 17 19 21 23]\r\n\r\nInput [n,a,d] = deal(5,2,-3)\r\nOutput seq = [2 -1 -4 -7 -10]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.875px; transform-origin: 407px 112.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven three numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, define an arithmetic sequence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e terms with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the initial term of the sequence and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the common difference of the sequence. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(10,5,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [5 7 9 11 13 15 17 19 21 23]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(5,2,-3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [2 -1 -4 -7 -10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = arithSequence(n,a,d)\r\n seq = [n a d];\r\nend","test_suite":"%%\r\n[n,a,d] = deal(10,5,2);\r\nseq_correct = [5 7 9 11 13 15 17 19 21 23];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(5,2,-3);\r\nseq_correct = [2 -1 -4 -7 -10];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(7,3,0.5);\r\nseq_correct = [3 3.5 4 4.5 5 5.5 6];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(0, 1, 2);\r\nassert(isempty(arithSequence(n,a,d)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":792819,"edited_by":792819,"edited_at":"2022-05-24T21:17:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-24T21:17:06.000Z","updated_at":"2026-03-05T13:32:48.000Z","published_at":"2022-05-24T21:17:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, define an arithmetic sequence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e terms with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the initial term of the sequence and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the common difference of the sequence. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input [n,a,d] = deal(10,5,2)\\nOutput seq = [5 7 9 11 13 15 17 19 21 23]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input [n,a,d] = deal(5,2,-3)\\nOutput seq = [2 -1 -4 -7 -10]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1486,"title":"Method of Common Differences part-2","description":"\r\nThis is the inverse problem to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1485 Problem 1485\u003e. Problem 1485 illustrates the method of differences takes a sequence and takes successive differences till it hits a constant. The output was the initial values and the final common difference. This output can be used to regenerate the original sequence. Thus this problem.\r\n\r\nUse the initial value and difference vector in the form output in 1485 and generate first n values of the sequence. \r\n\r\nEx: Consider the vector [1 3 2]. The last value '2' is the second order difference and the previous values are the initial values. This generates the sequence [1 4 9 16 25 36 ... ]\r\n\r\nProblem 10)\r\nPrev: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1485 1485\u003e \r\nPrev: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1496 1496\u003e ","description_html":"\u003cp\u003eThis is the inverse problem to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1485\"\u003eProblem 1485\u003c/a\u003e. Problem 1485 illustrates the method of differences takes a sequence and takes successive differences till it hits a constant. The output was the initial values and the final common difference. This output can be used to regenerate the original sequence. Thus this problem.\u003c/p\u003e\u003cp\u003eUse the initial value and difference vector in the form output in 1485 and generate first n values of the sequence.\u003c/p\u003e\u003cp\u003eEx: Consider the vector [1 3 2]. The last value '2' is the second order difference and the previous values are the initial values. This generates the sequence [1 4 9 16 25 36 ... ]\u003c/p\u003e\u003cp\u003eProblem 10)\r\nPrev: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1485\"\u003e1485\u003c/a\u003e \r\nPrev: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1496\"\u003e1496\u003c/a\u003e\u003c/p\u003e","function_template":"function y = commondiff2seq(x,n)\r\n y = [1 2 3];\r\nend","test_suite":"%%\r\nx = [1 3 2];\r\nn=5;\r\ny_correct = [1 4 9 16 25];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [1 4 6];\r\nn=6;\r\ny_correct = [1 5 15 31 53 81];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [10 -4 4];\r\nn=7;\r\ny_correct = [10 6 6 10 18 30 46];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [100 10 -5];\r\nn=5;\r\ny_correct = [100 110 115 115 110];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [0 -10 4 -2 6];\r\nn=10;\r\ny_correct = [ 0 -10 -16 -20 -18 0 50 154 340 642];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [3 0];\r\nn=4;\r\ny_correct = [3 3 3 3 ];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [6 1];\r\nn=4;\r\ny_correct = [6 7 8 9];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [-10 1 -5 2];\r\nn=10;\r\ny_correct = [-10 -9 -13 -20 -28 -35 -39 -38 -30 -13];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [ 1 3 -1 -2 2 1];\r\nn=10;\r\ny_correct = [ 1 4 6 5 1 -3 0 22 81 202];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n\r\n%%\r\nx = [0 0 0];\r\nn=5;\r\ny_correct = [0 0 0 0 0];\r\nassert(isequal(commondiff2seq(x,n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":11275,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-01T18:40:08.000Z","updated_at":"2026-01-02T17:21:44.000Z","published_at":"2013-05-01T18:40:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the inverse problem to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1485\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 1485\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Problem 1485 illustrates the method of differences takes a sequence and takes successive differences till it hits a constant. The output was the initial values and the final common difference. This output can be used to regenerate the original sequence. Thus this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the initial value and difference vector in the form output in 1485 and generate first n values of the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEx: Consider the vector [1 3 2]. The last value '2' is the second order difference and the previous values are the initial values. This generates the sequence [1 4 9 16 25 36 ... ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 10) Prev:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1485\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1485\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Prev:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1496\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1496\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56260,"title":"Leonardo primes","description":"Leonardo numbers are defined by following recurrence relation:\r\n\r\n\r\n\r\nLeonard prime is Leonardo number which is also prime (see https://en.wikipedia.org/wiki/Leonardo_number). \r\n\r\nFor given n, find all Leonardo primes.\r\n\r\nExample:\r\nn=5;\r\nLeoNumbers=[1 1 3 5 9 15];\r\nPrimes=[2 3 5 7 11 13];\r\nLeoPrimes=[3 5];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.375px; transform-origin: 407px 196.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonardo numbers are defined by following recurrence relation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; 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\" width=\"273.5\" height=\"61\" style=\"width: 273.5px; height: 61px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonard prime is Leonardo number which is also prime (see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Leonardo_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find all Leonardo primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.75px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.875px; transform-origin: 404px 40.875px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoNumbers=[1 1 3 5 9 15];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ePrimes=[2 3 5 7 11 13];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoPrimes=[3 5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function LeoPrimes = LeonardoPrimes(n)\r\n LeoPrimes=n;\r\nend","test_suite":"%%\r\nn = 5;\r\nLeoPrimes_correct = [3,5];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n\r\n%%\r\nn = 0;\r\n%LeoPrimes_correct = [];\r\nassert(isempty(LeonardoPrimes(n)))\r\n\r\n%%\r\nn = 25;\r\nLeoPrimes_correct = [3,5,41,67,109,1973,5167];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":2663765,"edited_by":2663765,"edited_at":"2022-10-10T14:54:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2022-10-10T13:22:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:53:17.000Z","updated_at":"2026-01-13T16:14:23.000Z","published_at":"2022-10-10T12:53:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonardo numbers are defined by following recurrence relation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL(n) = \\n \\\\begin{cases}\\n 1 \u0026amp; \\\\mbox{if }~n = 0 \\\\\\\\\\n 1 \u0026amp; \\\\mbox{if }~n = 1 \\\\\\\\\\n L(n - 1) + L(n - 2) + 1 \u0026amp; \\\\mbox{if }~n \u0026gt; 1 \\\\\\\\\\n \\\\end{cases}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonard prime is Leonardo number which is also prime (see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Leonardo_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find all Leonardo primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n=5;\\nLeoNumbers=[1 1 3 5 9 15];\\nPrimes=[2 3 5 7 11 13];\\nLeoPrimes=[3 5];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42581,"title":"Create sequnce 1 4 9 16 25.........","description":"Create sequnce 1 4 9 16 25......... upto entered input value using matlab scripting commands. Let y be output and x be input","description_html":"\u003cp\u003eCreate sequnce 1 4 9 16 25......... upto entered input value using matlab scripting commands. Let y be output and x be input\u003c/p\u003e","function_template":"function y = prntseq(x)\r\n% Enter code\r\nend","test_suite":"%%\r\nx = 25;\r\ny_correct = [1 4 9 16 25];\r\nassert(isequal(prntseq(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = [1 4 9 16 25 36 49 64 81 100];\r\nassert(isequal(prntseq(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = [1 4 9];\r\nassert(isequal(prntseq(x),y_correct))\r\n%%\r\nx = 36;\r\ny_correct = [1 4 9 16 25 36];\r\nassert(isequal(prntseq(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46868,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":414,"test_suite_updated_at":"2015-08-28T11:26:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-28T11:17:32.000Z","updated_at":"2026-02-08T06:17:39.000Z","published_at":"2015-08-28T11:26:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate sequnce 1 4 9 16 25......... upto entered input value using matlab scripting commands. Let y be output and x be input\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1132,"title":"Create a recurrence matrix for a vector of data","description":"In \u003chttps://en.wikipedia.org/wiki/Conversation_analysis conversation analysis\u003e, it's often useful to track the contributions from each speaker to see who talks when. One measurement of engagement between a pair of conversants is to see if they talk to each other more than they talk to other people; for example, at a double date, two old friends might talk to each other more than they talk to their spouses.\r\n\r\nAssuming we've coded up the conversation data (e.g. using Gail Jefferson's \u003chttp://mis.ucd.ie/wiki/JeffersonianTranscription transcription methods\u003e) and assigned a unique number to each participant, MATLAB makes an excellent tool to quickly gather some of these statistics.\r\n\r\nGiven a vector of speaker observations V, where element _V(i)_ indicates who spoke sentence _i_ in the data, find how many times each element occurs directly after each other element. Note that since we may only be analyzing a part of a larger transcripts, not all speaker numbers may appear in the vector.\r\n\r\nReturn a matrix containing this data, as well as the list of (ordered) unique elements.\r\n\r\nE.g., if V = [1 3 5 3 5 5], then\r\n\r\n [R, U] = recurrence(V)\r\n R =\r\n 0 1 0\r\n 0 0 2\r\n 0 1 1\r\n U =\r\n 1 3 5\r\n \r\nSuch a tool will have other uses, of course.","description_html":"\u003cp\u003eIn \u003ca href=\"https://en.wikipedia.org/wiki/Conversation_analysis\"\u003econversation analysis\u003c/a\u003e, it's often useful to track the contributions from each speaker to see who talks when. One measurement of engagement between a pair of conversants is to see if they talk to each other more than they talk to other people; for example, at a double date, two old friends might talk to each other more than they talk to their spouses.\u003c/p\u003e\u003cp\u003eAssuming we've coded up the conversation data (e.g. using Gail Jefferson's \u003ca href=\"http://mis.ucd.ie/wiki/JeffersonianTranscription\"\u003etranscription methods\u003c/a\u003e) and assigned a unique number to each participant, MATLAB makes an excellent tool to quickly gather some of these statistics.\u003c/p\u003e\u003cp\u003eGiven a vector of speaker observations V, where element \u003ci\u003eV(i)\u003c/i\u003e indicates who spoke sentence \u003ci\u003ei\u003c/i\u003e in the data, find how many times each element occurs directly after each other element. Note that since we may only be analyzing a part of a larger transcripts, not all speaker numbers may appear in the vector.\u003c/p\u003e\u003cp\u003eReturn a matrix containing this data, as well as the list of (ordered) unique elements.\u003c/p\u003e\u003cp\u003eE.g., if V = [1 3 5 3 5 5], then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[R, U] = recurrence(V)\r\nR =\r\n 0 1 0\r\n 0 0 2\r\n 0 1 1\r\nU =\r\n 1 3 5\r\n\u003c/pre\u003e\u003cp\u003eSuch a tool will have other uses, of course.\u003c/p\u003e","function_template":"function [A, V] = recurrence(DATA)\r\n A = [];\r\n V = [];\r\nend\r\n","test_suite":"%%\r\nv = [4 2 3 1 1 3 4 5 1 3];\r\nreal_r = [1 0 2 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 1 0 0 1; 1 0 0 0 0];\r\nreal_u = 1:5;\r\n[r,u] = recurrence(v);\r\nassert(and(isequal(r,real_r), isequal(u,real_u)));\r\n%%\r\nv = [1:6,1];\r\nreal_r = circshift(eye(6),[0 1]);\r\nreal_u = 1:6;\r\n[r,u] = recurrence(v);\r\nassert(and(isequal(r,real_r), isequal(u,real_u)));\r\n%%\r\nv = [0 0 0 0 0 0];\r\nreal_r = 5;\r\nreal_u = 0;\r\n[r,u] = recurrence(v);\r\nassert(and(isequal(r,real_r), isequal(u,real_u)));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":78,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-21T15:19:46.000Z","updated_at":"2025-12-08T02:41:57.000Z","published_at":"2012-12-21T15:20:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Conversation_analysis\\\"\u003e\u003cw:r\u003e\u003cw:t\u003econversation analysis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, it's often useful to track the contributions from each speaker to see who talks when. One measurement of engagement between a pair of conversants is to see if they talk to each other more than they talk to other people; for example, at a double date, two old friends might talk to each other more than they talk to their spouses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming we've coded up the conversation data (e.g. using Gail Jefferson's\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://mis.ucd.ie/wiki/JeffersonianTranscription\\\"\u003e\u003cw:r\u003e\u003cw:t\u003etranscription methods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) and assigned a unique number to each participant, MATLAB makes an excellent tool to quickly gather some of these statistics.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector of speaker observations V, where element\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV(i)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e indicates who spoke sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the data, find how many times each element occurs directly after each other element. Note that since we may only be analyzing a part of a larger transcripts, not all speaker numbers may appear in the vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn a matrix containing this data, as well as the list of (ordered) unique elements.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g., if V = [1 3 5 3 5 5], then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[R, U] = recurrence(V)\\nR =\\n 0 1 0\\n 0 0 2\\n 0 1 1\\nU =\\n 1 3 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuch a tool will have other uses, of course.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1894,"title":"GJam 2014 China Rd A: Library Sorting (Large)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2924486/dashboard#s=p2 GJam 2014 China Sorting\u003e. Subset of cases.\r\n\r\nThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations. \r\n\r\n*Input:* V a vector\r\n\r\n*Output:* Vout a sorted vector Odds Increasing/Evens Increasing\r\n\r\n*Example:*\r\n\r\nV= [-5 -12 87 2 88 20 11]\r\n\r\nVout=[-5 88 11 20 2 -12 87]\r\n\r\n\r\n*Contest Performance:* Best Time to Complete: \u003c 10 minutes","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\"\u003eGJam 2014 China Sorting\u003c/a\u003e. Subset of cases.\u003c/p\u003e\u003cp\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e V a vector\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eV= [-5 -12 87 2 88 20 11]\u003c/p\u003e\u003cp\u003eVout=[-5 88 11 20 2 -12 87]\u003c/p\u003e\u003cp\u003e\u003cb\u003eContest Performance:\u003c/b\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/p\u003e","function_template":"function vout=Sort_CH(v)\r\n vout=v;\r\nend","test_suite":"%%\r\ntic\r\nv=[1 ];\r\nvexp=[1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[2 1 ];\r\nvexp=[2 1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 ];\r\nvexp=[1 2 3 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 4 5 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[5 2 3 4 1 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[994 994 -981 -975 -971 980 -971 976 -969 -969 968 968 958 -963 -957 948 -955 932 926 -935 924 -931 -923 -917 922 -917 -909 -899 916 914 -899 -877 -871 -871 -867 -847 912 -829 912 -825 -819 -817 910 -811 -805 -803 -801 904 -791 -783 -745 -731 902 -725 -725 -715 900 896 -707 896 -705 -705 -693 -691 882 -687 -685 -683 -671 -663 882 -663 880 880 -651 -651 -637 876 -637 -623 -613 -605 -601 -577 -577 862 -571 -565 856 848 -559 -559 -555 -553 844 -551 840 828 -547 -539 -527 812 -525 806 802 -505 -503 -497 -497 -495 798 -493 -491 -483 -481 798 770 770 -481 770 762 758 -477 -469 -463 -457 756 -455 -451 -441 -439 -431 -429 752 -427 -413 -409 742 -403 726 -391 722 -389 -385 718 -379 -365 -363 -359 712 702 -355 -351 682 -347 682 674 672 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];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-891 962 792 -851 784 730 -789 -781 662 662 -765 -737 -713 644 -567 -525 -465 534 -451 526 454 -427 -399 -173 -15 454 -1 77 378 175 202 185 170 275 313 367 82 407 459 473 507 621 691 707 731 805 825 935 981 52 48 46 -10 -66 -162 -168 -192 -196 -218 -232 -262 -280 -288 -332 -358 -402 -438 -448 -490 -502 -516 -572 -590 -598 -832 -834 ];\r\nvexp=[-891 962 792 -851 784 730 -789 -781 662 662 -765 -737 -713 644 -567 -525 -465 534 -451 526 454 -427 -399 -173 -15 454 -1 77 378 175 202 185 170 275 313 367 82 407 459 473 507 621 691 707 731 805 825 935 981 52 48 46 -10 -66 -162 -168 -192 -196 -218 -232 -262 -280 -288 -332 -358 -402 -438 -448 -490 -502 -516 -572 -590 -598 -832 -834 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[990 988 -999 -995 -993 -993 -991 976 970 958 -989 -973 946 -965 -963 -957 -957 -941 938 -939 -937 -937 -913 -907 -901 938 938 924 -901 -893 924 -891 -889 918 -869 912 910 -869 -869 -845 -827 -811 -793 -741 906 868 -715 -715 844 836 -711 -709 812 -693 -693 -687 -665 808 786 774 -665 -663 -663 -615 -603 -593 -589 770 762 -587 756 -585 -581 -565 -565 -561 -555 -555 -553 -541 706 704 -539 -505 694 -503 -493 -455 -451 672 -427 -399 670 -385 658 -373 -359 656 -339 -335 654 -333 -327 636 -325 -313 -297 -297 -273 616 -263 -253 614 -251 604 590 -219 -209 550 -207 -203 -187 -185 -181 -177 -167 -159 546 -157 -145 -137 544 -135 -105 -77 -71 -67 -65 -41 540 -39 532 528 -37 526 -33 -31 -23 -21 -13 524 11 15 19 520 506 27 37 41 43 494 77 488 89 101 105 127 486 129 131 472 468 458 133 133 139 450 139 171 171 428 175 428 189 203 219 410 237 251 396 255 265 271 273 273 273 293 392 297 376 299 301 315 315 351 373 374 377 377 379 385 387 389 397 407 374 368 409 411 425 433 439 449 451 481 507 535 342 537 553 338 338 575 322 312 577 577 581 583 585 308 306 603 292 264 619 248 242 228 224 623 637 645 220 661 663 208 671 681 204 186 693 693 701 719 721 178 170 737 749 154 763 154 767 154 769 789 154 144 142 130 793 793 795 803 803 805 815 817 819 821 120 823 120 825 86 86 78 74 72 825 62 839 841 861 861 861 873 875 56 875 42 897 935 935 949 12 949 955 955 8 975 979 0 0 0 0 0 -52 -56 -60 -70 -70 -72 -94 -96 -98 -110 -110 -114 -116 -126 -126 -136 -158 -160 -176 -178 -182 -188 -196 -200 -206 -208 -208 -222 -224 -228 -276 -278 -296 -302 -316 -318 -324 -334 -346 -350 -350 -358 -364 -368 -370 -378 -378 -378 -386 -404 -416 -416 -418 -420 -432 -448 -462 -480 -482 -490 -502 -514 -516 -520 -546 -546 -546 -550 -564 -570 -570 -572 -574 -580 -600 -602 -624 -626 -626 -634 -650 -658 -658 -662 -686 -712 -716 -720 -726 -730 -732 -756 -756 -770 -780 -790 -798 -802 -824 -836 -882 -894 -906 -914 -914 -932 -950 -952 -966 -968 -978 -978 -990 -990 ];\r\nvexp=[990 988 -999 -995 -993 -993 -991 976 970 958 -989 -973 946 -965 -963 -957 -957 -941 938 -939 -937 -937 -913 -907 -901 938 938 924 -901 -893 924 -891 -889 918 -869 912 910 -869 -869 -845 -827 -811 -793 -741 906 868 -715 -715 844 836 -711 -709 812 -693 -693 -687 -665 808 786 774 -665 -663 -663 -615 -603 -593 -589 770 762 -587 756 -585 -581 -565 -565 -561 -555 -555 -553 -541 706 704 -539 -505 694 -503 -493 -455 -451 672 -427 -399 670 -385 658 -373 -359 656 -339 -335 654 -333 -327 636 -325 -313 -297 -297 -273 616 -263 -253 614 -251 604 590 -219 -209 550 -207 -203 -187 -185 -181 -177 -167 -159 546 -157 -145 -137 544 -135 -105 -77 -71 -67 -65 -41 540 -39 532 528 -37 526 -33 -31 -23 -21 -13 524 11 15 19 520 506 27 37 41 43 494 77 488 89 101 105 127 486 129 131 472 468 458 133 133 139 450 139 171 171 428 175 428 189 203 219 410 237 251 396 255 265 271 273 273 273 293 392 297 376 299 301 315 315 351 373 374 377 377 379 385 387 389 397 407 374 368 409 411 425 433 439 449 451 481 507 535 342 537 553 338 338 575 322 312 577 577 581 583 585 308 306 603 292 264 619 248 242 228 224 623 637 645 220 661 663 208 671 681 204 186 693 693 701 719 721 178 170 737 749 154 763 154 767 154 769 789 154 144 142 130 793 793 795 803 803 805 815 817 819 821 120 823 120 825 86 86 78 74 72 825 62 839 841 861 861 861 873 875 56 875 42 897 935 935 949 12 949 955 955 8 975 979 0 0 0 0 0 -52 -56 -60 -70 -70 -72 -94 -96 -98 -110 -110 -114 -116 -126 -126 -136 -158 -160 -176 -178 -182 -188 -196 -200 -206 -208 -208 -222 -224 -228 -276 -278 -296 -302 -316 -318 -324 -334 -346 -350 -350 -358 -364 -368 -370 -378 -378 -378 -386 -404 -416 -416 -418 -420 -432 -448 -462 -480 -482 -490 -502 -514 -516 -520 -546 -546 -546 -550 -564 -570 -570 -572 -574 -580 -600 -602 -624 -626 -626 -634 -650 -658 -658 -662 -686 -712 -716 -720 -726 -730 -732 -756 -756 -770 -780 -790 -798 -802 -824 -836 -882 -894 -906 -914 -914 -932 -950 -952 -966 -968 -978 -978 -990 -990 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-997 -995 994 -981 -977 -975 -971 988 -969 -931 -929 986 968 -903 -903 956 -897 -895 -887 -883 948 -879 -871 -871 -865 -863 946 -863 -861 -861 944 -853 934 924 -853 914 914 -847 -845 910 -829 898 -819 890 -807 -807 888 880 -803 -797 880 874 868 -793 860 842 -791 -783 840 -771 838 -767 -765 832 826 -763 826 -759 814 -759 -753 -733 812 -733 -729 -727 -727 -723 804 -715 802 -715 -707 798 -693 -671 -669 -669 -665 792 -663 -663 -663 -663 790 -653 -643 -635 -615 778 774 770 752 -611 -587 -579 746 -569 -569 -561 740 -555 -555 -553 -539 740 -537 -523 728 -517 -513 -509 -505 -497 -497 -493 -483 728 -479 -479 -475 -475 -467 722 722 -439 -431 -429 -425 706 -413 -407 704 702 690 678 676 -407 674 -393 -385 -385 672 670 -385 664 -383 -377 -371 -367 -355 -353 -353 -351 -347 658 -345 656 -327 652 -325 -323 650 616 -319 -315 616 604 602 602 -315 596 594 -313 572 572 566 -311 562 -295 -287 -285 -285 -275 -273 -273 -271 -261 -259 -259 -253 -249 550 -239 542 538 530 -233 -231 -231 -231 526 -217 520 -203 518 -189 518 -187 -183 516 -177 510 508 506 -173 -171 -145 506 504 504 -143 -143 494 492 482 -133 -129 478 474 -129 -125 -113 -111 -99 -93 -91 -81 472 -81 -77 -75 -63 -53 -45 -39 468 462 -39 -39 -13 7 9 13 21 23 35 43 452 43 450 49 49 51 55 67 71 448 73 77 77 81 91 446 93 97 101 105 115 119 121 125 428 151 422 151 171 173 181 187 420 189 195 410 400 392 197 207 211 211 392 221 221 376 376 223 225 364 229 231 231 342 235 241 340 241 336 332 245 326 247 253 322 253 312 255 308 261 269 306 279 291 286 309 286 315 323 266 258 323 329 341 343 256 347 357 379 381 385 397 401 403 403 407 421 427 244 427 429 242 429 433 433 238 433 437 441 234 220 208 443 208 196 451 455 459 467 469 186 182 178 469 475 483 483 505 511 513 539 539 557 559 561 565 168 168 567 166 156 575 156 585 593 154 150 593 148 144 136 130 595 597 597 609 613 617 120 633 637 639 647 661 671 118 114 112 679 110 679 679 110 681 683 687 106 98 98 693 693 695 98 76 699 72 699 713 715 721 64 727 62 731 733 62 56 735 739 741 745 52 749 749 52 28 22 20 759 14 759 763 8 763 765 767 8 6 4 0 0 0 0 0 0 767 767 785 791 801 -2 803 805 -8 -22 819 -24 825 833 -40 839 845 -44 847 847 847 -60 847 865 -64 865 871 909 -84 913 913 915 -84 919 -108 923 -110 929 933 933 -112 939 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898 -819 890 -807 -807 888 880 -803 -797 880 874 868 -793 860 842 -791 -783 840 -771 838 -767 -765 832 826 -763 826 -759 814 -759 -753 -733 812 -733 -729 -727 -727 -723 804 -715 802 -715 -707 798 -693 -671 -669 -669 -665 792 -663 -663 -663 -663 790 -653 -643 -635 -615 778 774 770 752 -611 -587 -579 746 -569 -569 -561 740 -555 -555 -553 -539 740 -537 -523 728 -517 -513 -509 -505 -497 -497 -493 -483 728 -479 -479 -475 -475 -467 722 722 -439 -431 -429 -425 706 -413 -407 704 702 690 678 676 -407 674 -393 -385 -385 672 670 -385 664 -383 -377 -371 -367 -355 -353 -353 -351 -347 658 -345 656 -327 652 -325 -323 650 616 -319 -315 616 604 602 602 -315 596 594 -313 572 572 566 -311 562 -295 -287 -285 -285 -275 -273 -273 -271 -261 -259 -259 -253 -249 550 -239 542 538 530 -233 -231 -231 -231 526 -217 520 -203 518 -189 518 -187 -183 516 -177 510 508 506 -173 -171 -145 506 504 504 -143 -143 494 492 482 -133 -129 478 474 -129 -125 -113 -111 -99 -93 -91 -81 472 -81 -77 -75 -63 -53 -45 -39 468 462 -39 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649 649 651 651 226 653 675 679 224 685 689 220 689 689 697 214 705 705 206 707 709 711 715 725 200 735 735 198 737 741 196 196 749 753 196 753 759 194 771 777 777 787 789 178 799 803 811 813 176 174 815 815 158 154 819 827 827 833 841 845 847 847 154 851 851 859 154 861 861 863 867 154 875 154 885 887 891 154 895 154 895 907 909 913 915 154 917 148 921 923 136 931 130 937 130 118 949 957 957 961 112 963 110 110 971 979 102 979 98 98 92 88 985 987 84 84 76 66 56 46 42 42 42 40 28 24 14 0 0 0 0 -2 -6 -26 -26 -26 -34 -34 -42 -42 -42 -44 -52 -58 -92 -94 -98 -100 -108 -110 -120 -126 -126 -134 -142 -144 -146 -150 -154 -154 -154 -154 -156 -156 -158 -174 -176 -182 -196 -228 -252 -252 -260 -264 -266 -266 -278 -278 -282 -286 -290 -296 -304 -310 -312 -316 -320 -326 -330 -334 -340 -342 -346 -348 -352 -362 -364 -374 -378 -382 -386 -388 -390 -392 -396 -404 -406 -406 -412 -414 -418 -426 -428 -432 -438 -442 -450 -462 -464 -468 -468 -472 -476 -486 -490 -492 -518 -520 -526 -526 -532 -532 -534 -546 -546 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];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[994 -969 988 986 -957 -931 966 -889 -889 -883 -881 -877 -877 960 -873 914 -861 912 -847 -845 -841 -835 900 -805 -803 -793 -793 886 864 -785 -765 -765 -737 -713 -713 -701 -661 -655 -621 840 -619 -615 -599 832 -595 -567 -553 828 -541 -497 -467 -455 -429 -419 -415 -387 794 -377 792 -375 -371 -365 -337 -333 -331 -321 -285 780 -285 762 -271 -263 758 -259 -257 732 728 -249 -235 -231 -231 -189 726 -189 -181 -175 698 -153 -149 696 684 -127 672 -119 -115 652 -115 -113 644 -93 -91 608 -91 602 -77 -49 -45 594 -35 -5 562 -3 11 540 538 518 506 41 43 506 57 111 121 474 123 161 177 191 203 207 217 217 247 259 269 273 468 464 442 297 303 319 321 333 343 349 420 418 353 410 397 406 427 384 427 429 384 455 455 467 378 370 493 505 364 525 364 533 348 336 539 541 583 589 611 330 316 619 627 647 651 681 717 719 308 725 739 757 767 282 777 274 779 797 847 264 262 252 853 873 242 933 947 969 971 979 232 208 182 999 999 174 170 138 132 126 110 108 98 98 70 44 44 22 4 0 0 0 -2 -22 -58 -66 -74 -94 -116 -148 -158 -182 -210 -214 -222 -226 -238 -248 -252 -256 -286 -310 -320 -336 -342 -370 -388 -402 -402 -416 -440 -440 -458 -460 -460 -490 -504 -514 -528 -560 -572 -588 -596 -600 -616 -638 -642 -654 -660 -676 -684 -702 -706 -708 -720 -726 -742 -746 -766 -786 -812 -832 -840 -846 -864 -910 -912 -916 -948 -966 -982 -986 -992 ];\r\nvexp=[994 -969 988 986 -957 -931 966 -889 -889 -883 -881 -877 -877 960 -873 914 -861 912 -847 -845 -841 -835 900 -805 -803 -793 -793 886 864 -785 -765 -765 -737 -713 -713 -701 -661 -655 -621 840 -619 -615 -599 832 -595 -567 -553 828 -541 -497 -467 -455 -429 -419 -415 -387 794 -377 792 -375 -371 -365 -337 -333 -331 -321 -285 780 -285 762 -271 -263 758 -259 -257 732 728 -249 -235 -231 -231 -189 726 -189 -181 -175 698 -153 -149 696 684 -127 672 -119 -115 652 -115 -113 644 -93 -91 608 -91 602 -77 -49 -45 594 -35 -5 562 -3 11 540 538 518 506 41 43 506 57 111 121 474 123 161 177 191 203 207 217 217 247 259 269 273 468 464 442 297 303 319 321 333 343 349 420 418 353 410 397 406 427 384 427 429 384 455 455 467 378 370 493 505 364 525 364 533 348 336 539 541 583 589 611 330 316 619 627 647 651 681 717 719 308 725 739 757 767 282 777 274 779 797 847 264 262 252 853 873 242 933 947 969 971 979 232 208 182 999 999 174 170 138 132 126 110 108 98 98 70 44 44 22 4 0 0 0 -2 -22 -58 -66 -74 -94 -116 -148 -158 -182 -210 -214 -222 -226 -238 -248 -252 -256 -286 -310 -320 -336 -342 -370 -388 -402 -402 -416 -440 -440 -458 -460 -460 -490 -504 -514 -528 -560 -572 -588 -596 -600 -616 -638 -642 -654 -660 -676 -684 -702 -706 -708 -720 -726 -742 -746 -766 -786 -812 -832 -840 -846 -864 -910 -912 -916 -948 -966 -982 -986 -992 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-991 -989 998 -987 -983 -973 996 982 980 -971 978 -965 -959 974 -957 -951 -947 966 -941 966 966 962 -931 -931 -909 -903 -895 -893 -889 -885 -883 944 -883 936 -869 912 -845 896 894 -845 -837 -833 -829 886 882 -817 880 -803 872 -791 -791 -777 -769 -765 -759 -753 870 -743 -729 864 -717 864 854 -711 -707 850 -695 -689 -683 840 826 -665 -661 -659 812 798 -659 766 -657 760 -653 -637 756 -631 -627 -621 -611 748 -609 -605 -605 -601 -597 -589 -573 -567 -541 -539 -539 740 730 -539 -535 -507 -483 728 -475 -469 714 -455 -453 710 704 -451 -447 -433 -433 -431 -421 -417 -417 686 -405 682 -403 680 -399 678 -391 672 -387 670 668 -385 660 -381 -381 636 -377 -367 -363 -353 -331 626 618 -325 -303 616 -299 -297 -291 584 -281 -277 578 578 572 570 -245 -243 -239 -231 -223 -221 -209 570 -205 -201 -185 -183 -175 -165 -163 -159 -157 568 -147 564 -139 562 -125 548 -117 544 542 -103 -101 528 -95 524 -95 -79 -71 -71 -61 -49 520 -41 -37 520 518 -33 -27 502 -25 490 -21 482 474 -17 474 -17 -9 -7 -7 7 13 15 446 17 23 446 31 35 440 35 39 45 49 49 426 59 418 406 67 91 404 93 103 388 105 107 113 388 117 119 121 123 131 141 143 143 161 173 173 179 378 195 358 197 203 231 257 356 263 271 273 275 277 287 297 338 301 303 338 305 323 325 336 330 369 381 399 322 308 407 308 413 308 296 419 419 296 425 439 292 445 280 451 451 260 451 453 246 469 469 469 483 246 495 242 501 242 511 517 232 212 529 539 206 180 178 539 178 549 549 553 559 561 561 565 567 573 585 585 595 607 623 633 641 657 683 689 719 727 733 735 741 759 168 779 783 166 164 791 807 817 819 823 861 865 869 869 162 903 907 138 907 913 913 917 923 132 132 941 130 953 957 126 122 965 971 981 985 993 995 104 98 98 94 88 88 86 80 78 76 68 66 66 60 58 52 36 36 22 16 0 0 0 -14 -20 -22 -26 -28 -52 -54 -56 -58 -70 -70 -72 -76 -118 -126 -126 -140 -140 -142 -154 -154 -168 -172 -174 -182 -188 -196 -196 -206 -208 -220 -220 -222 -226 -236 -262 -286 -300 -308 -308 -322 -322 -336 -342 -346 -366 -396 -396 -404 -444 -446 -450 -462 -462 -466 -468 -468 -486 -486 -490 -498 -498 -506 -520 -532 -546 -548 -588 -594 -594 -596 -596 -604 -608 -612 -616 -616 -616 -622 -622 -626 -626 -656 -656 -656 -664 -672 -680 -682 -682 -714 -718 -744 -750 -750 -756 -770 -788 -800 -806 -814 -816 -850 -858 -858 -864 -868 -868 -870 -882 -884 -910 -924 -928 -932 -942 -946 -950 -952 -980 -986 -988 ];\r\nvexp=[-991 -989 998 -987 -983 -973 996 982 980 -971 978 -965 -959 974 -957 -951 -947 966 -941 966 966 962 -931 -931 -909 -903 -895 -893 -889 -885 -883 944 -883 936 -869 912 -845 896 894 -845 -837 -833 -829 886 882 -817 880 -803 872 -791 -791 -777 -769 -765 -759 -753 870 -743 -729 864 -717 864 854 -711 -707 850 -695 -689 -683 840 826 -665 -661 -659 812 798 -659 766 -657 760 -653 -637 756 -631 -627 -621 -611 748 -609 -605 -605 -601 -597 -589 -573 -567 -541 -539 -539 740 730 -539 -535 -507 -483 728 -475 -469 714 -455 -453 710 704 -451 -447 -433 -433 -431 -421 -417 -417 686 -405 682 -403 680 -399 678 -391 672 -387 670 668 -385 660 -381 -381 636 -377 -367 -363 -353 -331 626 618 -325 -303 616 -299 -297 -291 584 -281 -277 578 578 572 570 -245 -243 -239 -231 -223 -221 -209 570 -205 -201 -185 -183 -175 -165 -163 -159 -157 568 -147 564 -139 562 -125 548 -117 544 542 -103 -101 528 -95 524 -95 -79 -71 -71 -61 -49 520 -41 -37 520 518 -33 -27 502 -25 490 -21 482 474 -17 474 -17 -9 -7 -7 7 13 15 446 17 23 446 31 35 440 35 39 45 49 49 426 59 418 406 67 91 404 93 103 388 105 107 113 388 117 119 121 123 131 141 143 143 161 173 173 179 378 195 358 197 203 231 257 356 263 271 273 275 277 287 297 338 301 303 338 305 323 325 336 330 369 381 399 322 308 407 308 413 308 296 419 419 296 425 439 292 445 280 451 451 260 451 453 246 469 469 469 483 246 495 242 501 242 511 517 232 212 529 539 206 180 178 539 178 549 549 553 559 561 561 565 567 573 585 585 595 607 623 633 641 657 683 689 719 727 733 735 741 759 168 779 783 166 164 791 807 817 819 823 861 865 869 869 162 903 907 138 907 913 913 917 923 132 132 941 130 953 957 126 122 965 971 981 985 993 995 104 98 98 94 88 88 86 80 78 76 68 66 66 60 58 52 36 36 22 16 0 0 0 -14 -20 -22 -26 -28 -52 -54 -56 -58 -70 -70 -72 -76 -118 -126 -126 -140 -140 -142 -154 -154 -168 -172 -174 -182 -188 -196 -196 -206 -208 -220 -220 -222 -226 -236 -262 -286 -300 -308 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315 966 999 -138 -449 -869 636 951 -266 -417 -127 -429 385 -406 -395 -75 -802 -929 -377 -290 882 -554 -529 233 -979 830 330 -737 845 309 670 -415 341 339 479 -550 -139 -47 -357 627 351 320 39 -291 182 -956 882 455 -308 781 -151 -349 33 -506 149 -325 315 -895 273 943 143 -357 -968 -923 163 526 446 -505 -497 59 -580 -89 -161 -39 777 671 832 -939 -185 263 -473 -321 514 -351 -276 294 231 699 -429 899 29 -678 -402 -958 -88 938 -80 285 -553 203 925 -790 471 -684 271 420 -559 -15 -582 -81 22 600 -903 455 -285 914 -382 -692 319 -986 363 -23 795 253 -257 -467 211 -908 -559 845 -478 687 -515 387 134 931 203 -7 303 572 737 669 945 -547 379 911 -117 882 704 454 -269 -488 756 -567 -125 -59 715 265 147 429 243 574 -197 -523 -462 -987 937 -305 347 394 462 373 517 -673 640 532 -720 32 185 -821 -749 -727 106 308 -572 721 -34 -803 -613 537 836 -489 -658 168 331 -368 871 -602 399 992 729 -325 -173 -765 -793 -901 -728 -109 -705 -40 -825 972 -46 884 76 471 -814 -753 -169 837 -499 381 178 -363 509 -847 -855 359 65 149 -481 -468 89 417 814 -358 -357 5 91 -924 -738 765 -15 -881 -634 -303 -769 -105 225 -245 -109 -437 -165 625 704 964 539 659 -357 -373 889 173 825 -963 -627 -529 -700 537 851 6 273 -637 -840 -576 -343 -992 9 145 551 -447 870 286 88 -850 440 661 -729 -279 556 588 870 -110 -723 429 -759 -616 361 815 60 861 -522 -29 455 -91 -917 -781 -469 -89 406 -231 -569 289 -84 -847 -199 912 64 748 389 781 -224 -525 -504 287 -605 559 722 -775 -879 991 689 721 -504 -362 988 99 949 202 -931 -920 -284 -213 616 581 847 495 363 -418 608 49 -832 157 763 -203 -581 -689 -632 -231 -91 376 -309 -352 672 253 -301 418 885 85 321 812 501 -79 366 -249 -175 65 737 -849 -453 871 -468 868 919 952 425 351 -935 -301 -595 372 -155 -21 913 50 597 548 825 299 465 -501 249 -583 734 -983 -224 19 -218 476 -364 392 211 580 717 557 942 255 972 -88 -420 -763 -438 -721 351 -289 661 -741 904 -949 -954 -103 858 155 -251 -245 429 -149 -752 657 -781 -583 -224 -202 -771 525 442 978 -13 681 430 198 -623 937 -897 -910 -155 708 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974 972 -913 -903 972 -901 972 968 -897 -895 -883 966 -881 -879 -871 966 964 960 -869 952 -857 -855 -855 -853 946 -849 -847 -847 -845 942 938 -845 938 -839 -825 932 -825 926 920 -821 -803 -793 -781 -781 918 914 912 912 -775 912 -775 910 -775 910 -773 -771 -769 -765 -763 904 898 -759 890 -753 -751 888 -749 -741 -739 -737 884 -737 -729 -727 -723 882 -721 -715 882 882 -705 -703 -689 882 872 -689 870 -689 870 -681 868 -673 -673 868 -663 -637 -631 -627 858 -627 852 -623 -613 848 -605 846 -595 -589 -589 -585 836 -583 -583 834 -581 -569 832 830 820 -569 -567 -559 814 812 -559 -553 -547 806 -537 -529 -529 -525 800 -523 -515 -509 -507 -505 796 -503 -501 786 782 774 -499 760 -499 -497 -495 -489 756 -481 -473 -469 -467 -463 -459 -453 -451 752 -449 -447 748 734 -445 -437 -429 728 -429 -429 -429 -421 -417 724 -415 -411 -403 -395 -385 722 -383 712 708 -383 -377 -377 -373 -373 704 704 704 704 702 700 -367 -363 -357 -357 698 -357 692 -357 686 -357 -351 676 -349 676 672 -343 -341 -335 670 668 650 -335 642 -327 -325 -325 -325 -321 -313 -313 640 -309 -307 636 -305 -305 -303 634 -303 -301 -301 -295 630 -291 -289 -285 -285 -279 -279 -269 630 624 622 -257 616 616 -255 -251 -249 -247 -245 -245 -243 -235 616 -231 -231 608 -231 -231 -217 -213 602 600 -203 -203 -199 592 588 584 580 -199 -197 -197 -187 580 580 574 -185 572 -181 -181 -179 570 -175 564 560 -175 556 -173 552 -169 548 -165 -161 -159 -155 -155 -151 546 -149 -139 546 -139 542 536 532 530 -127 528 -125 -117 -109 -109 -109 526 -105 -103 -91 -91 -91 -89 -89 -81 520 -79 -77 514 510 -75 -59 -47 504 504 -39 -29 -23 500 -23 -21 -19 -15 -15 -13 -9 -7 3 490 482 5 5 7 9 11 15 19 19 29 29 476 33 37 470 39 49 468 468 59 462 65 65 65 71 462 462 460 456 454 85 89 89 446 442 442 442 91 99 99 440 107 119 436 119 434 123 143 145 147 149 149 153 430 155 157 163 430 169 171 428 426 422 173 181 420 185 420 187 203 203 418 211 211 211 217 225 406 402 394 227 231 394 233 392 376 233 374 243 249 251 253 374 372 253 370 255 259 259 263 265 368 271 273 366 273 352 346 273 273 346 277 283 285 344 287 289 330 295 299 303 309 315 315 317 326 320 319 316 321 325 331 335 339 314 341 347 347 312 351 308 351 351 359 361 363 363 308 373 302 379 298 294 286 280 381 276 385 387 252 389 252 252 252 393 242 399 403 403 415 417 242 425 240 429 238 429 429 437 439 443 234 449 455 455 224 224 455 459 216 216 461 465 214 210 471 471 473 202 479 198 487 198 495 501 190 507 188 188 509 186 517 182 180 178 523 525 533 178 537 537 168 539 158 539 543 150 136 134 112 545 551 553 106 104 555 557 102 559 559 567 581 597 607 98 98 623 96 625 627 631 633 651 651 96 92 88 86 657 659 84 661 661 84 80 669 76 671 66 64 671 673 60 679 681 687 689 693 699 60 715 717 56 56 50 717 721 721 46 38 721 729 735 737 737 741 32 741 747 755 759 763 32 765 24 777 22 22 781 781 14 795 801 809 813 14 815 821 825 12 825 6 0 837 845 0 -2 -24 845 847 851 -26 857 861 -28 871 -28 -34 871 -40 885 889 889 897 897 899 905 911 -40 -44 -46 -70 913 913 919 -72 -74 923 -80 -82 925 -82 927 931 937 937 943 -84 945 945 -84 949 951 955 955 955 965 975 981 -86 983 -88 991 993 999 -88 -90 -104 -104 -110 -112 -132 -138 -138 -138 -146 -154 -156 -160 -178 -180 -182 -196 -202 -206 -210 -218 -220 -224 -224 -224 -224 -224 -234 -242 -246 -248 -252 -254 -256 -256 -266 -266 -270 -274 -276 -280 -282 -284 -284 -286 -288 -290 -290 -294 -294 -294 -300 -308 -308 -344 -346 -350 -350 -352 -352 -358 -362 -364 -364 -366 -368 -374 -376 -380 -382 -386 -394 -402 -406 -412 -416 -418 -418 -418 -420 -428 -438 -438 -438 -440 -444 -448 -450 -462 -462 -466 -468 -468 -472 -476 -478 -488 -504 -504 -504 -504 -506 -506 -512 -514 -514 -518 -522 -522 -528 -540 -544 -546 -550 -554 -554 -568 -572 -572 -574 -576 -580 -580 -582 -594 -598 -602 -602 -608 -610 -616 -616 -616 -618 -628 -628 -628 -630 -632 -634 -634 -636 -638 -640 -658 -660 -664 -668 -672 -672 -676 -678 -682 -682 -684 -684 -688 -690 -690 -692 -696 -700 -700 -702 -704 -716 -720 -724 -726 -728 -728 -728 -728 -730 -738 -740 -744 -746 -752 -754 -766 -768 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];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2013-09-26T04:17:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-26T04:12:00.000Z","updated_at":"2026-01-22T14:04:54.000Z","published_at":"2013-09-26T04:14:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2014 China Sorting\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Subset of cases.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e V a vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV= [-5 -12 87 2 88 20 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVout=[-5 88 11 20 2 -12 87]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContest Performance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2736,"title":"Pernicious Anniversary Problem","description":"Since Cody is 5 years old, it's pernicious. A \u003chttp://rosettacode.org/wiki/Pernicious_numbers Pernicious number\u003e is an integer whose population count is a prime. Check if the given number is pernicious.","description_html":"\u003cp\u003eSince Cody is 5 years old, it's pernicious. A \u003ca href = \"http://rosettacode.org/wiki/Pernicious_numbers\"\u003ePernicious number\u003c/a\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/p\u003e","function_template":"function y = isPernicious(x)\r\n y = false;\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2^randi(16);\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 17;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 18;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 61;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2115;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2114;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2017;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":1,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":837,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":34,"created_at":"2014-12-08T08:48:45.000Z","updated_at":"2026-03-18T13:27:13.000Z","published_at":"2017-10-16T01:45:06.000Z","restored_at":"2017-10-25T14:37:50.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince Cody is 5 years old, it's pernicious. A\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://rosettacode.org/wiki/Pernicious_numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePernicious number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42837,"title":"Increasing sub-sequence (Level 1)","description":"Given a vector, v, of real numbers, return a positive integer, n, representing the longest contiguous increasing sub-sequence contained in v.\r\n\r\nExample:\r\n\r\nv = [2 18 9 *6 11 20 25* 3]\r\n\r\nn = 4","description_html":"\u003cp\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest contiguous increasing sub-sequence contained in v.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ev = [2 18 9 \u003cb\u003e6 11 20 25\u003c/b\u003e 3]\u003c/p\u003e\u003cp\u003en = 4\u003c/p\u003e","function_template":"function n = subseq(v)\r\n n = numel(v);\r\nend","test_suite":"%%\r\nv = [2 18 9 6 11 20 25 3];\r\nn_correct = 4;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [-6 -18 -9 -4 -11 -20 -25 -3];\r\nn_correct = 3;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = zeros(1,30);\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [exp(-1) sqrt(2) sqrt(3) exp(1) pi exp(2)];\r\nn_correct = 6;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = 100:-10:-100;\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [0:5 1:7 3:9 2:8];\r\nn_correct = 7;\r\nassert(isequal(subseq(v),n_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-28T09:13:07.000Z","updated_at":"2025-10-06T19:31:12.000Z","published_at":"2016-04-28T09:13:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest contiguous increasing sub-sequence contained in v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = [2 18 9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6 11 20 25\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1893,"title":"GJam 2014 China Rd A: Library Sorting (Small)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2924486/dashboard#s=p2 GJam 2014 China Sorting\u003e. \r\n\r\nThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations. \r\n\r\n*Input:* V a vector\r\n\r\n*Output:* Vout a sorted vector Odds Increasing/Evens Increasing\r\n\r\n*Example:*\r\n\r\nV= [-5 -12 87 2 88 20 11]\r\n\r\nVout=[-5 88 11 20 2 -12 87]\r\n\r\n\r\n*Contest Performance:* Best Time to Complete: \u003c 10 minutes\r\n","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\"\u003eGJam 2014 China Sorting\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e V a vector\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eV= [-5 -12 87 2 88 20 11]\u003c/p\u003e\u003cp\u003eVout=[-5 88 11 20 2 -12 87]\u003c/p\u003e\u003cp\u003e\u003cb\u003eContest Performance:\u003c/b\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/p\u003e","function_template":"function vout=Sort_CH(v)\r\n vout=v;\r\nend","test_suite":"%%\r\ntic\r\nv=[1 ];\r\nvexp=[1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[2 1 ];\r\nvexp=[2 1 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 ];\r\nvexp=[1 2 3 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[1 2 3 4 5 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[5 2 3 4 1 ];\r\nvexp=[1 4 3 2 5 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 -87 -85 -83 -71 -71 98 96 -67 -63 -59 -53 -47 -41 96 -41 82 -37 -29 82 -25 -25 80 -21 -13 -11 5 76 72 72 66 66 66 9 60 15 31 35 56 52 52 46 42 39 45 42 40 36 45 30 24 18 51 18 12 53 0 63 -6 65 -10 -12 67 69 79 85 85 -14 89 -16 -22 89 -24 91 -24 -26 -30 -38 -38 -38 -42 -44 -58 -58 -60 -62 -66 -68 -70 -70 -82 -82 -86 -86 -86 -94 -100 ];\r\nvexp=[-87 -87 -85 -83 -71 -71 98 96 -67 -63 -59 -53 -47 -41 96 -41 82 -37 -29 82 -25 -25 80 -21 -13 -11 5 76 72 72 66 66 66 9 60 15 31 35 56 52 52 46 42 39 45 42 40 36 45 30 24 18 51 18 12 53 0 63 -6 65 -10 -12 67 69 79 85 85 -14 89 -16 -22 89 -24 91 -24 -26 -30 -38 -38 -38 -42 -44 -58 -58 -60 -62 -66 -68 -70 -70 -82 -82 -86 -86 -86 -94 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-95 98 -81 -55 90 -29 -19 35 37 75 79 85 93 97 56 54 14 14 0 -14 -22 -34 -38 -46 -62 -90 -98 ];\r\nvexp=[-95 98 -81 -55 90 -29 -19 35 37 75 79 85 93 97 56 54 14 14 0 -14 -22 -34 -38 -46 -62 -90 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-89 -75 -73 -65 86 86 68 66 -41 -37 -25 56 5 21 25 52 36 26 14 27 29 35 45 6 51 63 87 93 -22 95 -26 -48 -54 -70 95 -86 -92 -96 ];\r\nvexp=[-89 -75 -73 -65 86 86 68 66 -41 -37 -25 56 5 21 25 52 36 26 14 27 29 35 45 6 51 63 87 93 -22 95 -26 -48 -54 -70 95 -86 -92 -96 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[76 -7 ];\r\nvexp=[76 -7 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-93 96 -91 86 -87 -87 -67 -53 68 30 -33 0 -33 -13 1 0 3 -10 3 -10 -16 19 23 45 51 -18 53 -30 -36 -72 79 -82 -96 83 91 ];\r\nvexp=[-93 96 -91 86 -87 -87 -67 -53 68 30 -33 0 -33 -13 1 0 3 -10 3 -10 -16 19 23 45 51 -18 53 -30 -36 -72 79 -82 -96 83 91 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 100 96 -81 86 -79 -79 -77 -73 -69 -69 -65 82 -59 -59 70 70 -57 -49 -47 70 -43 -41 54 -35 -31 -31 -29 -25 -17 -13 -5 50 -5 -3 7 21 25 46 27 27 44 31 33 35 37 44 49 42 38 49 51 34 69 34 75 83 20 85 87 91 91 14 12 10 6 0 0 0 -8 -8 -20 -24 -26 -34 -36 -40 -52 -56 -60 -66 -68 -68 -72 -72 -80 -84 -84 -90 -90 ];\r\nvexp=[-87 100 96 -81 86 -79 -79 -77 -73 -69 -69 -65 82 -59 -59 70 70 -57 -49 -47 70 -43 -41 54 -35 -31 -31 -29 -25 -17 -13 -5 50 -5 -3 7 21 25 46 27 27 44 31 33 35 37 44 49 42 38 49 51 34 69 34 75 83 20 85 87 91 91 14 12 10 6 0 0 0 -8 -8 -20 -24 -26 -34 -36 -40 -52 -56 -60 -66 -68 -68 -72 -72 -80 -84 -84 -90 -90 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 100 -81 -75 96 86 -71 -71 86 -33 -27 -25 82 -21 76 -11 68 5 7 9 13 68 15 25 41 41 51 61 56 61 56 67 54 67 48 83 89 91 99 34 30 28 16 16 10 10 4 0 0 0 0 -24 -26 -26 -34 -48 -50 -62 -66 -92 -100 ];\r\nvexp=[-87 100 -81 -75 96 86 -71 -71 86 -33 -27 -25 82 -21 76 -11 68 5 7 9 13 68 15 25 41 41 51 61 56 61 56 67 54 67 48 83 89 91 99 34 30 28 16 16 10 10 4 0 0 0 0 -24 -26 -26 -34 -48 -50 -62 -66 -92 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-93 -89 -87 88 -85 -75 -65 -63 -61 -59 -49 84 -39 -37 80 80 -37 -25 -11 -7 78 -5 78 72 3 5 9 58 11 50 46 23 29 29 31 35 44 37 49 67 71 44 40 30 71 30 28 24 75 75 79 83 18 97 99 6 6 2 0 -4 -8 -10 -16 -18 -30 -32 -34 -36 -38 -46 -46 -48 -48 -52 -54 -56 -66 -68 -88 -90 -100 -100 -100 ];\r\nvexp=[-93 -89 -87 88 -85 -75 -65 -63 -61 -59 -49 84 -39 -37 80 80 -37 -25 -11 -7 78 -5 78 72 3 5 9 58 11 50 46 23 29 29 31 35 44 37 49 67 71 44 40 30 71 30 28 24 75 75 79 83 18 97 99 6 6 2 0 -4 -8 -10 -16 -18 -30 -32 -34 -36 -38 -46 -46 -48 -48 -52 -54 -56 -66 -68 -88 -90 -100 -100 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[90 -89 90 74 -87 62 -83 -79 58 -77 -75 -75 -63 52 52 -59 46 42 -49 -39 -31 36 12 -25 6 -13 -11 5 9 17 23 29 39 -2 -8 -10 47 63 -28 -54 -70 -74 -78 63 65 83 -82 -84 91 97 97 ];\r\nvexp=[90 -89 90 74 -87 62 -83 -79 58 -77 -75 -75 -63 52 52 -59 46 42 -49 -39 -31 36 12 -25 6 -13 -11 5 9 17 23 29 39 -2 -8 -10 47 63 -28 -54 -70 -74 -78 63 65 83 -82 -84 91 97 97 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-97 88 -93 74 70 46 38 36 -91 -85 -83 -77 -67 -63 -55 34 -45 32 -37 16 0 0 -23 -21 -2 -4 5 13 27 -10 -32 -38 -38 -50 39 -56 45 49 -56 77 -56 87 95 97 -62 -62 -68 -68 -72 -80 -94 ];\r\nvexp=[-97 88 -93 74 70 46 38 36 -91 -85 -83 -77 -67 -63 -55 34 -45 32 -37 16 0 0 -23 -21 -2 -4 5 13 27 -10 -32 -38 -38 -50 39 -56 45 49 -56 77 -56 87 95 97 -62 -62 -68 -68 -72 -80 -94 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[81 29 29 -71 -70 16 -70 -93 25 97 51 3 -8 39 -83 97 98 -86 -53 69 58 86 19 75 9 87 -84 66 75 82 85 -87 53 7 65 99 -93 59 -74 4 1 -15 -22 59 -35 -15 51 -10 -27 -98 60 -17 37 29 -98 69 83 9 51 13 -12 -13 50 -39 45 5 -34 75 -84 15 -91 18 -97 -8 0 -44 34 79 -13 -74 -92 80 -84 -92 -32 -46 -26 46 -16 -32 -72 16 84 -46 22 -32 84 58 28 -60 ];\r\nvexp=[-97 -93 -93 -91 98 86 84 -87 -83 -71 -53 -39 84 -35 -27 -17 82 80 -15 -15 66 60 -13 -13 1 3 58 58 5 50 7 9 9 13 15 19 25 29 46 34 29 29 28 37 39 45 51 22 51 18 16 51 53 59 16 59 65 69 69 75 4 75 0 75 79 81 -8 83 -8 85 87 -10 97 -12 -16 -22 -26 97 99 -32 -32 -32 -34 -44 -46 -46 -60 -70 -70 -72 -74 -74 -84 -84 -84 -86 -92 -92 -98 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[10 50 52 3 -29 51 29 -89 55 -34 -77 -41 65 7 -89 0 -44 -98 61 -21 11 -57 -10 95 -12 -25 91 28 90 -49 -57 97 57 -47 33 -59 7 -39 55 91 -89 -41 -7 -18 -61 -93 78 -57 97 45 44 -59 5 38 9 28 -38 11 -36 -92 15 -70 44 -84 18 -24 38 20 -54 0 2 44 28 12 42 -22 74 6 -72 -52 34 -50 30 -44 -6 -42 98 -96 42 38 64 92 -36 92 -90 2 -6 -44 -98 -2 ];\r\nvexp=[98 92 92 -93 -89 -89 -89 -77 -61 90 -59 -59 -57 -57 -57 78 74 64 -49 -47 -41 -41 52 -39 50 -29 -25 44 44 -21 -7 3 5 7 7 9 11 11 15 29 33 45 51 44 55 55 42 57 61 65 42 91 91 38 95 38 38 97 34 30 97 28 28 28 20 18 12 10 6 2 2 0 0 -2 -6 -6 -10 -12 -18 -22 -24 -34 -36 -36 -38 -42 -44 -44 -44 -50 -52 -54 -70 -72 -84 -90 -92 -96 -98 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[34 46 -93 78 -26 11 77 26 47 73 75 53 -89 -52 71 19 -52 -47 16 -19 74 49 21 1 -33 -89 5 -74 67 -55 88 -85 1 -41 93 53 -97 61 -71 -85 77 -45 -1 0 74 95 67 -65 -27 -2 -44 -8 -37 27 36 -58 71 -8 -95 43 17 -19 25 -5 -10 42 10 -64 27 94 41 -69 37 81 -97 -50 -54 66 -22 40 -62 90 -70 40 48 48 52 48 20 98 -42 92 88 40 36 -28 -10 -44 -52 96 ];\r\nvexp=[98 96 -97 94 92 -97 -95 90 -93 -89 -89 -85 -85 88 -71 -69 88 -65 78 -55 74 -47 -45 -41 -37 -33 -27 74 -19 -19 66 -5 -1 1 1 5 11 17 19 21 25 27 27 52 48 37 41 43 47 48 48 46 49 53 42 40 53 40 61 67 67 71 71 73 40 36 36 34 75 26 77 77 81 93 95 20 16 10 0 -2 -8 -8 -10 -10 -22 -26 -28 -42 -44 -44 -50 -52 -52 -52 -54 -58 -62 -64 -70 -74 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-27 ];\r\nvexp=[-27 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[53 75 55 -92 23 -19 83 -70 95 43 -57 1 -11 -9 42 -98 -30 -35 -35 94 -95 -43 -11 -44 96 53 23 -80 -77 -32 -34 45 -16 -2 -77 56 -92 0 -15 38 36 4 -18 72 -84 88 48 58 82 -4 88 -62 -10 -30 10 -100 22 0 -12 -40 -48 -74 ];\r\nvexp=[-95 -77 -77 96 -57 -43 -35 94 -35 -19 -15 -11 -11 -9 88 88 82 1 23 72 23 43 45 58 56 53 53 48 55 42 38 75 36 22 83 10 4 0 95 0 -2 -4 -10 -12 -16 -18 -30 -30 -32 -34 -40 -44 -48 -62 -70 -74 -80 -84 -92 -92 -98 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-87 63 -79 74 66 5 -51 -9 69 -58 -23 77 -75 -71 91 0 -40 41 -79 32 27 90 66 -56 100 -48 -80 14 -24 ];\r\nvexp=[-87 -79 -79 100 90 -75 -71 -51 -23 74 -9 5 27 41 63 66 66 69 77 32 91 14 0 -24 -40 -48 -56 -58 -80 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[91 34 34 -92 -34 42 99 51 0 54 17 -51 -31 -45 35 -33 92 7 -33 -45 0 -15 76 58 58 100 85 -68 5 -20 -13 83 -39 89 55 89 -90 84 -40 20 90 54 -84 -90 38 -100 60 64 54 32 -30 86 -60 90 -46 -58 -50 ];\r\nvexp=[-51 100 92 90 90 86 -45 -45 84 76 -39 -33 -33 -31 -15 -13 64 5 7 17 60 35 58 58 54 54 51 54 55 42 83 85 89 89 91 99 38 34 34 32 20 0 0 -20 -30 -34 -40 -46 -50 -58 -60 -68 -84 -90 -90 -92 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-41 25 30 -41 20 51 -75 -72 45 -73 75 -77 60 -79 -45 80 19 49 -25 -99 -16 71 55 -79 -35 31 -66 61 -19 -45 -55 -34 73 -55 17 -29 -41 65 -93 51 -58 62 99 73 59 -66 83 -95 -23 62 -82 -81 -31 -33 -9 -41 1 83 36 92 82 80 0 10 78 38 70 0 -52 4 -56 88 -92 -14 56 -6 -74 -90 92 96 86 96 -88 ];\r\nvexp=[-99 -95 96 -93 96 -81 -79 92 -79 -77 -75 -73 92 -55 -55 88 -45 -45 -41 -41 86 -41 -41 -35 -33 -31 82 -29 -25 -23 -19 80 -9 1 17 19 25 31 45 49 80 78 51 51 55 70 59 61 65 62 62 71 73 73 75 83 83 99 60 56 38 36 30 20 10 4 0 0 -6 -14 -16 -34 -52 -56 -58 -66 -66 -72 -74 -82 -88 -90 -92 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-55 93 -57 -68 25 48 -100 75 11 -82 -60 64 74 19 11 -87 -56 -10 45 74 -21 -5 1 12 55 66 -72 73 37 85 -97 -80 51 44 55 -54 -15 -79 32 -93 1 23 -77 -86 90 -71 82 4 14 -100 55 -51 33 -60 65 -30 -34 -37 -75 75 90 33 -35 38 -97 -72 49 4 24 42 88 -60 -78 -68 0 48 -44 -56 24 -12 -48 -78 100 68 -32 -58 24 -44 94 ];\r\nvexp=[-97 -97 -93 100 -87 94 90 -79 -77 90 88 82 74 -75 -71 -57 74 68 -55 66 -51 -37 -35 64 -21 48 48 -15 -5 1 1 44 11 42 11 38 19 23 32 25 33 33 37 24 24 45 24 14 12 4 49 51 55 4 55 0 -10 55 65 73 -12 75 75 -30 85 -32 93 -34 -44 -44 -48 -54 -56 -56 -58 -60 -60 -60 -68 -68 -72 -72 -78 -78 -80 -82 -86 -100 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-41 97 83 0 -33 87 29 18 21 30 90 4 -10 -56 -66 79 -25 55 -40 -55 1 1 0 85 -66 -15 36 -68 -100 65 -8 -77 64 -47 -60 -96 83 -67 12 -85 11 24 -63 -50 17 -60 ];\r\nvexp=[-85 -77 -67 90 -63 -55 -47 64 -41 36 30 24 18 12 4 -33 -25 -15 0 1 1 11 0 17 -8 21 -10 -40 -50 29 -56 55 -60 65 -60 -66 79 83 -66 83 85 -68 87 -96 97 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-75 77 13 57 62 43 -9 13 -61 -37 -19 49 -1 65 -53 -87 -40 -73 -33 80 -11 15 73 -42 -58 -20 85 -97 -57 22 -46 -60 8 62 30 -84 66 40 58 -44 -100 ];\r\nvexp=[-97 -87 -75 -73 80 -61 -57 -53 -37 -33 -19 -11 -9 -1 13 13 66 15 43 62 49 57 65 62 58 40 73 77 85 30 22 8 -20 -40 -42 -44 -46 -58 -60 -84 -100 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[80 30 85 -54 -87 -32 47 33 57 -57 -64 50 67 -84 58 -79 37 -39 77 65 55 26 -58 47 -24 50 -34 72 65 30 38 -57 -49 13 -81 -3 -90 73 -69 91 -38 -49 -52 87 81 -70 51 -98 82 80 0 96 -68 -34 -54 -96 ];\r\nvexp=[96 82 -87 80 -81 80 -79 -69 -57 -57 72 58 -49 50 50 -49 -39 -3 13 33 37 38 30 47 30 26 0 -24 47 -32 -34 51 55 57 65 65 -34 67 73 77 -38 81 -52 85 87 -54 91 -54 -58 -64 -68 -70 -84 -90 -96 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[45 7 -49 57 7 -11 -7 53 -83 99 -90 9 87 100 16 -58 45 33 -98 30 -58 -50 -29 15 -66 76 -86 58 4 -82 ];\r\nvexp=[-83 -49 -29 -11 -7 7 7 9 15 33 100 45 45 76 58 30 53 57 16 4 -50 -58 87 99 -58 -66 -82 -86 -90 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[-13 20 -29 34 47 -38 -55 -25 37 41 -87 47 31 -63 -27 -68 -35 32 77 11 -7 -91 -67 -32 59 41 -11 -81 10 96 -50 -11 74 0 -42 -22 92 -72 46 0 0 -80 78 -32 58 4 24 -22 -56 -34 60 ];\r\nvexp=[-91 96 -87 92 -81 78 -67 -63 -55 -35 -29 -27 -25 -13 -11 74 -11 60 -7 11 31 37 41 58 41 47 47 59 46 34 32 77 24 20 10 4 0 0 0 -22 -22 -32 -32 -34 -38 -42 -50 -56 -68 -72 -80 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\n%%\r\nv=[35 69 33 35 -7 -54 -89 95 -95 -72 2 42 -89 -10 17 -65 -99 -43 27 95 71 61 -5 -95 -82 21 47 79 -59 52 -44 -10 -19 53 35 -92 -35 -61 -95 -43 35 -98 95 -2 -19 66 89 -54 32 -18 36 72 -64 -10 -88 -50 -8 38 88 -50 ];\r\nvexp=[-99 -95 -95 -95 -89 88 -89 -65 -61 72 66 52 -59 42 -43 -43 -35 -19 -19 -7 -5 17 21 27 38 33 35 35 35 36 32 2 35 47 53 -2 61 69 71 79 89 -8 95 -10 95 -10 95 -10 -18 -44 -50 -50 -54 -54 -64 -72 -82 -88 -92 -98 ];\r\nvout=Sort_CH(v);\r\nassert(isequal(vout,vexp))\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-26T03:58:52.000Z","updated_at":"2026-03-11T15:29:23.000Z","published_at":"2013-09-26T04:09:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2924486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2014 China Sorting\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to take a vector of Odd/Even values; Sort Odd Values Increasing and place into original Odd locations; Sort Even Values Decreasing and place into original Even locations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e V a vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Vout a sorted vector Odds Increasing/Evens Increasing\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV= [-5 -12 87 2 88 20 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVout=[-5 88 11 20 2 -12 87]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContest Performance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Time to Complete: \u0026lt; 10 minutes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":566,"title":"Sum of first n terms of a harmonic progression","description":"Given inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 21px; vertical-align: baseline; perspective-origin: 332px 21px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = harmonicSum(a,d,n)\r\n s=0;\r\nend","test_suite":"%%\r\na=1;d=1;n=1;\r\ny_correct = 1;\r\nassert(isequal(harmonicSum(a,d,n),y_correct));\r\n\r\n%%\r\na=2;d=2;n=5;\r\ny_correct = round(3.5746,4);\r\nassert(isequal(round(harmonicSum(a,d,n),4),y_correct));\r\n\r\n%%\r\na=4;d=5;n=2;\r\ny_correct = round(4.6667,4);\r\nassert(isequal(round(harmonicSum(a,d,n),4),y_correct));","published":true,"deleted":false,"likes_count":3,"comments_count":14,"created_by":2974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":501,"test_suite_updated_at":"2020-09-29T02:43:20.000Z","rescore_all_solutions":false,"group_id":27,"created_at":"2012-04-08T16:38:19.000Z","updated_at":"2026-04-01T16:06:03.000Z","published_at":"2012-04-08T18:58:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44523,"title":"Pattern Sum","description":"Write a function which receives two single digit positive integers, (k and m) as parameters and calculates the total sum as: \r\nk + kk + kkk + .... (the last number in the sequence should have m digits) \r\nFor example, if the two integers are:\r\n(4, 5).\r\nYour function should return the total sum of: \r\n4 + 44 + 444 + 4444 + 44444.\r\nNotice the last number in this sequence has 5 digits. The return value should be 49380.","description_html":"\u003cp\u003eWrite a function which receives two single digit positive integers, (k and m) as parameters and calculates the total sum as: \r\nk + kk + kkk + .... (the last number in the sequence should have m digits) \r\nFor example, if the two integers are:\r\n(4, 5).\r\nYour function should return the total sum of: \r\n4 + 44 + 444 + 4444 + 44444.\r\nNotice the last number in this sequence has 5 digits. The return value should be 49380.\u003c/p\u003e","function_template":"function y = pattern_sum(a,b)\r\n \r\nend","test_suite":"%%\r\na = 4;\r\nb = 5;\r\ny_correct = 49380;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 7;\r\nb = 4;\r\ny_correct = 8638;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 5;\r\nb = 3;\r\ny_correct = 615;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 1;\r\nb = 1;\r\ny_correct = 1;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 2;\r\nb = 2;\r\ny_correct = 24;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 9;\r\nb = 9;\r\ny_correct = 1111111101;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 0;\r\nb = 0;\r\ny_correct = 0;\r\nassert(isequal(pattern_sum(a,b),y_correct))\r\n\r\n%%\r\na = 3;\r\nb = 8;\r\ny_correct = 37037034;\r\nassert(isequal(pattern_sum(a,b),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":181342,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":237,"test_suite_updated_at":"2018-07-13T17:24:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-02-15T01:05:11.000Z","updated_at":"2026-03-24T20:17:24.000Z","published_at":"2018-02-15T01:18:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function which receives two single digit positive integers, (k and m) as parameters and calculates the total sum as: k + kk + kkk + .... (the last number in the sequence should have m digits) For example, if the two integers are: (4, 5). Your function should return the total sum of: 4 + 44 + 444 + 4444 + 44444. Notice the last number in this sequence has 5 digits. The return value should be 49380.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42839,"title":"Identify the sequence","description":"Given a row vector, x, return 1 if it is an arithmetic series, or 2 if it is a geometric series. If it is neither, return 0.\r\n\r\nExample 1:\r\n\r\nx = 1:8\r\n\r\ny = 1\r\n\r\nExample 2:\r\n\r\nx = 2^(1:8)\r\n\r\ny = 2\r\n\r\nExample 3:\r\n\r\nx = [1 1 2 3 5 8 13 21 34]\r\n\r\ny = 0","description_html":"\u003cp\u003eGiven a row vector, x, return 1 if it is an arithmetic series, or 2 if it is a geometric series. If it is neither, return 0.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003ex = 1:8\u003c/p\u003e\u003cp\u003ey = 1\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003ex = 2^(1:8)\u003c/p\u003e\u003cp\u003ey = 2\u003c/p\u003e\u003cp\u003eExample 3:\u003c/p\u003e\u003cp\u003ex = [1 1 2 3 5 8 13 21 34]\u003c/p\u003e\u003cp\u003ey = 0\u003c/p\u003e","function_template":"function y = stype(x)\r\n y = -1;\r\nend","test_suite":"%%\r\nx = 1:8;\r\ny_correct = 1;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = 2.^(1:8);\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [1 1 2 3 5 8 13 21 34];\r\ny_correct = 0;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = ones(1,80);\r\ny_correct1 = 1;\r\ny_correct2 = 2;\r\nassert(isequal(stype(x),y_correct1)|isequal(stype(x),y_correct2))\r\n\r\n%%\r\nx = [ones(1,40) 0 ones(1,40)];\r\ny_correct = 0;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [exp(1) exp(3) exp(5) exp(7) exp(9)];\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n\r\n%%\r\nx = [-64 32 -16 8 -4 2 -1 0.5 -0.25];\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [-9.6 -9.7 -9.8 -9.9 -10 -10.1 -10.2 -10.3 -10.4];\r\ny_correct = 1;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [1 1 -1 -1];\r\ny_correct = 0;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [i 3i 5i 7i];\r\ny_correct = 1;\r\nassert(isequal(stype(x),y_correct))\r\n\r\n%%\r\nx = [i -2 -4i 8 16i];\r\ny_correct = 2;\r\nassert(isequal(stype(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2016-05-27T18:43:30.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-28T17:52:25.000Z","updated_at":"2025-12-30T12:59:47.000Z","published_at":"2016-04-28T17:52:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a row vector, x, return 1 if it is an arithmetic series, or 2 if it is a geometric series. If it is neither, return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 1:8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 2^(1:8)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 3:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = [1 1 2 3 5 8 13 21 34]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2329,"title":"Finding the next number in a number list, are you able to crack it!","description":"So it goes like this, I give a number list and you find the next value!\r\n\r\nI found a way to do it, just wondering how many others can to! \r\n\r\nThis could be a fun test of skill! Please try and see if you can get it!\r\n\r\nExample:\r\n\r\n x = [ ...\r\n 11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3];\r\n NextValue = 3;\r\n\r\n %% Next value after x(1), so your finding the ? in sequence x = [?; 11; 4; 16; 3; ... 3];\r\n\r\nGood luck, just saying, it is tricky! Many have solved this, but the key is to find the pattern...","description_html":"\u003cp\u003eSo it goes like this, I give a number list and you find the next value!\u003c/p\u003e\u003cp\u003eI found a way to do it, just wondering how many others can to!\u003c/p\u003e\u003cp\u003eThis could be a fun test of skill! Please try and see if you can get it!\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e x = [ ...\r\n 11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3];\r\n NextValue = 3;\u003c/pre\u003e\u003cpre\u003e %% Next value after x(1), so your finding the ? in sequence x = [?; 11; 4; 16; 3; ... 3];\u003c/pre\u003e\u003cp\u003eGood luck, just saying, it is tricky! Many have solved this, but the key is to find the pattern...\u003c/p\u003e","function_template":"function NextNumber = FindNextNumber(x)\r\n NextNumber = x;\r\nend","test_suite":"%%\r\nx = [11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3];\r\nNextNumber= 3;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [9;\r\n 1;\r\n 7;\r\n 1;\r\n 7;\r\n 9;\r\n 2;\r\n 8;\r\n 4;\r\n 8;\r\n 16;\r\n 21;\r\n 13;\r\n 15;\r\n 1;\r\n 13;\r\n 10];\r\nNextNumber= 8;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [6;\r\n 20;\r\n 9;\r\n 3;\r\n 25;\r\n 4;\r\n 1;\r\n 4;\r\n 8;\r\n 9;\r\n 1;\r\n 7];\r\nNextNumber= 1;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [17;\r\n 5;\r\n 12;\r\n 33;\r\n 5;\r\n 7;\r\n 4];\r\nNextNumber= 4;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [8;\r\n 6;\r\n 11;\r\n 4;\r\n 1;\r\n 6;\r\n 2;\r\n 1;\r\n 3;\r\n 11;\r\n 4;\r\n 16;\r\n 3;\r\n 3;\r\n 15;\r\n 6;\r\n 17;\r\n 10;\r\n 18;\r\n 7;\r\n 13;\r\n 15;\r\n 5;\r\n 24;\r\n 5;\r\n 3;\r\n 3;\r\n 1;\r\n 2;\r\n 5;\r\n 16;\r\n 1;\r\n 2;\r\n 17;\r\n 9;\r\n 8;\r\n 5;\r\n 12;\r\n 16;\r\n 11;\r\n 8;\r\n 5;\r\n 10;\r\n 11;\r\n 10;\r\n 10;\r\n 2;\r\n 4;\r\n 17;\r\n 5;\r\n 12;\r\n 33;\r\n 5;\r\n 7;\r\n 4;\r\n 11;\r\n 16;\r\n 5;\r\n 1;\r\n 6;\r\n 20;\r\n 9;\r\n 3;\r\n 25;\r\n 4;\r\n 1];\r\nNextNumber= 5;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [4;\r\n 4;\r\n 18;\r\n 12;\r\n 27;\r\n 20;\r\n 24;\r\n 25;\r\n 14;\r\n 29;\r\n 16;\r\n 25;\r\n 15;\r\n 6;\r\n 6;\r\n 3;\r\n 20;\r\n 9;\r\n 20;\r\n 5;\r\n 12;\r\n 24;\r\n 16;\r\n 27];\r\nNextNumber= 20;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [14;\r\n 22;\r\n 27;\r\n 15;\r\n 8;\r\n 30;\r\n 24;\r\n 33;\r\n 28;\r\n 27;\r\n 31;\r\n 31;\r\n 38;\r\n 29;\r\n 30;\r\n 35;\r\n 12;\r\n 7;\r\n 15;\r\n 22;\r\n 10;\r\n 26;\r\n 35;\r\n 15;\r\n 25;\r\n 18;\r\n 32;\r\n 30;\r\n 31;\r\n 35;\r\n 22;\r\n 15;\r\n 21;\r\n 13;\r\n 19;\r\n 24;\r\n 32;\r\n 18;\r\n 30;\r\n 31;\r\n 28;\r\n 32;\r\n 40;\r\n 17;\r\n 15;\r\n 28;\r\n 41;\r\n 42;\r\n 35;\r\n 30;\r\n 35;\r\n 39;\r\n 33;\r\n 17;\r\n 34;\r\n 26;\r\n 13;\r\n 14;\r\n 19;\r\n 40;\r\n 13;\r\n 27;\r\n 16;\r\n 23;\r\n 22;\r\n 29;\r\n 42;\r\n 33;\r\n 37;\r\n 28;\r\n 36;\r\n 30;\r\n 26;\r\n 6;\r\n 25;\r\n 39;\r\n 26;\r\n 23;\r\n 39;\r\n 27;\r\n 28;\r\n 14;\r\n 25;\r\n 29;\r\n 7;\r\n 16];\r\nNextNumber= 35;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%% \r\nx = [27;\r\n 31;\r\n 31;\r\n 38;\r\n 29;\r\n 30;\r\n 35;\r\n 12;\r\n 7;\r\n 15;\r\n 22;\r\n 10;\r\n 26;\r\n 35;\r\n 15;\r\n 25;\r\n 18;\r\n 32;\r\n 30;\r\n 31;\r\n 35;\r\n 22;\r\n 15;\r\n 21;\r\n 13;\r\n 19;\r\n 24;\r\n 32;\r\n 18;\r\n 30;\r\n 31;\r\n 28;\r\n 32;\r\n 40;\r\n 17;\r\n 15;\r\n 28;\r\n 41;\r\n 42;\r\n 35;\r\n 30;\r\n 35;\r\n 39;\r\n 33;\r\n 17;\r\n 34;\r\n 26;\r\n 13;\r\n 14;\r\n 19;\r\n 40;\r\n 13;\r\n 27;\r\n 16;\r\n 23;\r\n 22;\r\n 29;\r\n 42;\r\n 33;\r\n 37;\r\n 28;\r\n 36;\r\n 30;\r\n 26;\r\n 6;\r\n 25;\r\n 39;\r\n 26;\r\n 23;\r\n 39;\r\n 27;\r\n 28;\r\n 14;\r\n 25;\r\n 29;\r\n 7;\r\n 16;\r\n 28;\r\n 11;\r\n 14];\r\nNextNumber= 28;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [39;\r\n 46;\r\n 39;\r\n 21;\r\n 46;\r\n 46;\r\n 45;\r\n 31;\r\n 47;\r\n 45;\r\n 39;\r\n 44;\r\n 47];\r\nNextNumber= 45;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n%%\r\nx = [7;\r\n 8;\r\n 18;\r\n 7;\r\n 9;\r\n 2;\r\n 11;\r\n 2;\r\n 2;\r\n 2;\r\n 13;\r\n 4;\r\n 4;\r\n 13;\r\n 11;\r\n 6;\r\n 3;\r\n 15;\r\n 16;\r\n 17;\r\n 4;\r\n 7;\r\n 17;\r\n 12;\r\n 3;\r\n 12;\r\n 9;\r\n 3;\r\n 17;\r\n 2;\r\n 4;\r\n 17;\r\n 5;\r\n 18;\r\n 1;\r\n 4;\r\n 15;\r\n 2;\r\n 11;\r\n 6;\r\n 19;\r\n 4;\r\n 2;\r\n 1;\r\n 18;\r\n 15;\r\n 12;\r\n 17;\r\n 11;\r\n 2;\r\n 1;\r\n 3;\r\n 17;\r\n 15;\r\n 4;\r\n 12;\r\n 10;\r\n 11;\r\n 16;\r\n 4;\r\n 2;\r\n 13;\r\n 13;\r\n 8;\r\n 16;\r\n 2;\r\n 9;\r\n 19;\r\n 7;\r\n 15;\r\n 12;\r\n 5;\r\n 17;\r\n 6;\r\n 9;\r\n 16;\r\n 9;\r\n 11;\r\n 4;\r\n 12;\r\n 7;\r\n 12;\r\n 9;\r\n 18;\r\n 2;\r\n 8;\r\n 14];\r\nNextNumber= 4;\r\nassert(isequal(FindNextNumber(x),NextNumber))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-16T23:24:44.000Z","updated_at":"2014-05-19T14:19:51.000Z","published_at":"2014-05-16T23:24:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo it goes like this, I give a number list and you find the next value!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI found a way to do it, just wondering how many others can to!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis could be a fun test of skill! Please try and see if you can get it!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ ...\\n 11;\\n 4;\\n 16;\\n 3;\\n 3;\\n 15;\\n 6;\\n 17;\\n 10;\\n 18;\\n 7;\\n 13;\\n 15;\\n 5;\\n 24;\\n 5;\\n 3;\\n 3];\\n NextValue = 3;\\n\\n %%Next value after x(1), so your finding the ? in sequence x = [?; 11; 4; 16; 3; ... 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck, just saying, it is tricky! Many have solved this, but the key is to find the pattern...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43649,"title":"4 Digit Sequence Repetitions","description":"Given a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.\r\n\r\nFor example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:\r\n\r\n2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...\r\n\r\nGiven a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.\r\n\r\nFor example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.\r\n\r\nTaken from L-S Hahn's New Year's Puzzle for 2009","description_html":"\u003cp\u003eGiven a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.\u003c/p\u003e\u003cp\u003eFor example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:\u003c/p\u003e\u003cp\u003e2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...\u003c/p\u003e\u003cp\u003eGiven a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.\u003c/p\u003e\u003cp\u003eFor example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.\u003c/p\u003e\u003cp\u003eTaken from L-S Hahn's New Year's Puzzle for 2009\u003c/p\u003e","function_template":"function i = seq_appears(yr, tst)\r\n i=0;\r\nend","test_suite":"%%\r\nyr = [2 0 0 9];\r\ntst = [2 0 1 0];\r\nia = 0;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 2 3 4];\r\ntst = [5 6 7 8];\r\nia = 621;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 2 3 4];\r\ntst = [4 5 6 7];\r\nia = 1125;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 1 1 1];\r\ntst = [4 7 3 5];\r\nia = 5;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 1 1 1];\r\ntst = [2 2 2 2];\r\nia = 0;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [1 1 1 1];\r\ntst = [7 7 7 7];\r\nia = 1171;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n%%\r\nyr = [0 0 0 1];\r\ntst = [9 0 0 0];\r\nia = 780;\r\nassert(isequal(seq_appears(yr, tst),ia))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2016-11-01T17:01:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-11-01T16:59:37.000Z","updated_at":"2026-01-18T13:14:50.000Z","published_at":"2016-11-01T16:59:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTaken from L-S Hahn's New Year's Puzzle for 2009\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46615,"title":"Find terms in the Connell sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.742px 7.79167px; transform-origin: 375.742px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Connell sequence starts with the first odd number and continues with the next two even numbers, the next three odd numbers, the next four even numbers, and so on. Therefore, the first ten terms are 1, 2, 4, 5, 7, 9, 10, 12, 14, and 16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 7.79167px; transform-origin: 373.275px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the terms at the specified positions in the Connell sequence. FOR and WHILE loops are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Connell(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nfiletext = fileread('Connell.m');\r\nnoloops = isempty(strfind(filetext, 'for')) \u0026\u0026 isempty(strfind(filetext, 'while'));\r\nassert(noloops, 'No loops allowed')\r\n\r\n%%\r\nn = 1:10;\r\ny_correct = [1 2 4 5 7 9 10 12 14 16];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 35:40;\r\ny_correct = [62 64 65 67 69 71];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 628:633;\r\ny_correct = [1221 1223 1225 1226 1228 1230];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 1620:1625;\r\ny_correct = 3183:2:3193;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 11111:11111:66666;\r\ny_correct = [22073 44233 66408 88590 110777 132967];\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 12457910;\r\ny_correct = 24910828;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 12457910121416;\r\ny_correct = 24915815251257;\r\nassert(isequal(Connell(n),y_correct))\r\n\r\n%%\r\nn = 15053\r\ny_correct = 59619;\r\nassert(isequal(Connell(Connell(n)),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2020-12-31T19:26:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-25T12:18:07.000Z","updated_at":"2025-12-09T15:00:13.000Z","published_at":"2020-09-25T13:32:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Connell sequence starts with the first odd number and continues with the next two even numbers, the next three odd numbers, the next four even numbers, and so on. Therefore, the first ten terms are 1, 2, 4, 5, 7, 9, 10, 12, 14, and 16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the terms at the specified positions in the Connell sequence. FOR and WHILE loops are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53004,"title":"Collect a set of candy wrappers","description":"This past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) their many neighbors with their costumes inspired by “mundane Halloween”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\r\n“This wrapper has a proof of the infinitude of primes!”, said Matilda.\r\n“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\r\n“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\r\nThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the Handbook of Mathematical Functions by Abramowitz and Stegun. \r\nMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\r\nWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 369px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.5px; transform-origin: 407px 184.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276.975px 8.05px; transform-origin: 276.975px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51251\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003etheir many neighbors\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8917px 8.05px; transform-origin: 31.8917px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with their costumes inspired by “\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003emundane Halloween\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.658px 8.05px; transform-origin: 244.658px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.317px 8.05px; transform-origin: 207.317px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“This wrapper has a proof of the infinitude of primes!”, said Matilda.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.475px 8.05px; transform-origin: 253.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242.983px 8.05px; transform-origin: 242.983px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.025px 8.05px; transform-origin: 359.025px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.475px 8.05px; transform-origin: 117.475px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e Handbook of Mathematical Functions\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4583px 8.05px; transform-origin: 89.4583px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by Abramowitz and Stegun. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.15px 8.05px; transform-origin: 383.15px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8.05px; transform-origin: 383px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = collectWrappers(n)\r\n y = factorial(factorial(n));","test_suite":"%%\r\nn = 5;\r\ny_correct = 12;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 25;\r\ny_correct = 96;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 40;\r\ny_correct = 172;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 1526;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 500;\r\ny_correct = 3397;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 1000:25:1125;\r\ny_correct = [7486 7698 7911 8125 8339 8554];\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2500;\r\ny_correct = 21004;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny_correct = 97877;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 250000;\r\ny_correct = 3251609;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e6;\r\ny_correct = 80010822;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e7;\r\ny_correct = 440290052;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 5e8;\r\ny_correct = 10303667162;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%%\r\nn = 2.5e9;\r\ny_correct = 55541930585;\r\nassert(isequal(collectWrappers(n),y_correct))\r\n\r\n%% Anti-lookup\r\nn = [7 17 71 77 117 171 177 711 717 771 777];\r\nyy_correct = [68 276 2216 2478 4393 7308 7647 46281 46777 51268 51779];\r\nindx = randi(11,[1 randi(11)]);\r\nassert(isequal(collectWrappers(collectWrappers(n(indx))),yy_correct(indx)))\r\n\r\n%%\r\nfiletext = fileread('collectWrappers.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2021-11-06T13:42:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-06T13:09:20.000Z","updated_at":"2026-01-02T17:08:42.000Z","published_at":"2021-11-06T13:12:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51251\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etheir many neighbors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e with their costumes inspired by “\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.spoon-tamago.com/2021/11/01/japan-jimi-mundane-halloween-2021/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emundane Halloween\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e”, a Japanese tradition started in 2014. As they sifted through and sampled the candy they collected, they noticed something odd as they opened one type of candy, an Oh Leonhard! bar:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e“This wrapper has a proof of the infinitude of primes!”, said Matilda.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e“I got that one too,” said Labrun. “And here’s one with the Twin Prime Conjecture!”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e“Here’s the Pythagorean Theorem. And this one has the Riemann hypothesis.”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe precocious pair determined that these wrappers were part of the Oh Leonhard! “Great Theorems and Unsolved Problems” promotion. In this promotion, wrappers with one of forty theorems, conjectures, or other famous math problems were distributed evenly among all of the Oh Leonhard! Bars produces. Anyone who collected all wrappers in the set would get a copy of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Handbook of Mathematical Functions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by Abramowitz and Stegun. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMatilda and Labrun computed that, on average, they would have to open 172 wrappers to complete a set and win the prize. Their calculation accounted for the contest’s rule that all pieces of the wrapper had to be submitted—that is, no fractional wrappers were allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the number of wrappers in a set and compute the expected number of wrappers that would need to be opened to collect the set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52462,"title":"Easy Sequences 1: Find the index of an element","description":"The nth element of a series is defined by: . Obviously, the first element . Given the nth element , find the value of the corresponding index .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 66px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 33px; transform-origin: 407px 33px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe nth element of a series \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined by: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 155.5px; height: 45px;\" width=\"155.5\" height=\"45\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Obviously, the first element \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.5px 8px; transform-origin: 36.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Given the nth element \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18.5px;\" width=\"33\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the value of the corresponding index \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = index(a)\r\n n = a;\r\nend","test_suite":"%%\r\na = 1;\r\nn = index(a);\r\nassert(isequal(1,n))\r\n%%\r\na = 25;\r\nn = index(a);\r\nbs = arrayfun(@(x) sum(arrayfun(@(k) k*(-1)^(k^3+1),1:x)),1:n);\r\nb = bs(end);\r\nassert(isequal(a,b))\r\n%%\r\na = 100;\r\nn = index(a);\r\nbs = arrayfun(@(x) sum(arrayfun(@(k) k*(-1)^(k^3+1),1:x)),1:n);\r\nb = bs(end);\r\nassert(isequal(a,b))\r\n%%\r\na = randi([1000,ceil(exp(log(double(intmax)/2)))]);\r\nn = index(a);\r\nassert(isequal(index(-a+(1-(-1)^(n+1))/2),n+1))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":"2021-08-11T04:47:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-10T10:31:40.000Z","updated_at":"2026-04-01T20:40:04.000Z","published_at":"2021-08-10T10:34:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe nth element of a series \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined by: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(n) = \\\\displaystyle\\\\sum\\\\limits_{k=1}^n (k\\\\cdot(-1)^{k^3+1})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, the first element \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Given the nth element \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the value of the corresponding index \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46676,"title":"List the erauqs","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.825px 8.16667px; transform-origin: 33.825px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter I told \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/players/8608872-jessicar\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eJessicaR\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3917px 8.16667px; transform-origin: 21.3917px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e about \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46624\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.558px 8.16667px; transform-origin: 230.558px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involves the emirps, she asked, \"What about the erauqs?\" As I will do with you, she let me deduce what they are.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.742px 8.16667px; transform-origin: 222.742px 8.16667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the erauqs less than or equal to the input number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = erauqs(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 99;\r\nassert(isempty(erauqs(n)))\r\n \t\r\n%%\r\nn = 1000;\r\ny_correct = [100 144 169 400 441 900 961];\r\nassert(isequal(erauqs(n),y_correct))\r\n \t\r\n%%\r\nn = 10000;\r\ny_correct = [100 144 169 400 441 900 961 1089 9801 10000];\r\nassert(isequal(erauqs(n),y_correct))\r\n \t\r\n%%\r\nn = 100000;\r\ny = erauqs(n);\r\nlen_correct = 29;\r\nyp_correct = [10404 10609 12100 12544 12769 14400 14884 16900 40000 40401 44100 44521 48400 48841 67600 90000 90601 96100 96721];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(11:29),yp_correct))\r\n\t\r\n%%\r\nn = 1000000;\r\ny = erauqs(n);\r\nlen_correct = 32;\r\nyp_correct = [108900 980100 1000000];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(end-2:end),yp_correct))\r\n \t\r\n%%\r\nn = 1e8;\r\ny = erauqs(n);\r\nlen_correct = 100;\r\nyp_correct = [4456321 4498641 4888521 9678321];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y([76 78 83 94]),yp_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T01:35:23.000Z","updated_at":"2026-02-27T09:58:31.000Z","published_at":"2020-10-06T02:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter I told \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/8608872-jessicar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJessicaR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e about \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46624\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involves the emirps, she asked, \\\"What about the erauqs?\\\" As I will do with you, she let me deduce what they are.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the erauqs less than or equal to the input number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44628,"title":"The other half of the Fibonacci sequence","description":"The \u003chttp://mathworld.wolfram.com/FibonacciNumber.html \"Fibonacci sequence\"\u003e — \r\nF = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from _circa_ 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \"Fibonacci\") _circa_ 1202 CE. \r\n\r\nThis sequence can be defined by \r\n\r\n*F(n+2) = F(n+1) + F(n)*\r\n\r\nin which F(1) = 1, F(2) = 1, F(3) = 2, ....\r\n\r\nLater in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0). \r\n\r\nYour job in this Cody Problem is to 'create history'(?) by extending this sequence to _negative values of n_, to discover the missing half of this sequence!\r\n\r\nEXAMPLE:\r\n\r\nIf n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.\r\n\r\nYou are only required to provide outputs for n \u003c 3 that can be represented by an \u003chttps://au.mathworks.com/help/matlab/ref/int64.html |int64|\u003e \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e. To enforce this, your output needs to be of this data type. ","description_html":"\u003cp\u003eThe \u003ca href = \"http://mathworld.wolfram.com/FibonacciNumber.html\"\u003e\"Fibonacci sequence\"\u003c/a\u003e — \r\nF = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from \u003ci\u003ecirca\u003c/i\u003e 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \"Fibonacci\") \u003ci\u003ecirca\u003c/i\u003e 1202 CE.\u003c/p\u003e\u003cp\u003eThis sequence can be defined by\u003c/p\u003e\u003cp\u003e\u003cb\u003eF(n+2) = F(n+1) + F(n)\u003c/b\u003e\u003c/p\u003e\u003cp\u003ein which F(1) = 1, F(2) = 1, F(3) = 2, ....\u003c/p\u003e\u003cp\u003eLater in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0).\u003c/p\u003e\u003cp\u003eYour job in this Cody Problem is to 'create history'(?) by extending this sequence to \u003ci\u003enegative values of n\u003c/i\u003e, to discover the missing half of this sequence!\u003c/p\u003e\u003cp\u003eEXAMPLE:\u003c/p\u003e\u003cp\u003eIf n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.\u003c/p\u003e\u003cp\u003eYou are only required to provide outputs for n \u0026lt; 3 that can be represented by an \u003ca href = \"https://au.mathworks.com/help/matlab/ref/int64.html\"\u003e\u003ctt\u003eint64\u003c/tt\u003e\u003c/a\u003e \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e. To enforce this, your output needs to be of this data type.\u003c/p\u003e","function_template":"% This was my logic: ...\r\nfunction F = negativeRabbits(n)\r\n % Here's how I implemented that conceptual logic in code:\r\n n = F\r\nend","test_suite":"%% Ban str2num \u0026 str2double; regexp \u0026 regexpi\r\n% Banning these to discourage hard-coded answers and silly 'scoring cheats'. Sorry if it disrupts some legitimate usage. \r\n% Please don't try any other hacks or workarounds. \r\nassessFunctionAbsence({'str2num','str2double','regexp', 'regexpi'}, 'FileName','negativeRabbits.m');\r\nFR = fileread('negativeRabbits.m');\r\nmsg = 'Don''t hard-code your ''solution''.';\r\nassert( ~any( cellfun( @(z) contains(FR, z) , {'54800875592', '716768017756', '9845401187926'} ) ) , msg )\r\n\r\n%% Ban \"ans\" and a few hard-coded values (digits stripped)\r\n% I don't think it's very good style to be using \"ans\". \r\nRE = regexp(fileread('negativeRabbits.m'), '\\w+', 'match');\r\ntabooWords = {'ans'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not include the following banned strings in your code!' char([10 13]) ...\r\n strjoin(RE(testResult)) char([10 13])];\r\nassert(~any( cellfun( @(z) ismember(z, tabooWords), RE ) ), msg)\r\n\r\n%% Check data type\r\n% This is important.\r\nassert( isequal( class(negativeRabbits(0)) , 'int64' ) , 'Wrong data type.')\r\n\r\n%% Initial conditions and other such key values. \r\n% Test Suite shall ensure it only ever checks n \u003c 3. \r\nassert( isequal(negativeRabbits(+2), 1) , 'Failed at n =+2.' )\r\nassert( isequal(negativeRabbits(+1), 1) , 'Failed at n =+1.' )\r\nassert( isequal(negativeRabbits( 0), 0) , 'Failed at n = 0.' )\r\nassert( isequal(negativeRabbits(-1), 1) , 'Failed at n =-1.' )\r\n\r\n%% Terms from 0 down to -10\r\nfor n = 0 : -1 : -10\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -10 down to -20\r\nfor n = -10 : -1 : -20\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -20 down to -40\r\nfor n = -20 : -1 : -40\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -40 down to -77\r\nfor n = -40 : -1 : -77\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n\r\n%% Terms from -77 down to -92\r\n% This is difficult, but feasible within the parameters of the problem. \r\nfor n = -77 : -1 : -92\r\n assert( isequal(negativeRabbits(n)+negativeRabbits(n+1), negativeRabbits(n+2)) , ['Failed at n =' num2str(n) '.'])\r\nend;\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2018-05-03T02:41:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-04-28T14:33:34.000Z","updated_at":"2026-02-21T13:17:20.000Z","published_at":"2018-04-28T16:25:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://mathworld.wolfram.com/FibonacciNumber.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"Fibonacci sequence\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e — F = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...] — appeared in Indian mathematical expositions from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecirca\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 700 CE or earlier, and in the writings of Leonardo of Pisa (a.k.a. \\\"Fibonacci\\\")\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecirca\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1202 CE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence can be defined by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF(n+2) = F(n+1) + F(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein which F(1) = 1, F(2) = 1, F(3) = 2, ....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLater in history, it was recognised that F(0) = 0. Of course, this still satisfies the formula in bold above [for n=0]: F(2) = F(1) + F(0).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour job in this Cody Problem is to 'create history'(?) by extending this sequence to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enegative values of n\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to discover the missing half of this sequence!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf n=-1, then F(-1) must be 1, to ensure that F(1) = F(0) + F(-1) — thus satisfying the formula in bold above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are only required to provide outputs for n \u0026lt; 3 that can be represented by an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/ref/int64.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eint64\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. To enforce this, your output needs to be of this data type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61018,"title":"Find the logic and return the nth number","description":"given a sequence of numbers arranged in the following order:\r\nA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\r\nWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\r\neg:\r\nn=5\r\n--\u003e output=9","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 85.5px; transform-origin: 408px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003egiven a sequence of numbers arranged in the following order:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeg:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en=5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--\u0026gt; output=9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(n)\r\n y=n;\r\nend","test_suite":"%%\r\nn = 15;\r\ny_correct = 39;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 325;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 100;\r\ny_correct = 976;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 150;\r\ny_correct = 2278;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 200;\r\ny_correct = 2929;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 3268;\r\nassert(isequal(your_fcn_name(n),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4946338,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-20T06:08:57.000Z","updated_at":"2026-03-23T12:09:51.000Z","published_at":"2025-10-20T06:08:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a sequence of numbers arranged in the following order:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeg:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--\u0026gt; output=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52594,"title":"Easy Sequences 10: Sum of Cumsums of Fibonacci Sequence","description":"The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:\r\n \u003e\u003e Fn = [1 1 2 3 5 8 13 21 34 55];\r\n \u003e\u003e Sn = sum(cumsum(Fn))\r\n \u003e\u003e Sn =\r\n 364\r\nIt has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation. \r\nGiven a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. In the example above we have, 'n = 10' for 's = 364' . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 236.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 118.367px; transform-origin: 407px 118.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.5px 8px; transform-origin: 130.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function F(n) is defined as the set of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFibonacci numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.5px 8px; transform-origin: 188.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 144px 8.5px; tab-size: 4; transform-origin: 144px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; Fn = [1 1 2 3 5 8 13 21 34 55];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100px 8.5px; tab-size: 4; transform-origin: 100px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; Sn = sum(cumsum(Fn))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; Sn =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 32px 8.5px; tab-size: 4; transform-origin: 32px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 364\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327px 8px; transform-origin: 327px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.5px 8px; transform-origin: 47.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the example above we have,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'n = 10' for 's = 364' . \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = N(s)\r\n n = inv_cumsum(inv_sum(s));\r\nend","test_suite":"%%\r\ns = 364;\r\nn_correct = 10;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = 2000;\r\nn_correct = 13;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = 5000:100:10000;\r\nn_correct = 798;\r\nn_answer = sum(arrayfun(@(i) N(i),s));\r\nassert(isequal(n_answer,n_correct))\r\n%%\r\ns = intmax;\r\nn_correct = 42;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = 10^10;\r\nn_correct = 45;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = intmax('uint64');\r\nn_correct = 89;\r\nassert(isequal(N(s),n_correct))\r\n%%\r\ns = realmax/10;\r\nn_correct = 1467;\r\nassert(isequal(N(s),n_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-23T07:31:32.000Z","updated_at":"2025-12-16T04:43:30.000Z","published_at":"2021-08-23T12:03:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function F(n) is defined as the set of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFibonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e Fn = [1 1 2 3 5 8 13 21 34 55];\\n \u003e\u003e Sn = sum(cumsum(Fn))\\n \u003e\u003e Sn =\\n 364]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIn the example above we have,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'n = 10' for 's = 364' . \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52654,"title":"Easy Sequences 13: Average Speed of Spaceship","description":"A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around. \r\nGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops. Please round-off your answer to the nearest integer.\r\nNOTE: Use clasical physics only. Ignore any relativistic effects.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e Please round-off your answer to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = mean_velocity(s,v)\r\n y = x;\r\nend","test_suite":"%%\r\ns = 10000;\r\nv = 10000;\r\nv_correct = 1022;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1234567;\r\nv = 1234567;\r\nv_correct = 84539;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = '1234567891011121314151617181920';\r\nv = 123456789;\r\nv_correct = 6427156;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1e100;\r\nvs = 1:1000;\r\nv_correct = 72076;\r\nassert(isequal(sum(arrayfun(@(v) mean_velocity(s,v),vs)),v_correct))\r\n%%\r\ns = intmax;\r\nv = double(intmax);\r\nv_correct = 97326319;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = intmax('int64')/100;\r\nv = double(intmax('int64'))/100;\r\nv_correct = 2326765408587627;\r\nassert(isequal(mean_velocity(s,v),v_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-09-05T14:22:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T08:20:36.000Z","updated_at":"2025-12-22T16:16:27.000Z","published_at":"2021-09-05T08:20:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \\\"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Please round-off your answer to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52584,"title":"Easy Sequences 9: Faithful Pairs","description":"A \"faithful number\" is a non-prime number that is one less or one more than some prime number but not both. For example, for numbers up to 20, the numbers 1 8, 10, 14, 16 and 20 are faithful. The number 4 does not qualify because it is equal to \"3 + 1\" and \"5 - 1\". \r\nIf both 'x' and 'x+2' are faithful but not to the same prime, the pair (x, x+2) is called a faithful pair. So, from 1 to 20 the faithful pairs are (8, 10) and (14, 16). Faithful pairs are scarse and rarer than primes themselves. We can only find 1 faithful pair for numbers 1 to 10, 5 pairs for numbers up to 50 and 8 pairs up to 100.\r\nLet \"P\" be the set of all faithful pairs from 1 to a given number \"n\". We define \"F\" as the set of all p1, p1 \u003c p2 ∀pairs (p1,p2) ∈ P. Write a function \"S(n)\", that sums all the elements of F. \r\nFor 1 to 20, P(20) = [8 10; 14 16], F(20) = [8 14] and S(20) = 22. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 237px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA \"faithful number\" is a non-prime number that is one less or one more than some prime number but not both. For example, for numbers up to 20, the numbers 1 8, 10, 14, 16 and 20 are faithful. The number 4 does not qualify because it is equal to \"3 + 1\" and \"5 - 1\". \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIf both 'x' and 'x+2' are faithful but not to the same prime, the pair (x, x+2) is called a faithful pair. So, from 1 to 20 the faithful pairs are (8, 10) and (14, 16). Faithful pairs are scarse and rarer than primes themselves. We can only find 1 faithful pair for numbers 1 to 10, 5 pairs for numbers up to 50 and 8 pairs up to 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eLet \"P\" be the set of all faithful pairs from 1 to a given number \"n\". We define \"F\" as the set of all p1, p1 \u0026lt; p2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e∀\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003epairs (p1,p2) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e∈\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e P. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite a function \"S(n)\", that sums all the elements of F.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor 1 to 20, P(20) = [8 10; 14 16], F(20) = [8 14] and S(20) = 22. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n n = 20;\r\n p = [8 10; 14 16];\r\n f = [8 14];\r\n s = 22;\r\nend\r\n","test_suite":"%%\r\nn = 20;\r\ns_correct = 22;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 9;\r\ns_correct = 0;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 5:5:100;\r\ns_correct = [0 8 8 22 42 42 42 80 80 124 124 124 124 192 192 192 272 272 272 370];\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 17216;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = 2^20;\r\ns_correct = 4054100250;\r\nassert(isequal(S(n),s_correct))\r\n%%\r\nn = intmax;\r\ns_correct = 6921757389660954;\r\nassert(isequal(S(n),s_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-22T10:45:18.000Z","updated_at":"2025-11-30T19:31:23.000Z","published_at":"2021-08-22T11:03:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \\\"faithful number\\\" is a non-prime number that is one less or one more than some prime number but not both. For example, for numbers up to 20, the numbers 1 8, 10, 14, 16 and 20 are faithful. The number 4 does not qualify because it is equal to \\\"3 + 1\\\" and \\\"5 - 1\\\". \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf both 'x' and 'x+2' are faithful but not to the same prime, the pair (x, x+2) is called a faithful pair. So, from 1 to 20 the faithful pairs are (8, 10) and (14, 16). Faithful pairs are scarse and rarer than primes themselves. We can only find 1 faithful pair for numbers 1 to 10, 5 pairs for numbers up to 50 and 8 pairs up to 100.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \\\"P\\\" be the set of all faithful pairs from 1 to a given number \\\"n\\\". We define \\\"F\\\" as the set of all p1, p1 \u0026lt; p2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e∀\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epairs (p1,p2) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e∈\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e P. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function \\\"S(n)\\\", that sums all the elements of F.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor 1 to 20, P(20) = [8 10; 14 16], F(20) = [8 14] and S(20) = 22. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46624,"title":"List the emirps","description":"An emirp is a prime number that becomes a different prime when reversed. The numbers 13, 17, and 149 are emirps, but 11, 19, and 101 are not. \r\nList the emirps less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 36px; transform-origin: 407.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.5px 7.66667px; transform-origin: 10.5px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/Emirp.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eemirp\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 348.383px 7.66667px; transform-origin: 348.383px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a prime number that becomes a different prime when reversed. The numbers 13, 17, and 149 are emirps, but 11, 19, and 101 are not. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.417px 7.66667px; transform-origin: 168.417px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eList the emirps less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = emirps(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 10;\r\nassert(isempty(emirps(n)))\r\n\r\n%%\r\nn = 100;\r\ny_correct = [13 17 31 37 71 73 79 97];\r\nassert(isequal(emirps(n),y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny_correct = [13 17 31 37 71 73 79 97 107 113 149 157 167 179 199 311 337 347 359 389 701 709 733 739 743 751 761 769 907 937 941 953 967 971 983 991];\r\nassert(isequal(emirps(n),y_correct))\r\n\r\n%%\r\nn = 10007;\r\ny = emirps(n);\r\nlen_correct = 241;\r\nyp_correct = [3049 3371 3803 7321 7717 9173 9551 9967];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(100:20:end),yp_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = emirps(n);\r\nlen_correct = 1646;\r\nyp_correct = [17417 33287 39827 76607 92993 99401];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(y(530:220:end),yp_correct))\r\n\r\n%%\r\nn = 1e6;\r\ny = emirps(n);\r\nsum_correct = 5129429596;\r\nlen_correct = 11184;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('emirps.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'webread') || contains(filetext, 'urlread'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":142,"test_suite_updated_at":"2022-01-30T17:10:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-30T05:34:18.000Z","updated_at":"2026-01-06T08:07:22.000Z","published_at":"2020-09-30T05:52:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/Emirp.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eemirp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a prime number that becomes a different prime when reversed. The numbers 13, 17, and 149 are emirps, but 11, 19, and 101 are not. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eList the emirps less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":12,"title":"Fibonacci sequence","description":"Calculate the nth Fibonacci number.\r\nGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\r\nExamples:\r\n Input n = 5\r\n Output f is 5\r\n\r\n Input n = 7\r\n Output f is 13","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 181px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 90.5px; transform-origin: 468.5px 90.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the nth Fibonacci number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.117px 8px; transform-origin: 199.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 45px; transform-origin: 464.5px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Input \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 19.25px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 19.25px 8.5px; \"\u003en = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 23.1px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 23.1px 8.5px; \"\u003ef is 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Input \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 19.25px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 19.25px 8.5px; \"\u003en = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 26.95px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 26.95px 8.5px; \"\u003ef is 13\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = fib(n)\r\n f = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('fib.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n contains(filetext, '610') || contains(filetext, '1597');\r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\nf = 1;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 6;\r\nf = 8;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 7;\r\nf = 13;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 10;\r\nf = 55;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 12;\r\nf = 144;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 15;\r\nf = 610;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 17;\r\nf = 1597;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 20;\r\nf = 6765;\r\nassert(isequal(fib(n),f))","published":true,"deleted":false,"likes_count":108,"comments_count":25,"created_by":1,"edited_by":223089,"edited_at":"2026-02-05T13:22:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14133,"test_suite_updated_at":"2026-02-05T13:22:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:18.000Z","updated_at":"2026-04-03T07:15:44.000Z","published_at":"2012-01-18T01:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the nth Fibonacci number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input n = 5\\n Output f is 5\\n\\n Input n = 7\\n Output f is 13]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44466,"title":"The twelve days of Christmas","description":"Traditionally there are twelve days of Christmas to celebrate (\"Twelvetide\"), typically starting with Christmas Day (25 December) as the \"First Day of Christmas\" and finishing on the 5th of January. \r\n\r\nIn the traditional Christmas carol, helpfully entitled \u003chttp://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/ _The Twelve Days of Christmas_\u003e, the singer recounts receiving gifts on each day, sent to them by their True Love. \r\n\r\nOn the *first* day, they receive *one* gift (1 × \"partridge in a pear tree\"). \r\n\r\nOn the *second* day they receive *two* _new_ gifts (2 × \"turtle doves\") *plus* a repeat of each gift corresponding to the previous days — in this case meaning plus *one* _repeat_ gift (1 × \"partridge in a pear tree\"). Therefore they have _accumulated_ a total of four gifts: one from the first day, and three from the second day. \r\n\r\nOn the *third* day they receive *three* _new_ gifts (3 × \"French hens\") *plus* a repeat of each gift corresponding to the previous days — in this case meaning plus *three* _repeat_ gifts (1 × \"partridge in a pear tree\" and 2 × \"turtle doves\"). By now they have _accumulated_ a total of ten gifts: one from the first day, three from the second day, and six from the third day. \r\n\r\nThis continues until the twelfth day (the _last_ day of Christmas). \r\n\r\nFor this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)\r\n\r\nEXAMPLE\r\n\r\n day = 2\r\n accumulatedGifts = 4\r\n","description_html":"\u003cp\u003eTraditionally there are twelve days of Christmas to celebrate (\"Twelvetide\"), typically starting with Christmas Day (25 December) as the \"First Day of Christmas\" and finishing on the 5th of January.\u003c/p\u003e\u003cp\u003eIn the traditional Christmas carol, helpfully entitled \u003ca href = \"http://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/\"\u003e\u003ci\u003eThe Twelve Days of Christmas\u003c/i\u003e\u003c/a\u003e, the singer recounts receiving gifts on each day, sent to them by their True Love.\u003c/p\u003e\u003cp\u003eOn the \u003cb\u003efirst\u003c/b\u003e day, they receive \u003cb\u003eone\u003c/b\u003e gift (1 × \"partridge in a pear tree\").\u003c/p\u003e\u003cp\u003eOn the \u003cb\u003esecond\u003c/b\u003e day they receive \u003cb\u003etwo\u003c/b\u003e \u003ci\u003enew\u003c/i\u003e gifts (2 × \"turtle doves\") \u003cb\u003eplus\u003c/b\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus \u003cb\u003eone\u003c/b\u003e \u003ci\u003erepeat\u003c/i\u003e gift (1 × \"partridge in a pear tree\"). Therefore they have \u003ci\u003eaccumulated\u003c/i\u003e a total of four gifts: one from the first day, and three from the second day.\u003c/p\u003e\u003cp\u003eOn the \u003cb\u003ethird\u003c/b\u003e day they receive \u003cb\u003ethree\u003c/b\u003e \u003ci\u003enew\u003c/i\u003e gifts (3 × \"French hens\") \u003cb\u003eplus\u003c/b\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus \u003cb\u003ethree\u003c/b\u003e \u003ci\u003erepeat\u003c/i\u003e gifts (1 × \"partridge in a pear tree\" and 2 × \"turtle doves\"). By now they have \u003ci\u003eaccumulated\u003c/i\u003e a total of ten gifts: one from the first day, three from the second day, and six from the third day.\u003c/p\u003e\u003cp\u003eThis continues until the twelfth day (the \u003ci\u003elast\u003c/i\u003e day of Christmas).\u003c/p\u003e\u003cp\u003eFor this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)\u003c/p\u003e\u003cp\u003eEXAMPLE\u003c/p\u003e\u003cpre\u003e day = 2\r\n accumulatedGifts = 4\u003c/pre\u003e","function_template":"% Comments...\r\nfunction accumulatedGifts = twelvetide(day)\r\n accumulatedGifts = 12\r\nend","test_suite":"%% Please do not try to hack the Test Suite. \r\n% The Test Suite will be updated if inappropriate submissions are received. \r\n% This includes hard-coded (pre-calculated, externally calculated, manually calculated) 'solutions'.\r\n\r\n% EDIT (2019-06-24). Anti-hacking provision\r\n% Ensure builtin function will be called. (Probably only the second of these will work.) \r\n! del fileread.m\r\n! rm -v fileread.m\r\n% Probably only the second of these will work. \r\nRE = regexp(fileread('twelvetide.m'), '\\w+', 'match');\r\n%tabooWords = {'ans', 'assert', 'freepass', 'tic'};\r\ntabooWords = {'assert', 'freepass'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not do that in your code!' char([10 13]) ...\r\n 'Found: ' strjoin(RE(testResult)) '.' char([10 13]) ...\r\n 'Banned word.' char([10 13])];\r\nassert(~any( cellfun( @(z) ismember(z, tabooWords), RE ) ), msg)\r\n% END EDIT (2019-06-24)\r\n\r\n\r\n%% Anti-hardcoding test\r\n% Adapted from the code of Alfonso Nieto-Castanon in a comment at \r\n% https://www.mathworks.com/matlabcentral/cody/problems/44343 .\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[120,165,220,286]),regexp(fileread('twelvetide.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))), 'Please do not hard-code your ''solution''.') \r\n%assert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[120,165,220,286,364]),regexp(fileread('twelvetide.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))), 'Please do not hard-code your ''solution''.') \u003c-- prior to 2018-01-02.\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[55,66,78]),regexp(fileread('twelvetide.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))), 'No, really: please do not hard-code your ''solution''.') % Added on 2018-01-06.\r\n\r\n%% Before Christmas\r\nday = 0 - randi(50);\r\naccumulatedGifts = 0;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%% Before Christmas\r\nday = 0;\r\naccumulatedGifts = 0;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%% First day of Christmas\r\nday = 1;\r\naccumulatedGifts = 1;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 2;\r\naccumulatedGifts = 4;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 3;\r\naccumulatedGifts = 10;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 4;\r\naccumulatedGifts = 20;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 5;\r\naccumulatedGifts = 35;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 6;\r\naccumulatedGifts = 56;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 7;\r\naccumulatedGifts = 84;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 8;\r\naccumulatedGifts = 120;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 9;\r\naccumulatedGifts = 165;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 10;\r\naccumulatedGifts = 220;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 11;\r\naccumulatedGifts = 286;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%% Last day of Christmas\r\nday = 12;\r\naccumulatedGifts = 364;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 13;\r\naccumulatedGifts = 364;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nday = 100;\r\naccumulatedGifts = 364;\r\nassert( isequal(twelvetide(day), accumulatedGifts) )\r\n\r\n%%\r\nfor i = 1 : 10\r\n day = 12 + randi(300);\r\n accumulatedGifts = 364;\r\n assert( isequal(twelvetide(day), accumulatedGifts) )\r\nend;","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":158,"test_suite_updated_at":"2019-06-24T08:48:56.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2017-12-23T07:03:22.000Z","updated_at":"2026-02-02T10:48:27.000Z","published_at":"2017-12-23T07:42:59.000Z","restored_at":"2018-02-06T15:11:41.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTraditionally there are twelve days of Christmas to celebrate (\\\"Twelvetide\\\"), typically starting with Christmas Day (25 December) as the \\\"First Day of Christmas\\\" and finishing on the 5th of January.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the traditional Christmas carol, helpfully entitled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://christmas-lyrics.com/christmas-carols-lyrics/the-twelve-days-of-christmas-lyrics/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Twelve Days of Christmas\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the singer recounts receiving gifts on each day, sent to them by their True Love.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efirst\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day, they receive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gift (1 × \\\"partridge in a pear tree\\\").\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esecond\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day they receive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enew\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gifts (2 × \\\"turtle doves\\\")\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erepeat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gift (1 × \\\"partridge in a pear tree\\\"). Therefore they have\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaccumulated\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a total of four gifts: one from the first day, and three from the second day.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethird\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day they receive\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enew\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gifts (3 × \\\"French hens\\\")\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a repeat of each gift corresponding to the previous days — in this case meaning plus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erepeat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gifts (1 × \\\"partridge in a pear tree\\\" and 2 × \\\"turtle doves\\\"). By now they have\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaccumulated\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a total of ten gifts: one from the first day, three from the second day, and six from the third day.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis continues until the twelfth day (the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elast\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e day of Christmas).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem you must calculate the cumulative total of all gifts received up to the specified day that is provided as input. (Day 1 is the 25th of December, day 2 is the 26th of December, and so on.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ day = 2\\n accumulatedGifts = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52689,"title":"Easy Sequences 18: Set Bits of Triple Summations","description":"The function S(n) is defined by the following triple summations:\r\n \r\nThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. Write the function 'bitS(n)', which is the number of bits set in the binary representation of S(n).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 127px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function S(n) is defined by the following triple summations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"186\" height=\"46\" style=\"width: 186px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite the function 'bitS(n)', which is the number of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.quora.com/What-do-we-mean-by-a-set-bit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ebits set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e in the binary representation of S(n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bitS(n)\r\n y = x;\r\nend","test_suite":"%%\r\nn = 100;\r\ny_correct = 7;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 10000;\r\ny_correct = 17;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 1000000;\r\ny_correct = 19;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 100000000;\r\ny_correct = 25;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 12345678910;\r\ny_correct = 30;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nns = 1000:2000;\r\ny = sum(arrayfun(@(n) bitS(n),ns))\r\ny_correct = 10663;\r\nassert(isequal(y,y_correct))\r\n%%\r\nn = intmax-123;\r\ny_correct = 33;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = intmax('int64')-123456;\r\ny_correct = 74;\r\nassert(isequal(bitS(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-12T09:14:05.000Z","updated_at":"2025-12-22T16:36:34.000Z","published_at":"2021-09-12T10:34:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function S(n) is defined by the following triple summations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)=\\\\left [\\\\sum_{k=2}^{n}\\\\sum_{j=2}^{k} \\\\sum_{i=2}^{j}\\\\frac{1}{\\\\log {_{i}}{\\\\left ( j! \\\\right )}} \\\\right ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite the function 'bitS(n)', which is the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.quora.com/What-do-we-mean-by-a-set-bit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebits set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in the binary representation of S(n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57720,"title":"The Yellowstone Permutation","description":"The Yellowstone Permutation is a sequence of positive integers, defined by the following rules:\r\nNo term is repeated.\r\nGiven n terms, the next term, a(n+1), is always the smallest possible integer.\r\nEvery term, a(n), must be relatively prime to the previous term, a(n-1).\r\nEvery term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).\r\nThe first three terms of the sequence, after which we start applying the rules, are [1 2 3]. \r\nGiven a positive integer, n, return the n-th term of the sequence, a(n).\r\nExample:\r\nn = 4;\r\na = 4","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 264.659px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 132.33px; transform-origin: 406.996px 132.33px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe Yellowstone Permutation is a sequence of positive integers, defined by the following rules:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7614px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.994px 40.8807px; transform-origin: 390.994px 40.8807px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eNo term is repeated.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven n terms, the next term, a(n+1), is always the smallest possible integer.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEvery term, a(n), must be relatively prime to the previous term, a(n-1).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEvery term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe first three terms of the sequence, after which we start applying the rules, are [1 2 3]. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a positive integer, n, return the n-th term of the sequence, a(n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8807px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.991px 20.4403px; transform-origin: 403.999px 20.4403px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en = 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ea = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = yellowstone(n)\r\n a = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('yellowstone.m');\r\nassert(isempty(strfind(filetext,'regexp')))\r\nassert(isempty(strfind(filetext,'assign')))\r\nassert(isempty(strfind(filetext,'eval')))\r\nassert(isempty(strfind(filetext,'echo')))\r\nassert(isempty(strfind(filetext,'!')))\r\n\r\n%%\r\nn = 1;\r\nassert(isequal(yellowstone(n),1))\r\n\r\n%%\r\nn = 2;\r\nassert(isequal(yellowstone(n),2))\r\n\r\n%%\r\nn = 3;\r\nassert(isequal(yellowstone(n),3))\r\n\r\n%%\r\nn = 11;\r\nassert(isequal(yellowstone(n),25))\r\n\r\n%%\r\nn = 13;\r\nassert(isequal(yellowstone(n),35))\r\n\r\n%%\r\nn = 15;\r\nassert(isequal(yellowstone(n),7))\r\n\r\n%%\r\nn = 21;\r\nassert(isequal(yellowstone(n),39))\r\n\r\n%%\r\nn = 28;\r\nassert(isequal(yellowstone(n),51))\r\n\r\n%%\r\nn = 32;\r\nassert(isequal(yellowstone(n),85))\r\n\r\n%%\r\nn = 38;\r\nassert(isequal(yellowstone(n),91))\r\n\r\n%%\r\nn = 45;\r\nassert(isequal(yellowstone(n),95))\r\n\r\n%%\r\nn = 53;\r\nassert(isequal(yellowstone(n),115))\r\n\r\n%%\r\nn = 70;\r\nassert(isequal(yellowstone(n),119))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-18T10:49:57.000Z","updated_at":"2023-02-18T10:49:57.000Z","published_at":"2023-02-18T10:49:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Yellowstone Permutation is a sequence of positive integers, defined by the following rules:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNo term is repeated.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n terms, the next term, a(n+1), is always the smallest possible integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery term, a(n), must be relatively prime to the previous term, a(n-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first three terms of the sequence, after which we start applying the rules, are [1 2 3]. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return the n-th term of the sequence, a(n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n = 4;\\na = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":594,"title":"\"Look and say\" sequence","description":"What's the next number in this sequence?\r\n\r\n* [0]\r\n* [1 0]\r\n* [1 1 1 0]\r\n* [3 1 1 0]\r\n* [1 3 2 1 1 0]\r\n\r\nThis a variant on the well-known \u003chttp://en.wikipedia.org/wiki/Look-and-say_sequence \"look and say\" or Morris sequence\u003e, where each new iteration is made up by 'saying' the number of numbers you see. That last line is \"one 3; then two 1s; then one 0\".\r\n\r\nCreate a function that returns the next element of this sequence, given a vector as a starting seed..","description_html":"\u003cp\u003eWhat's the next number in this sequence?\u003c/p\u003e\u003cul\u003e\u003cli\u003e[0]\u003c/li\u003e\u003cli\u003e[1 0]\u003c/li\u003e\u003cli\u003e[1 1 1 0]\u003c/li\u003e\u003cli\u003e[3 1 1 0]\u003c/li\u003e\u003cli\u003e[1 3 2 1 1 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThis a variant on the well-known \u003ca href = \"http://en.wikipedia.org/wiki/Look-and-say_sequence\"\u003e\"look and say\" or Morris sequence\u003c/a\u003e, where each new iteration is made up by 'saying' the number of numbers you see. That last line is \"one 3; then two 1s; then one 0\".\u003c/p\u003e\u003cp\u003eCreate a function that returns the next element of this sequence, given a vector as a starting seed..\u003c/p\u003e","function_template":"function NEXT = look_and_say(SEED)\r\n NEXT = SEED;\r\nend","test_suite":"%%\r\nassert(isequal(look_and_say([1]),[1 1]))\r\n%%\r\nassert(isequal(look_and_say([1 1 1 1 1]),[5 1]))\r\n%%\r\nassert(isequal(look_and_say([1 3 3 1 5 2 2]),[1 1 2 3 1 1 1 5 2 2]))\r\n%%\r\nassert(isequal(look_and_say([8 6 7 5 3 0 9]),[1 8 1 6 1 7 1 5 1 3 1 0 1 9]))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":78,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":238,"test_suite_updated_at":"2012-04-17T19:20:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-04-17T15:20:45.000Z","updated_at":"2026-03-25T05:08:20.000Z","published_at":"2012-04-17T15:21:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat's the next number in this sequence?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1 1 1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[3 1 1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1 3 2 1 1 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis a variant on the well-known\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Look-and-say_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"look and say\\\" or Morris sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, where each new iteration is made up by 'saying' the number of numbers you see. That last line is \\\"one 3; then two 1s; then one 0\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function that returns the next element of this sequence, given a vector as a starting seed..\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47833,"title":"List the delete-a-digit primes","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.267px 7.91667px; transform-origin: 331.267px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence starting 23, 37, 53, 73, 113, 131, 137, 173, 179, 197… is interesting because each term is a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.4083px 7.91667px; transform-origin: 42.4083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003edelete-a-digit prime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361.342px 7.91667px; transform-origin: 361.342px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, a prime number of two or more digits such that deleting any one digit leaves a prime number. For example, deleting the 1 from 137 leaves 37, deleting the 3 leaves 17, and deleting the 7 leaves 13. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 268.258px 7.91667px; transform-origin: 268.258px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that lists the delete-a-digit primes less than or equal the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = deleteADigitPrimes(n)\r\n y = primes(n);\r\nend","test_suite":"%%\r\nn = 20;\r\ny_correct = [];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 100;\r\ny_correct = [23 37 53 73];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 400;\r\ny_correct = [23 37 53 73 113 131 137 173 179 197 311 317];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny_correct = [23 37 53 73 113 131 137 173 179 197 311 317 431 617 719 1013 1031 1097 1499 1997 2239 2293 3137 4019 4919 6173 7019 7433 9677];\r\nassert(isequal(deleteADigitPrimes(n),y_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = deleteADigitPrimes(n);\r\nyp_correct = [30011 37019 40013 47933 73331 74177 90011 91733 93491 94397];\r\nlen_correct = 45;\r\nassert(isequal(y(end-9:end),yp_correct) \u0026\u0026 isequal(length(y),len_correct))\r\n\r\n%%\r\nn = 2e6;\r\ny = deleteADigitPrimes(n);\r\nyp_correct = [746099 779699 901499 901997 944777 962233 991733 1367777 1440731 1799999];\r\nlen_correct = 66;\r\nsum_correct = 16944054;\r\nassert(isequal(y(end-9:end),yp_correct) \u0026\u0026 isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('deleteADigitPrimes.m');\r\ncheating = ~isempty(strfind(filetext, 'urlread')) || ~isempty(strfind(filetext, 'oeis')); \r\nassert(~cheating)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-06T02:18:24.000Z","updated_at":"2025-11-29T22:19:33.000Z","published_at":"2020-12-06T02:49:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence starting 23, 37, 53, 73, 113, 131, 137, 173, 179, 197… is interesting because each term is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edelete-a-digit prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, a prime number of two or more digits such that deleting any one digit leaves a prime number. For example, deleting the 1 from 137 leaves 37, deleting the 3 leaves 17, and deleting the 7 leaves 13. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that lists the delete-a-digit primes less than or equal the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1696,"title":"Morse Code Generator! Try it!","description":" .... . .-.. .-.. --- . ...- . .-. -.-- --- -. . -.-.-- \r\n .-.. . - ... -.. --- ... --- -- . -- --- .-. ... . -.-. --- -.. . -.-.-- .-- . .-.. .-.. - .... .. ... -- --- .-. ... . -.-. --- -.. . --. . -. . .-. .- - --- .-. ..- ... . ... - .... . .. -. - . .-. -. .- - .. --- -. .- .-.. ... - -.-- .-.. . -- --- .-. ... . -.-. --- -.. . .-.-.- - .... . .-.-.- .- -. -.. -- .- -.- . ..- .--. .- .-.. .-.. - .... . -.-. --- -.. . --..-- - .... . .-. . .. ... --- -. . ... .--. .- -.-. . - .... .- - ... . .--. .- .-. .- - . ... .-.. . - - . .-. ... .- -. -.. ..... ... .--. .- -.-. . ... - .... .- - ... . .--. .- .-. .- - . .-- --- .-. -.. ... .-.-.- ... --- -- . .--. ..- -. -.-. - ..- .- - .. --- -. .. ... ..- ... . -.. .-.-.- .-.-.- .-.-.- --- - .... . .-. - .... . -. - .... .- - --..-- .- .-.. .-.. -.-- --- ..- -. . . -.. - --- -.. --- .. ... - .- -.- . .. -. ... --- -- . - -.-- .--. . --- ..-. - . -..- - .. -. - .... . ..-. --- .-. -- --- ..-. .- ... - .-. .. -. --. .- -. -.. - ..- .-. -. .. - .. -. - --- .- -- --- .-. ... . -.-. --- -.. . .-.. .. -. . -.-. .... .- .-. -.-. .-.. .- ... ... --..-- .- ... - .... . . -..- .- -- .--. .-.. . -... . .-.. --- .-- ... .... --- .-- ... \r\n \r\n\r\n\r\n \r\n\r\n text = 'Morse code is FUN!'\r\n Morse_code_out = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--'\r\n\r\n\r\nJust a note: this uses international style Morse code found in:\r\n\r\nhttp://en.wikipedia.org/wiki/American_Morse_code\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003e.... . .-.. .-.. --- . ...- . .-. -.-- --- -. . -.-.-- \r\n .-.. . - ... -.. --- ... --- -- . -- --- .-. ... . -.-. --- -.. . -.-.-- .-- . .-.. .-.. - .... .. ... -- --- .-. ... . -.-. --- -.. . --. . -. . .-. .- - --- .-. ..- ... . ... - .... . .. -. - . .-. -. .- - .. --- -. .- .-.. ... - -.-- .-.. . -- --- .-. ... . -.-. --- -.. . .-.-.- - .... . .-.-.- .- -. -.. -- .- -.- . ..- .--. .- .-.. .-.. - .... . -.-. --- -.. . --..-- - .... . .-. . .. ... --- -. . ... .--. .- -.-. . - .... .- - ... . .--. .- .-. .- - . ... .-.. . - - . .-. ... .- -. -.. ..... ... .--. .- -.-. . ... - .... .- - ... . .--. .- .-. .- - . .-- --- .-. -.. ... .-.-.- ... --- -- . .--. ..- -. -.-. - ..- .- - .. --- -. .. ... ..- ... . -.. .-.-.- .-.-.- .-.-.- --- - .... . .-. - .... . -. - .... .- - --..-- .- .-.. .-.. -.-- --- ..- -. . . -.. - --- -.. --- .. ... - .- -.- . .. -. ... --- -- . - -.-- .--. . --- ..-. - . -..- - .. -. - .... . ..-. --- .-. -- --- ..-. .- ... - .-. .. -. --. .- -. -.. - ..- .-. -. .. - .. -. - --- .- -- --- .-. ... . -.-. --- -.. . .-.. .. -. . -.-. .... .- .-. -.-. .-.. .- ... ... --..-- .- ... - .... . . -..- .- -- .--. .-.. . -... . .-.. --- .-- ... .... --- .-- ... \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003etext = 'Morse code is FUN!'\r\nMorse_code_out = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--'\r\n\u003c/pre\u003e\u003cp\u003eJust a note: this uses international style Morse code found in:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://en.wikipedia.org/wiki/American_Morse_code\"\u003ehttp://en.wikipedia.org/wiki/American_Morse_code\u003c/a\u003e\u003c/p\u003e","function_template":"function Morse_code_out = MorseCodeGenerator(text)\r\n Morse_code_out = text_in;\r\nend","test_suite":"%%\r\nx = 'Morse code is FUN!';\r\ny_correct = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n%%\r\nx = 'Am I 20, (who knows?)';\r\ny_correct = '.- -- .. ..--- ----- --..-- -.--. .-- .... --- -.- -. --- .-- ... ..--.. -.--.-';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n%%\r\nx = 'THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG: or does he...';\r\ny_correct = '- .... . --.- ..- .. -.-. -.- -... .-. --- .-- -. ..-. --- -..- .--- ..- -- .--. ... --- ...- . .-. - .... . .-.. .- --.. -.-- -.. --- --. ---... --- .-. -.. --- . ... .... . .-.-.- .-.-.- .-.-.-';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n%%\r\nx = '1234567890';\r\ny_correct = '.---- ..--- ...-- ....- ..... -.... --... ---.. ----. -----';\r\nassert(isequal(MorseCodeGenerator(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":"2019-09-16T11:37:52.000Z","rescore_all_solutions":false,"group_id":28,"created_at":"2013-07-05T18:50:09.000Z","updated_at":"2025-12-29T01:11:58.000Z","published_at":"2013-07-09T15:55:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[.... . .-.. .-.. --- . ...- . .-. -.-- --- -. . -.-.-- \\n .-.. . - ... -.. --- ... --- -- . -- --- .-. ... . -.-. --- -.. . -.-.-- .-- . .-.. .-.. - .... .. ... -- --- .-. ... . -.-. --- -.. . --. . -. . .-. .- - --- .-. ..- ... . ... - .... . .. -. - . .-. -. .- - .. --- -. .- .-.. ... - -.-- .-.. . -- --- .-. ... . -.-. --- -.. . .-.-.- - .... . .-.-.- .- -. -.. -- .- -.- . ..- .--. .- .-.. .-.. - .... . -.-. --- -.. . --..-- - .... . .-. . .. ... --- -. . ... .--. .- -.-. . - .... .- - ... . .--. .- .-. .- - . ... .-.. . - - . .-. ... .- -. -.. ..... ... .--. .- -.-. . ... - .... .- - ... . .--. .- .-. .- - . .-- --- .-. -.. ... .-.-.- ... --- -- . .--. ..- -. -.-. - ..- .- - .. --- -. .. ... ..- ... . -.. .-.-.- .-.-.- .-.-.- --- - .... . .-. - .... . -. - .... .- - --..-- .- .-.. .-.. -.-- --- ..- -. . . -.. - --- -.. --- .. ... - .- -.- . .. -. ... --- -- . - -.-- .--. . --- ..-. - . -..- - .. -. - .... . ..-. --- .-. -- --- ..-. .- ... - .-. .. -. --. .- -. -.. - ..- .-. -. .. - .. -. - --- .- -- --- .-. ... . -.-. --- -.. . .-.. .. -. . -.-. .... .- .-. -.-. .-.. .- ... ... --..-- .- ... - .... . . -..- .- -- .--. .-.. . -... . .-.. --- .-- ... .... --- .-- ... \\n\\ntext = 'Morse code is FUN!'\\nMorse_code_out = '-- --- .-. ... . -.-. --- -.. . .. ... ..-. ..- -. -.-.--']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJust a note: this uses international style Morse code found in:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/American_Morse_code\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/American_Morse_code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52497,"title":"Easy Sequences 3: Prime 44-number Squares","description":"The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a \"44-number\".\r\nIf 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. Write a function that returns P(n), given that P(3) = 2 and P(10) = 5.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 156px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 78px; transform-origin: 407px 78px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a \"44-number\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that returns P(n),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given that P(3) = 2 and P(10) = 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function prime_count = P(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 3 10 15 20];\r\ny_correct = [0 2 5 8 11];\r\nassert(isequal(arrayfun(@(i) P(i),x),y_correct))\r\n%%\r\nx = 1:20;\r\ny_correct = 108;\r\nassert(isequal(sum(arrayfun(@(i) P(i),x)),y_correct))\r\n%%\r\nx = arrayfun(@(i) P(i),15:30);\r\ny_correct = 118;\r\nassert(isequal(sum(arrayfun(@(i) P(i),x)),y_correct))\r\n%%\r\nx = 25:100;\r\ny_correct = 3077;\r\nassert(isequal(sum(arrayfun(@(i) P(i),x)),y_correct))\r\n%%\r\nx = floor(sqrt(double(intmax)));\r\ny_correct = 17862;\r\nassert(isequal(P(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":"2021-08-12T04:00:36.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-08-11T10:45:05.000Z","updated_at":"2025-11-30T19:35:26.000Z","published_at":"2021-08-11T19:07:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a \\\"44-number\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that returns P(n),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e given that P(3) = 2 and P(10) = 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1779,"title":"Oh Zero Zero Zero!!!","description":"Hello all,\r\nSo you have to find the largest section of zeros in a vector and then find the length of those zeros and there starting position...\r\nFor example:\r\n \r\n x = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\r\n %then the output is:\r\n LP = [9 10] %[Length Position]\r\n \r\n %Or another example:\r\n \r\n x = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\r\n %then the output is:\r\n LP = [6 9]\r\n \r\n %Or another example:\r\n \r\n x = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\r\n %then the output is:\r\n LP = [7 3];\r\n\r\nHave Fun!\r\n","description_html":"\u003cp\u003eHello all,\r\nSo you have to find the largest section of zeros in a vector and then find the length of those zeros and there starting position...\r\nFor example:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\r\n%then the output is:\r\nLP = [9 10] %[Length Position]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e%Or another example:\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\r\n%then the output is:\r\nLP = [6 9]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e%Or another example:\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\r\n%then the output is:\r\nLP = [7 3];\r\n\u003c/pre\u003e\u003cp\u003eHave Fun!\u003c/p\u003e","function_template":"function y = LengthAndPosnZeros(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\r\nLP = [9 10] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\r\nLP = [6 9]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\r\nLP = [7 3];\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 2 0 0];\r\nLP = [2 3] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 2 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0];\r\nLP = [9 3] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 0 0 0 0 0 0 0 0 0 1];\r\nLP = [9 2] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [111 541 0 45 3 0 0 0 15 26 0 4 84 3 84 0 9];\r\nLP = [3 6] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n%%\r\nx = [1 0 1];\r\nLP = [1 2] %[Length Position]\r\nassert(isequal(LengthAndPosnZeros(x),LP))\r\n\r\n","published":true,"deleted":false,"likes_count":15,"comments_count":1,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":540,"test_suite_updated_at":"2013-08-08T19:35:25.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2013-08-08T18:54:26.000Z","updated_at":"2026-03-24T00:57:27.000Z","published_at":"2013-08-08T19:35:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHello all, So you have to find the largest section of zeros in a vector and then find the length of those zeros and there starting position... For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = [1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1];\\n%then the output is:\\nLP = [9 10] %[Length Position]\\n\\n%Or another example:\\n\\nx = [1 0 3 49 3 2 232 3 0 0 0 0 0 0 8 290 0 0 0 12 323 34];\\n%then the output is:\\nLP = [6 9]\\n\\n%Or another example:\\n\\nx = [1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0];\\n%then the output is:\\nLP = [7 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHave Fun!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":49803,"title":"Compute expulsions from the Kimberling shuffle","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 311.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 155.583px; transform-origin: 407px 155.583px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.983px 7.79167px; transform-origin: 368.983px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.8917px 7.79167px; transform-origin: 10.8917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.05px 7.79167px; transform-origin: 26.05px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.79167px; transform-origin: 20.6167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eexcept\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 235.725px 7.79167px; transform-origin: 235.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 2 3 4 5 6 7 8 9 10...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e2 3 4 5 6 7 8 9 10 11...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e4 2 5 6 7 8 9 10 11 12...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e6 2 7 4 8 9 10 11 12 13...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 157.85px 8.25px; transform-origin: 157.85px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 146.3px 8.25px; transform-origin: 146.3px 8.25px; \"\u003e8 7 9 2 10 6 11 12 13 14.\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.25px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.25px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.008px 7.79167px; transform-origin: 369.008px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the row after which the input number is expelled. For example, because 5 appears on the main diagonal of row 3, your function should return 3. An optional challenge is to determine whether all numbers are eventually expelled from the array.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = KimberlingExpulsion(m)\r\n n = f(m);\r\nend","test_suite":"%%\r\nm = 1;\r\nn_correct = 1;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 5;\r\nn_correct = 3;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 10;\r\nn_correct = 5;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 18;\r\nn_correct = 11;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 19;\r\nn_correct = 49595;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 23;\r\nn_correct = 24;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 27;\r\nn_correct = 7598;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 31;\r\nn_correct = 13;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n%%\r\nm = 37;\r\nn_correct = 58;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 40;\r\nn_correct = 93167;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 43;\r\nn_correct = 1523;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 46;\r\nn_correct = 20;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 50;\r\nn_correct = 123;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 89;\r\nn_correct = 15803;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 101;\r\nn_correct = 95;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 108;\r\nn_correct = 63;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 117;\r\nn_correct = 390;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 8899;\r\nn_correct = 76973;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 8979;\r\nn_correct = 3465;\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nm = 1691;\r\nn_correct = 32633;\r\nassert(isequal(KimberlingExpulsion(KimberlingExpulsion(KimberlingExpulsion(m))),n_correct));\r\n\r\n%%\r\nk = randi(14);\r\nm = 9*2^k-3*k-10;\r\nn_correct = 3*(2^k-1);\r\nassert(isequal(KimberlingExpulsion(m),n_correct));\r\n\r\n%%\r\nfiletext = fileread('KimberlingExpulsion.m');\r\ncheating = contains(filetext, 'urlread') || contains(filetext, 'oeis'); \r\nassert(~cheating)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-09T19:48:53.000Z","updated_at":"2025-12-16T21:01:56.000Z","published_at":"2021-01-09T19:57:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexcept\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 2 3 4 5 6 7 8 9 10...\\n2 3 4 5 6 7 8 9 10 11...\\n4 2 5 6 7 8 9 10 11 12...\\n6 2 7 4 8 9 10 11 12 13...\\n8 7 9 2 10 6 11 12 13 14....]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the row after which the input number is expelled. For example, because 5 appears on the main diagonal of row 3, your function should return 3. An optional challenge is to determine whether all numbers are eventually expelled from the array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57730,"title":"Easy Sequences 97: One-line Code Challenge - Sequence with Constant Difference","description":"While answering Problem #57725, I noticed a pattern that immediately led me to a solution, namely: the -th difference of the sequence is constant. In that problem's case the constant is 6:\r\n diff(A,4) == [6 6 6 6 ...]\r\nwhere is the sequence.\r\nGiven an integer and a vector that enumerates the first elements of , write a function that outputs the -th element of , such that the -th difference is a constant:\r\n diff(A,k-1) == [c c c c ...]\r\n-------------\r\nNOTE: The following restrictions apply:\r\nThe function should only have one (1) line of code, excluding the function start line.\r\nSemicolons (;) are considered end-of-line characters.\r\nTo encourage vectorization, for and while loops are not allowed\r\nRegular expressions, string manipulation and curve fitting are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 335px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 167.5px; transform-origin: 407px 167.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhile answering \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57725\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem #57725\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e diff(A,4) == [6 6 6 6 \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e that enumerates the first \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e elements of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a function that outputs the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, such that the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAmCAYAAABJVvz/AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXKADAAQAAAABAAAAJgAAAADSajFxAAAEb0lEQVRoBe2Zb2hWVRzHl02baZI4X2hTF1ozcSlojKwpYgMN9EXWixz6ohJRI/+9USFCIkqlRNAXInuhoEI4FSpEtKAJy1eGGqUy2opNRHNYiW3Vpp/vnnPkGd17Os+9m7t7nvuF7z33nPP7nXt+33PuOec+T1FRilSBVIFUgVSBQlFgGYH+DJ8olIAdcdZS1wifdtjEqlqLdzd8O6CV4ZRVwtfgNvgl3AEHK8rp+Gew1BFAMXVfwRtwssMuUlUVXn/Dj0K8N1DeDDUg9ww3kw42TKDD+6BiVRxToAsjqTwPv4clLsNc6kZj3AKPw0egCweptILPdhkmrO4p+rMHdkLbfx/BFcZ4eB3WKdMXOEEj/0Cf1+YkdupoOxwCBwvq6eiHcDlUrFb0/5vhmPbgPa7yeSuTjX7VJqmG9ns0IYFvG/tjHvZJNfnBxKC4fQXXctIG70AtM5HxNZ56cLlHCy8YW9mv8bBPqsm5rDh8BVcsm4xf5FmuDaQLasR9sAUjiS1W+Dgk1Caq4M+Z2BtccRU7Kmup0zKhWe6DGmPUSnoFPg6fNWXZSQsZLT35hp8ISJtnNdSb0QRzwrdYa7Yu8fCSuB3G/oCxH0uqk032JqSPpjdNfVKTqDNc8RyG0mylMkHQDA7DRFPxY5hBVvnL3D9m8mdMepN0HfwL/gH1waSRPwLzFZdNYFqOAxG2pOi8rfOlcCuTOK92OZGRXYLKuD8Ff4X6Ar0K8x1WK8UeiLAZruVgGOyCPuvtK6Z1jfA1OAN+B3+BL8JCEJswH0zOUMHDZvg4eQN7rs7kgq8aHAksaDnRGl0HD8HV8F+YC57H+BuotywqLuI4P6pzDD87OfV1HogwwXWAF0oyifO6gForzmLu34V6MzbCXMXGpWiMoe6jYlRUx5h++hFPCI07TPC2jF/RCFJthp0mH5TY5UR1k4zBo6Qr4F6TzyW5gvGqXBwCbH8LKHsYRZosQmsmye2qnx11xLGbZ5h3i7FrJq2Ed01e51I787kdNIhzLNQvpNJsV1i0YZum7O0ouQR/Bjs7q49yfwl+DoWpcFHPXeFc7N5ntftP5C7BNUOF6kwSeM1eTrRhCrszSc9VI24hW633SUect3KuCe5ClCBfxUmvxxcO53pj00FqNwyZnzbl8tcZXLu2zuMLYdLRQgfVb3E69EUpht1Q+59rIoe2p41PZ+rfYXGAlerboTqmY1w2qsjo4aqTv87hGpwkQ/Gsh1ZspZ/CodAHb2Akn50+xmE2200jKwIMppk6PWRrQP3HWfV6xZ4MsElK0Sd0REfhbLHtvSaMzy+mWlLlo++IyCjHUw9sgkGznGInNCg1UEfLfMY8gpPY9sAQK9alprF3YrWS384NhKdJ2WcfXFrL/oQzYYreCrxPVh+Gs3oXx8tpOTkLtQOXxWsqr7z1J42WEv2c0efQsacRagPUjl7oeAkBdBz+oD+F0E+2r8NI58z+7NgAtF3BM+cMwHPTR6YKpAqkCqQKpAqkCqQK9IMC9wHuKd8tRkmQ8AAAAABJRU5ErkJggg==\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-th difference is a constant:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e diff(A,k-1) == [c c c c \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003e...\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe following restrictions apply:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 80px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40px; transform-origin: 391px 40px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSemicolons (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e) are considered end-of-line characters.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTo encourage vectorization, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ewhile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eloops are not allowed\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"background-position-x: 0px; background-position-y: 50%; block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = nthElement(V,n)\r\n x = A(n);\r\nend","test_suite":"format longg\r\n%%\r\nV = [1 2 3 4 5 6]; n = 10000;\r\nx_correct = n;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [790 1303 2033 3034 4366]; n = [10 100 1000];\r\nx_correct = [18511 32160346 256563524446];\r\nassert(isequal(arrayfun(@(i) nthElement(V,i),n),x_correct))\r\n%%\r\nV = [12 23 34 56 78]; n = 6:10;\r\nds = diff([V arrayfun(@(i) nthElement(V,i),n)],length(V)-1);\r\nd_correct = -22;\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = [123456 234567 345678 456789]; n = 10000;\r\nx_correct = 1111122346;\r\nassert(isequal(nthElement(V,n),x_correct))\r\n%%\r\nV = [123 456 789 101112 131415 161718 192021 222324 252627 282930]; n = 11:18;\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\ns_correct = sum(x)\r\nds = diff([V x],length(V)-1);\r\nd_correct = 2170350;\r\nassert(isequal(sum(x),s_correct))\r\nassert(isequal(ds(randi(length(ds))),d_correct))\r\n%%\r\nV = sort(randi(100,1,10)); n = (length(V)+1):(length(V)+20);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(~any(diff([V x],length(V))))\r\n%%\r\nV = sort(randi(1000,1,10)); n = (length(V)+1):(length(V)+10);\r\nx = arrayfun(@(i) nthElement(V,i),n);\r\nassert(isequal(diff(V,length(V)-1),diff(x,length(V)-1)))\r\n%%\r\nfiletext = fileread('nthElement.m');\r\nnot_allowed = contains(filetext, 'str') || contains(filetext, 'regex') || contains(filetext, 'eval') || contains(filetext, 'assignin') || contains(filetext, 'for') || contains(filetext, 'while') || contains(filetext, 'fit');\r\nassert(~not_allowed)\r\nc = 0;\r\nfor s = deblank(strtrim(splitlines(filetext)))'\r\n if ~isempty(s{1}) \u0026\u0026 ~isequal(s{1}(1),'%')\r\n c = c + numel(find(s{1}==';'));\r\n if ~isequal(s{1}(end),';')\r\n c = c + 1;\r\n end\r\n end\r\nend\r\nassert(c\u003c=2)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-02-25T18:40:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-25T12:35:50.000Z","updated_at":"2023-02-25T18:40:33.000Z","published_at":"2023-02-25T18:35:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile answering \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57725\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem #57725\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, I noticed a pattern that immediately led me to a solution, namely: the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th difference of the sequence is constant. In that problem's case the constant is 6:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ diff(A,4) == [6 6 6 6 ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e that enumerates the first \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e elements of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a function that outputs the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(k-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th difference is a constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ diff(A,k-1) == [c c c c ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe following restrictions apply:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should only have one (1) line of code, excluding the function start line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSemicolons (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) are considered end-of-line characters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo encourage vectorization, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eloops are not allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRegular expressions, string manipulation and curve fitting are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55325,"title":"increasing sequences","description":"Given a string of digits, insert commas to create a sequence of strictly increasing numbers so as to minimize the magnitude of the last number. For this problem, leading zeros are allowed in front of a number. The solution is not necessary unique, see test2.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a string of digits, insert commas to create a sequence of strictly increasing numbers so as to minimize the magnitude of the last number. For this problem, leading zeros are allowed in front of a number. The solution is not necessary unique, see test2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = incr(str)\r\n y = str;\r\nend","test_suite":"%%\r\nx = '3456';\r\ny_correct = [3,4,5,6];\r\nassert(isequal(incr(x),y_correct))\r\n\r\n%%\r\nx = '3546';\r\ny_correct1 = [3,5,46];\r\ny_correct2 = [35,46];\r\nassert(isequal(incr(x),y_correct1) || isequal(incr(x),y_correct2) )\r\n\r\n%%\r\nx = '100000000011';\r\ny_correct = [10,11];\r\ny_correct2 = [1,11];\r\nassert( isequal(incr(x),y_correct) || isequal(incr(x),y_correct2) )\r\n\r\n%%\r\nx = '570344446780361';\r\ny_correct = [5,7,34,44,46,78,361];\r\nassert(isequal(incr(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":2197980,"edited_by":2197980,"edited_at":"2023-02-20T09:27:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-02-20T09:27:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T03:55:48.000Z","updated_at":"2025-07-26T02:53:26.000Z","published_at":"2022-08-20T03:55:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string of digits, insert commas to create a sequence of strictly increasing numbers so as to minimize the magnitude of the last number. For this problem, leading zeros are allowed in front of a number. The solution is not necessary unique, see test2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42838,"title":"Increasing sub-sequence (Level 2)","description":"This is the next step up from \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42837-increasing-sub-sequence-level-1 Problem 42837\u003e.\r\n\r\nGiven a vector, v, of real numbers, return a positive integer, n, representing the longest non-contiguous increasing sub-sequence contained in v.\r\n\r\nExample:\r\n\r\nv = [ *2* 18 9 *6 11 20 25* 3]\r\n\r\nn = 5","description_html":"\u003cp\u003eThis is the next step up from \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42837-increasing-sub-sequence-level-1\"\u003eProblem 42837\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest non-contiguous increasing sub-sequence contained in v.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ev = [ \u003cb\u003e2\u003c/b\u003e 18 9 \u003cb\u003e6 11 20 25\u003c/b\u003e 3]\u003c/p\u003e\u003cp\u003en = 5\u003c/p\u003e","function_template":"function n = subseq(v)\r\n n = numel(v);\r\nend","test_suite":"%%\r\nv = [2 18 9 6 11 20 25 3];\r\nn_correct = 5;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [-2 -18 -9 -6 -11 -20 -25 -3];\r\nn_correct = 4;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = zeros(1,30);\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [exp(-1) sqrt(2) sqrt(3) exp(1) pi exp(2)];\r\nn_correct = 6;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = 100:-10:-100;\r\nn_correct = 1;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [9 0:5 1:7 3:9 2:8];\r\nn_correct = 10;\r\nassert(isequal(subseq(v),n_correct))\r\n\r\n%%\r\nv = [0 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15];\r\nn_correct = 6;\r\nassert(isequal(subseq(v),n_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2017-12-09T06:56:32.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-28T09:14:17.000Z","updated_at":"2017-12-09T06:56:32.000Z","published_at":"2016-04-28T09:14:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the next step up from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42837-increasing-sub-sequence-level-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42837\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector, v, of real numbers, return a positive integer, n, representing the longest non-contiguous increasing sub-sequence contained in v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 18 9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6 11 20 25\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54,"title":"Maximum running product for a string of numbers","description":"Given a string s representing a list of numbers, find the five consecutive numbers that multiply to form the largest number. Specifically, given s return the index i to the first of those five numbers. You can assume the maximum product is unique.\r\n \r\nExample: \r\n\r\n Input s = '123454321'\r\n Output i = 3\r\n\r\nsince the product of [3 4 5 4 3] is larger than any of the alternatives.\r\n \r\n_Inspired by \u003chttp://projecteuler.net/index.php?section=problems\u0026id=8 Problem 8 from Project Euler\u003e_\r\n","description_html":"\u003cp\u003eGiven a string s representing a list of numbers, find the five consecutive numbers that multiply to form the largest number. Specifically, given s return the index i to the first of those five numbers. You can assume the maximum product is unique.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input s = '123454321'\r\n Output i = 3\u003c/pre\u003e\u003cp\u003esince the product of [3 4 5 4 3] is larger than any of the alternatives.\u003c/p\u003e\u003cp\u003e\u003ci\u003eInspired by \u003ca href=\"http://projecteuler.net/index.php?section=problems\u0026amp;id=8\"\u003eProblem 8 from Project Euler\u003c/a\u003e\u003c/i\u003e\u003c/p\u003e","function_template":"function i = running_product(s)\r\n i = 1;\r\nend","test_suite":"%%\r\n\r\ns = '123454321';\r\ni_correct = 3;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%%\r\n\r\ns = '5820974944592307816406286208998628034825342117067';\r\ni_correct = 28;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%%\r\n\r\ns = '141592653589793238462643383279502884197169399399999';\r\ni_correct = 47;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%% \r\n\r\ns = '7831652712019091456485669234603486104543266482133936072602';\r\ni_correct = 21;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%% \r\n\r\ns = '70066063155881748815209209628292540917153643678925903600113305305488';\r\ni_correct = 44;\r\nassert(isequal(running_product(s),i_correct))\r\n\r\n%% \r\n\r\ns = '11111';\r\ni_correct = 1;\r\nassert(isequal(running_product(s),i_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2254,"test_suite_updated_at":"2012-01-18T19:50:09.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:24.000Z","updated_at":"2026-03-04T13:30:28.000Z","published_at":"2012-01-18T01:00:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string s representing a list of numbers, find the five consecutive numbers that multiply to form the largest number. Specifically, given s return the index i to the first of those five numbers. You can assume the maximum product is unique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input s = '123454321'\\n Output i = 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince the product of [3 4 5 4 3] is larger than any of the alternatives.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://projecteuler.net/index.php?section=problems\u0026amp;id=8\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 8 from Project Euler\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51282,"title":"Compute a row of the Kimberling shuffle","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 320.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.083px; transform-origin: 407px 160.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.2417px 7.91667px; transform-origin: 90.2417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem continues from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/18242/problems/49803\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 49803\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.983px 7.91667px; transform-origin: 368.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.8917px 7.91667px; transform-origin: 10.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.05px 7.91667px; transform-origin: 26.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eexcept\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 235.725px 7.91667px; transform-origin: 235.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 2 3 4 5 6 7 8 9 10...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e2 3 4 5 6 7 8 9 10 11...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e4 2 5 6 7 8 9 10 11 12...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 7.91667px; transform-origin: 154px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e6 2 7 4 8 9 10 11 12 13...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 157.85px 7.91667px; transform-origin: 157.85px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; \"\u003e8 7 9 2 10 6 11 12 13 14.\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 7.91667px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.4333px 7.91667px; transform-origin: 99.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 277.208px 7.91667px; transform-origin: 277.208px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth row of this array, up to and including the first number beyond which the numbers are in order. For example, given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.7417px 7.91667px; transform-origin: 86.7417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e your function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[8 7 9 2 10 6 11]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = KimberlingShuffleRow(n)\r\n r = 1:n;\r\nend","test_suite":"%%\r\nn = 1;\r\nr_correct = 1;\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 2;\r\nr_correct = 2;\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 3;\r\nr_correct = [4 2 5];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 5;\r\nr_correct = [8 7 9 2 10 6 11];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 26;\r\nr_correct = [60 58 44 48 26 54 65 64 16 30 19 45 51 50 66 34 38 29 47 40 32 49 67 63 39 55 56 12 41 61 68 13 59 25 69 57 37 17 70 62 27 52 71 43 72 11 73 21 74];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 53;\r\nr_correct = [101 118 73 81 43 56 68 21 88 131 136 71 143 32 45 110 40 142 119 109 57 72 77 80 19 90 61 51 144 114 49 112 134 93 124 92 69 102 121 111 39 16 74 85 145 129 27 47 17 141 108 94 67 127 132 64 50 98 38 29 146 96 137 139 117 128 130 41 147 107 100 37 120 75 30 106 148 113 103 12 63 140 89 104 149 123 126 87 150 66 105 78 151 135 86 125 152 116 153 60 154 133 155];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nn = 151;\r\nr_correct = [383 377 319 392 360 103 85 187 375 136 299 309 125 432 398 258 270 410 40 411 189 372 168 311 380 74 231 176 306 167 123 425 239 159 284 295 393 17 335 206 205 260 282 386 133 363 171 337 433 152 139 387 196 242 340 57 127 424 254 417 142 226 381 388 288 357 150 241 199 323 217 56 43 287 385 308 368 431 365 155 215 60 32 170 268 420 419 312 303 253 105 63 251 220 356 314 89 324 145 404 193 106 116 371 137 184 203 225 274 333 237 182 434 291 427 113 262 132 301 202 294 397 317 98 423 409 224 339 329 272 180 281 345 164 163 66 102 78 154 428 252 207 195 197 435 300 396 292 289 367 112 322 334 148 77 332 415 179 384 266 304 320 257 181 213 351 173 390 256 348 261 364 394 235 418 354 436 313 117 305 209 107 407 328 290 190 273 338 280 265 344 92 219 111 395 325 271 248 68 330 353 370 183 27 277 430 326 336 437 416 185 421 315 399 379 422 400 234 94 177 391 346 426 267 438 298 69 316 307 369 279 297 412 143 285 247 250 186 401 342 439 246 343 310 188 134 362 19 149 293 131 276 278 201 405 406 440 361 373 359 212 218 296 118 441 378 321 429 331 350 318 109 442 214 87 140 259 403 347 129 443 414 413 147 444 269 174 349 445 51 408 286 446 221 447 240 448 75 449];\r\nassert(isequal(KimberlingShuffleRow(n),r_correct))\r\n\r\n%%\r\nr1 = KimberlingShuffleRow(1776);\r\nr2 = KimberlingShuffleRow(r1(1));\r\nsum_correct = 9180392;\r\nassert(isequal(sum(r2),sum_correct))\r\n\r\n%%\r\nr1 = KimberlingShuffleRow(4881);\r\nr2 = KimberlingShuffleRow(r1(1));\r\nsump_correct = 11284849;\r\nassert(isequal(sum(r2(isprime(r2))),sump_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-04T13:38:50.000Z","updated_at":"2025-12-16T21:10:34.000Z","published_at":"2021-04-04T13:48:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem continues from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/18242/problems/49803\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 49803\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Kimberling shuffle uses a semi-infinite array of numbers in which the first row is simply the numbers 1, 2, 3, 4, 5,… Subsequent rows are generated by shuffling the previous row: the first number is the number to the right of the main diagonal of the previous row, the second is the number to the left of the main diagonal, the third is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e slots to the right of the main diagonal, etc. When numbers run out on the left of the main diagonal, the rest of the numbers are the remaining numbers of the previous row--\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexcept\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the number on the main diagonal of the previous row, which is expelled. The first few rows of the array are \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 2 3 4 5 6 7 8 9 10...\\n2 3 4 5 6 7 8 9 10 11...\\n4 2 5 6 7 8 9 10 11 12...\\n6 2 7 4 8 9 10 11 12 13...\\n8 7 9 2 10 6 11 12 13 14....]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth row of this array, up to and including the first number beyond which the numbers are in order. For example, given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e your function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[8 7 9 2 10 6 11]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2640,"title":"Find similar sequences","description":"Another problem inspired by a question on the \u003chttp://www.mathworks.com/matlabcentral/answers answers\u003e forum.\r\n\r\nGiven a matrix of positive integer numbers, find all the rows that are similar to the first rows and return these rows as a new matrix.\r\n\r\nRows are considered similar if the numbers common to both rows are in the exact same order with no other numbers in between. 0s in a row are always ignored and only occur at the end of the row.\r\n\r\nFor example:\r\n\r\n [3 1 5 0 0] and [4 2 1 5 0] are similar (1 5 are the common numbers and occur in the same order)\r\n [3 1 5 0 0] and [3 4 1 5 0] are not similar (3 1 5 are the common numbers, there's a 4 in between)\r\n ","description_html":"\u003cp\u003eAnother problem inspired by a question on the \u003ca href = \"http://www.mathworks.com/matlabcentral/answers\"\u003eanswers\u003c/a\u003e forum.\u003c/p\u003e\u003cp\u003eGiven a matrix of positive integer numbers, find all the rows that are similar to the first rows and return these rows as a new matrix.\u003c/p\u003e\u003cp\u003eRows are considered similar if the numbers common to both rows are in the exact same order with no other numbers in between. 0s in a row are always ignored and only occur at the end of the row.\u003c/p\u003e\u003cp\u003eFor example:\u003c/p\u003e\u003cpre\u003e [3 1 5 0 0] and [4 2 1 5 0] are similar (1 5 are the common numbers and occur in the same order)\r\n [3 1 5 0 0] and [3 4 1 5 0] are not similar (3 1 5 are the common numbers, there's a 4 in between)\u003c/pre\u003e","function_template":"function rows = findsimilar(m)\r\n rows = [];\r\nend","test_suite":"%%\r\nm = [3 1 5 0 0\r\n 3 4 1 5 0\r\n 4 2 1 5 0];\r\nsrows = [3 1 5 0 0;4 2 1 5 0];\r\nassert(isequal(findsimilar(m),srows))\r\n\r\n%%\r\nm = [3 1 5 0 0\r\n 1 2 5 0 0\r\n 1 3 4 1 5\r\n 2 1 5 0 0];\r\nsrows = [3 1 5 0 0; 2 1 5 0 0];\r\nassert(isequal(findsimilar(m),srows))\r\n\r\n%%\r\nm = [3 1 5 7 0\r\n 3 2 5 7 0\r\n 3 5 7 2 0\r\n 1 5 7 2 0\r\n 4 6 7 8 9\r\n 4 5 7 8 0\r\n 4 5 6 7 8];\r\nsrows = [3 1 5 7 0;1 5 7 2 0;4 6 7 8 9;4 5 7 8 0];\r\nassert(isequal(findsimilar(m),srows))\r\n\r\n%%\r\nm = [3 1 5 0 0\r\n 3 1 6 0 0\r\n 3 2 6 0 0\r\n 2 1 5 6 0];\r\nsrows = m;\r\nassert(isequal(findsimilar(m), srows))","published":true,"deleted":false,"likes_count":1,"comments_count":8,"created_by":999,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":140,"test_suite_updated_at":"2014-10-24T06:14:05.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2014-10-23T08:06:10.000Z","updated_at":"2026-03-17T14:55:43.000Z","published_at":"2014-10-23T08:06:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother problem inspired by a question on the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/answers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eanswers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e forum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix of positive integer numbers, find all the rows that are similar to the first rows and return these rows as a new matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRows are considered similar if the numbers common to both rows are in the exact same order with no other numbers in between. 0s in a row are always ignored and only occur at the end of the row.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ [3 1 5 0 0] and [4 2 1 5 0] are similar (1 5 are the common numbers and occur in the same order)\\n [3 1 5 0 0] and [3 4 1 5 0] are not similar (3 1 5 are the common numbers, there's a 4 in between)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61019,"title":"Find the logic and return the nth number (plus)","description":"This problem is the harder version of Problem 61015\r\ngiven a sequence of numbers arranged in the following order:\r\nA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\r\nWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\r\nnote: with this plus version you have to find the Nth number with extremely large N. Because the result can be extremely large, we will take the modulus of the nth number by 1e9+7\r\neg:\r\nn=5\r\n--\u003e output=9","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 252px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 126px; transform-origin: 408px 126px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem is the harder version of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61015\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 61015\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003egiven a sequence of numbers arranged in the following order:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enote: with this plus version you have to find the Nth number with extremely large N. Because the result can be extremely large, we will take the modulus of the nth number by 1e9+7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeg:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en=5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--\u0026gt; output=9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1e6;\r\ny_correct = 726671849;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1e10;\r\ny_correct = 671604939;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e11;\r\ny_correct = 126443114;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e12;\r\ny_correct = 570892696;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e13;\r\ny_correct = 41690901;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e14;\r\ny_correct = 719068874;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1e15;\r\ny_correct = 468399005;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4946338,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-20T06:24:55.000Z","updated_at":"2026-03-26T05:55:02.000Z","published_at":"2025-10-20T06:24:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is the harder version of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61015\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61015\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a sequence of numbers arranged in the following order:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA=0,1,3,4,9,10,12,13,27,28,30,31,36,37,......\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes n as a parameter, we expect the output to be the nth number of this sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003enote: with this plus version you have to find the Nth number with extremely large N. Because the result can be extremely large, we will take the modulus of the nth number by 1e9+7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeg:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--\u0026gt; output=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":24,"title":"Function Iterator","description":"Given a handle fh to a function which takes a scalar input and returns a scalar output and an integer n \u003e= 1, return a handle fh2 to a function which applies the given function n times.\n\nExamples:\n\n \u003e\u003e addOne = @(x)x+1;\n \u003e\u003e addTen = iterate_fcn(addOne, 10);\n \u003e\u003e addTen(3)\n ans =\n 13\n\n \u003e\u003e squarer = @(a) a^2;\n \u003e\u003e fh2 = iterate_fcn(squarer, 3);\n \u003e\u003e fh2(3)\n ans =\n 6561\n\n % Golden Ratio\n \u003e\u003e fh = @(y)sqrt(y+1);\n \u003e\u003e fh2 = iterate_fcn(fh,30);\n \u003e\u003e fh2(1)\n ans =\n 1.6180\n","description_html":"\u003cp\u003eGiven a handle fh to a function which takes a scalar input and returns a scalar output and an integer n \u003e= 1, return a handle fh2 to a function which applies the given function n times.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e \u003e\u003e addOne = @(x)x+1;\n \u003e\u003e addTen = iterate_fcn(addOne, 10);\n \u003e\u003e addTen(3)\n ans =\n 13\u003c/pre\u003e\u003cpre\u003e \u003e\u003e squarer = @(a) a^2;\n \u003e\u003e fh2 = iterate_fcn(squarer, 3);\n \u003e\u003e fh2(3)\n ans =\n 6561\u003c/pre\u003e\u003cpre\u003e % Golden Ratio\n \u003e\u003e fh = @(y)sqrt(y+1);\n \u003e\u003e fh2 = iterate_fcn(fh,30);\n \u003e\u003e fh2(1)\n ans =\n 1.6180\u003c/pre\u003e","function_template":"function fh2 = iterate_fcn(fh, n)\nfh2 = fh;\nend","test_suite":"%%\nnoOp = @(x)x;\nfh2 = iterate_fcn(noOp, 50);\nassert(isequal(fh2(pi),pi));\n\n\n%%\naddOne = @(x)x+1;\naddTen = iterate_fcn(addOne, 10);\nassert(isequal(addTen(3),13));\n\n%%\naddOne = @(x)x+1;\naddOne2 = iterate_fcn(addOne, 1);\nassert(isequal(addOne2(3),4));\n\n%%\nsquarer = @(a) a^2;\nfh2 = iterate_fcn(squarer, 3);\nassert(isequal(fh2(3),6561));\n\n%%\nfh = @(y)sqrt(y+1);\nfh2 = iterate_fcn(fh,30);\nassert(abs(fh2(1) - (1+sqrt(5))/2) \u003c 100*eps);","published":true,"deleted":false,"likes_count":61,"comments_count":27,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2244,"test_suite_updated_at":"2012-01-18T01:00:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:20.000Z","updated_at":"2026-03-15T20:56:03.000Z","published_at":"2012-01-18T01:00:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a handle fh to a function which takes a scalar input and returns a scalar output and an integer n \u0026gt;= 1, return a handle fh2 to a function which applies the given function n times.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e addOne = @(x)x+1;\\n \u003e\u003e addTen = iterate_fcn(addOne, 10);\\n \u003e\u003e addTen(3)\\n ans =\\n 13\\n\\n \u003e\u003e squarer = @(a) a^2;\\n \u003e\u003e fh2 = iterate_fcn(squarer, 3);\\n \u003e\u003e fh2(3)\\n ans =\\n 6561\\n\\n % Golden Ratio\\n \u003e\u003e fh = @(y)sqrt(y+1);\\n \u003e\u003e fh2 = iterate_fcn(fh,30);\\n \u003e\u003e fh2(1)\\n ans =\\n 1.6180]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52609,"title":"Easy Sequences 11: Factorial Digits without Trailing Zeros","description":"Here is an easy one...\r\nIt is not difficult to count the number of digits of the factorial of a given number. For example for 'n = 10', we have:\r\n \u003e\u003e length(num2str(factorial(10)))\r\n \u003e\u003e ans =\r\n 7\r\nBut 2 of those digits are just trailing zeros. So, for 10!, if we remove the trailing zeros, there would only be 5 digits left.\r\nWrite a function that outputs the number of digits of factorials excluding trailing zeros.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.65px; transform-origin: 407px 91.65px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere is an easy one...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354.5px 8px; transform-origin: 354.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is not difficult to count the number of digits of the factorial of a given number. For example for 'n = 10', we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 140px 8.5px; tab-size: 4; transform-origin: 140px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; length(num2str(factorial(10)))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut 2 of those digits are just trailing zeros. So, for 10!, if we remove the trailing zeros, there would only be 5 digits left.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 303px 8px; transform-origin: 303px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that outputs the number of digits of factorials excluding trailing zeros.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = numFacDigits(x)\r\n n = length_of(num2string(x!)) - '0';\r\nend\r\n","test_suite":"%%\r\nx = randi(3);\r\nn_correct = 1;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 10;\r\nn_correct = 5;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 100;\r\nn_correct = 134;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 5000;\r\nn_correct = 15077;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = intmax;\r\nn_correct = 18570655587;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = double(intmax)*10;\r\nn_correct = 207181392197;\r\nassert(isequal(numFacDigits(x),n_correct))\r\n%%\r\nx = 3:12;\r\nn_correct = uint64([2319 33161 431575 5315711 63157061 731570558 8315705525 93157055190 1031570551819 11315705518107]);\r\nassert(isequal(numFacDigits(10.^x),n_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":223089,"edited_at":"2023-06-03T06:48:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2023-06-03T06:48:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-24T11:46:25.000Z","updated_at":"2025-11-30T19:40:35.000Z","published_at":"2021-08-24T12:11:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere is an easy one...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is not difficult to count the number of digits of the factorial of a given number. For example for 'n = 10', we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e length(num2str(factorial(10)))\\n \u003e\u003e ans =\\n 7]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut 2 of those digits are just trailing zeros. So, for 10!, if we remove the trailing zeros, there would only be 5 digits left.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs the number of digits of factorials excluding trailing zeros.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56220,"title":"Easy Sequences 75: Easy as Pisano Pi","description":"Pisano period , of an integer , is the period in which the sequence of Fibonacci numbers modulo repeats. For example it is not hard to show that , and are , and , respectively:\r\n \r\nI have used Pisano period in the solutions of Problem 56050. Easy Sequences 73: Emergence of Fibonacci Insects and Problem 56065. Easy Sequences 74: Fibonacci Bank Account.\r\nIn this problem, we are asked to simply output the Pisano period of given integer .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.45px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 12.6px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 327.95px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 163.975px; transform-origin: 407px 163.975px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 37.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.9px; text-align: left; transform-origin: 384px 18.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pisano_period\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePisano period\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 28px; height: 16px;\" width=\"28\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 7px; transform-origin: 44.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e of an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 7px; transform-origin: 4px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123px 7px; transform-origin: 123px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eis the period in which the sequence of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFibonacci numbers \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26px 7px; transform-origin: 26px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emodulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 7px; transform-origin: 29.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e repeats. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.5px 7px; transform-origin: 11.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example it is not hard to show that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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style=\"width: 28px; height: 16px;\" width=\"28\" height=\"16\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 7px; transform-origin: 4px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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aeO9uv3ZuCsnlttjI3bMnhjjPYYwT1FcD/bcL/F+O4FhrP2f+zWsPPOjXYj84zg43+Vt24Gd+duOc0L40vX8n+oS+Fv0/Nfoa1x4zki+IFj4bTRbzyLkSq2pTfuot6R+ZtjUjMnHVhhQeMk5A6iuB8U61DF8QvDsn2DWZotNe5+1S2+jXc0ab4cLh0jIbJOPlJx3rvgcjNC2DqFFFFAGbPLjxVYxeZjdZXLeX5mN2Hg52+YM4z18tsZ+8mcSaVZs8uPFVjF5mN1lct5fmY3YeDnb5gzjPXy2xn7yZxJpUAFFFFAHL+I/GcmheINK0yHRby7S+uooJr0/u4LcSEhfmI/ePkfdXoOSRxm7r+p69YBjoOhW+pLHC0sjXN/8AZgSOiJiNyzHB+8FXkcnnGD8Q9TSO40S1jsdVuZLbVbW8lNppVzcIsSsdx3xxsuR/dzn2qPxx4juLmGy0XT7XWra01SHzLzU7fSLqVre3PBjVUjLLMwyPmA2DJPOAZ1cdN7tfgv8Ag/cPRT12svzf/AOs8P61B4i8OafrNokkcF9bpOiSrhlDDOCPUVo1Q0I2P9g2aaTby21lFEIoIZraSBo0X5QCkgDL07ir9aStzOxMb2VwrN16XytOibzPKze2q7vM2ZzcRjGfMTrnGNxznG2TPltpVm69L5WnRN5nlZvbVd3mbM5uIxjPmJ1zjG45zjbJny2kZpUUUUAFYfi3xHJ4Y0GW+ttJvNWnAby7a2XAJCliXc/LGgAOWP0AJIB3KwfGd/HZeFb+N4L2eS6t5YIks7Ka5YuyNjIiVio9zge9RUbUW1uVBJySZIusahe+FrDU9H0tLm6voYpVt5boRRxB1DEvJtJwAcfKhJOOMZIj8M+Ip9am1Sz1GxjsdQ0u5FvcRQ3HnxHciurI+1SQVYdVBByPesTTdVtG+Gml29/p/iJYo4ILO6FrZXlvcQOsaknagWYruAXdGGHPPG4iT4f2ktpe659it72DQpp0lsv7RgeO4kkKnzmbzAJmBbbhpfmPODtC1tJJTklt/wAMZRb5It7na0UUVBYVm+HJfO8K6VL5nm77KFvM8zzN+UHO7zJN2fXzHz/ebqdKs3w5L53hXSpfM83fZQt5nmeZvyg53eZJuz6+Y+f7zdSAaVFFFAEF9drYafPdyRTSrBGXMdvE0sj4GcKiglj6AVi+DfE8/irTr24utJl0mW0vpLQ200qu42gEFtvAJDDKgnHqa3Lu5Szs5bmZZWjiUuwhhaVyB6IgLMfYAmuB8I3NxqNr4r0+xGqaRe39/dXNnd3mj3EaojqirIPMRVJB52Eg8dMUle79Pxuv0uD2Xr+j/wCAamm+PV1X4iT+G7XTmNpFbzSJqRm4lkidEkRUx0VpMbs9VYY4zXX15fovhXxHoXxL0GH7TYzabY6JNb+fBpU0aBfNiPll2nf942N24k9G+U5yPUKrTlXz/Ni+0/66IKKKKQzN0uXzNR1lfM3+Xequ3zN2z/R4TjHmNt65xtj652nPmPpVm6XL5mo6yvmb/LvVXb5m7Z/o8JxjzG29c42x9c7TnzH0qACiiigDl9L8Zyap46u/D/8AYt5aQQWrTx3t1+7NwVk8ttsZG7Zk8McZ7DGCWWXiTX9V1rUrbTNE01rLTr77HJPcapJHI2FRiwjFuw6PwN/OO1Zn9twv8X47gWGs/Z/7Naw886NdiPzjODjf5W3bgZ35245zWZ400/SdXa9i0DwpdW/jA3Ki21NNHeErIrDExvAoQptGT8+SPlxk7aI6qLfn+e/3fmEt5fL8v8z1GikXO0buTjmloAKzZ5ceKrGLzMbrK5by/Mxuw8HO3zBnGevltjP3kziTSrNnlx4qsYvMxusrlvL8zG7Dwc7fMGcZ6+W2M/eTOJADSooooAK5fxH4zk0LxBpWmQ6LeXaX11FBNen93BbiQkL8xH7x8j7q9BySOM9RXDfEPU0juNEtY7HVbmS21W1vJTaaVc3CLErHcd8cbLkf3c59qPtR9V919Qfwu3Zm3rPiC6tdYt9G0PT49R1OaI3DJPc+RDBCDje7hXPLcABSSc9ACa1rF7ySyjbUoILe6I/eRW8xlRTns5VSeP8AZFeeeI9M0q6+IFp4g8ReHrjWNFvdHW3jVtIluzbzLIzjzLfYzqSrkAleCCDjPPRfDnTb7SfBNta6jFNb4lma3tp23PbW5lYwxMcnlUKjGeOnahfDrv8A8F/pqD30/rS/56HU0UUUAeJftV/8ks03/sNRf+iJ69trxL9qv/klmm/9hqL/ANET17bQAUUUUAFfOX7OMmop8ONT+xWtrKo1SQoZbloyW+zrwQI2wNwiGeeHc4+QB/o2vn39mj/kmuof9heT/wBEw18rxZJRyxtq+q3v+jRvQ+M9Tll1UeZ5NlZvjd5e+8dd3+s25/dHGcQ5643yddg8wll1UeZ5NlZvjd5e+8dd3+s25/dHGcQ5643yddg8y9RX5D7aH/Ptf+Tf/JHoWfcoyy6qPM8mys3xu8vfeOu7/Wbc/ujjOIc9cb5OuweYSy6qPM8mys3xu8vfeOu7/Wbc/ujjOIc9cb5OuweZeoo9tD/n2v8Ayb/5ILPuUZZdVHmeTZWb43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZdVHmeTZWb43eXvvHXd/rNuf3RxnEOeuN8nXYPMpat4l/s3WbfSrbSL/U7ueB7gJaGFQqKyqSTLIg6sOBmta2mee1jllt5LZ3UM0MpUvGfQ7SVz9CR71pJqMVJ0o2fm/y5ri62uVpZdVHmeTZWb43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZdVHmeTZWb43eXvvHXd/rNuf3RxnEOeuN8nXYPMvUVn7aH/Ptf+Tf/JDs+5Rll1UeZ5NlZvjd5e+8dd3+s25/dHGcQ5643yddg8wll1UeZ5NlZvjd5e+8dd3+s25/dHGcQ5643yddg8y9RR7aH/Ptf+Tf/JBZ9zzX4sSaht8JFbW2Lr4rsjbKblsSNum2hzs+QFRGSQGwWYYO0F/Q5ZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPM4b4r/e8Ef9jdYf8As9ekV+s8LSUsti1FLV7X/Vs8zE/GUJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMv0V9McxQlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8wlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8y/WXbeJdHvPEVzoVpfxTanaxCae3jyxiUnHzEcA5x8uc8g4ph5kss2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmX6KQFCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzL9FAGBo13rEvhyxlitbG4LWiMkjai7eZ8jlSWxLnOIcnzJP9ZIdz7AZdCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzDQpfO8O6bL5nm77SJvM8zzN+UHO7zJN2fXzHz/ebqb9N7gUJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMv0UgKEs2rjzPJsbJ8bvL33jru/wBZtz+6OM4hz1xvk67B5hLNq48zybGyfG7y99467v8AWbc/ujjOIc9cb5OuweZFqfiXR9G1GwsNSv4oLzUZRDawHLPKx9AMkD/aPA455rUp9LgUJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMv0UgKEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmZ9nd6w1/rKxWtjL5V2VjVtRfj9xlQRh9mf3JIwmPNkO1toeffqhp0vmX2qr5m/y7tV2+Zu2fuIjjHmNt65xtj652nPmOwCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzL9FIChLNq48zybGyfG7y99467v9Ztz+6OM4hz1xvk67B5hLNq48zybGyfG7y99467v9Ztz+6OM4hz1xvk67B5l+s7VtdsdFWH7c05eYkRxW1tJcSPgZJCRqzYHGTjAyM9RRcB0s2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmP0nVrHXNLh1HSbhbm0nGUkUEZwcEEHkEEEEEAgjBq5T2AoSzauPM8mxsnxu8vfeOu7/Wbc/ujjOIc9cb5OuweYSzauPM8mxsnxu8vfeOu7/Wbc/ujjOIc9cb5OuweZfopAYF3d6wniO3ihtbFgbS6ZI31F037XAUlcf8AXHJ8t9vmyDcu0CfQlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8wmlx4is4vMxutJ28vzMbsPDzt8wZxnr5bYz95M4kv0wKEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmX6KQFCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzJ7+/ttMsZby+l8qCIZZsEn0AAHJJOAAMkkgDmqekeJNM1ya4gsJJhcW20zQXNrLbyoG+62yVVbBwcHGOD6UwJZZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMv0UgKEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmZ+vXesQWG6C1sV/wBLhVGfUXi3ZnIUEgJjdiEEZb/WSDbLsCTb9UNZl8qxjbzPKzd2y7vM2ZzOgxnzE65xjcc5xtkz5bNbgEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmX6KQFCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzL9FAFCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzKOneMdI1W7W308ahMWkaITDS7kQ7lJDfvTHs4IIzuxmt2mBQlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8wlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8y/RSAoSzauPM8mxsnxu8vfeOu7/Wbc/ujjOIc9cb5OuweZn6Nd6xL4csZYrWxuC1ojJI2ou3mfI5UlsS5ziHJ8yT/WSHc+wGXfqhoUvneHdNl8zzd9pE3meZ5m/KDnd5km7Pr5j5/vN1L6AEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmX6KQFCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzL9YWreMtE0S7mtr+4nMtvEJrgW9nNcC3Q5w0hjRhGMAn5scAmgC9LNq48zybGyfG7y99467v8AWbc/ujjOIc9cb5OuweYSzauPM8mxsnxu8vfeOu7/AFm3P7o4ziHPXG+TrsHmXIZo7iCOaCRZYpFDo6HKspGQQe4p9MVyhLNq48zybGyfG7y99467v9Ztz+6OM4hz1xvk67B5hLNq48zybGyfG7y99467v9Ztz+6OM4hz1xvk67B5l+ikMwLO71hr/WVitbGXyrsrGrai/H7jKgjD7M/uSRhMebIdrbQ8+hLNq48zybGyfG7y99467v8AWbc/ujjOIc9cb5OuweYadL5l9qq+Zv8ALu1Xb5m7Z+4iOMeY23rnG2Prnac+Y9+mBQlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8wlm1ceZ5NjZPjd5e+8dd3+s25/dHGcQ5643yddg8y/RSAoSzauPM8mxsnxu8vfeOu7/AFm3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/wBZtz+6OM4hz1xvk67B5kVt4l0e88RXOhWl/FNqdrEJp7ePLGJScfMRwDnHy5zyDiq03jPQ7fUxYzXMyuZxbecbSb7P5p4Cefs8vdnjG7OeOvFPcP0L0s2rjzPJsbJ8bvL33jru/wBZtz+6OM4hz1xvk67B5hLNq48zybGyfG7y99467v8AWbc/ujjOIc9cb5OuweZfopAUJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMz7u71hPEdvFDa2LA2l0yRvqLpv2uApK4/wCuOT5b7fNkG5doE+/VCaXHiKzi8zG60nby/Mxuw8PO3zBnGevltjP3kziRgEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmEs2rjzPJsbJ8bvL33jru/1m3P7o4ziHPXG+TrsHmX6KQFCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzCWbVx5nk2Nk+N3l77x13f6zbn90cZxDnrjfJ12DzL9YereMtD0S6eDUrqWIxbPOlW1lkhg3HC+ZKqlI85B+Yjgg9Dmn5AXZZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMJZtXHmeTY2T43eXvvHXd/rNuf3RxnEOeuN8nXYPMi13xNo3hmyju9d1CKzhlkWOMtktIxOAFUZLdew4HPStSgChLNq48zybGyfG7y99467v9Ztz+6OM4hz1xvk67B5hLNq48zybGyfG7y99467v9Ztz+6OM4hz1xvk67B5l+ikBh6zd6xBbxtb2tiD9tgWMvqLw78zkKCQFxuxCCMt/rJBtl2BJujln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzMzU5fKgt28zys3tqu7zNmczoMZ8xOucY3HOcbZM+W3S1tDYuOxmyz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmaVFWUZss+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweYSz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hrGv6foSw/b2nZ52IihtbWW5lfAySI4lZsDjJxgZGTyKl0jWLDXdLj1DSrgT20mQH2lSCDhlZWAKsCCCCAQRzQBFLPrg8zydO098bvL337ru/wBZtz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmR+HvFOjeK7a5uPD96t7Da3DW0sioygSAAkAsBuGGBDDIOeDWtQBmyz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmaVFAHN6Bea5L4V02WGz0+43WUbRyPqbt5nyPtJbbLnOIcnzJP9ZJ8z7AZdKWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMPDkvneFdKl8zzd9lC3meZ5m/KDnd5km7Pr5j5/vN1OlQBmyz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmaVU9W1Wz0PSbnU9TlMNpaoZJZAjPtUf7Kgk/QCgCGWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMJZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8yLT/E+n6lFcSQx6jCltH5kjXml3NqNvPQyxru6dBk1FonjDSvELxjS11Jkli82OafSbqCJ04IIkkjVTnPHPPagC1LPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmEs+uDzPJ07T3xu8vffuu7/AFm3P7k4ziHPXG+TrsHmaVFAGbLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmZthea42o66sNnp83lXu2NX1N+P9HBUEbX2Z/ckjamPNkO1tokn6Ss3S5fM1HWV8zf5d6q7fM3bP9HhOMeY23rnG2Prnac+Y4ASz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/wBZtz+5OM4hz1xvk67B5mlRQBmyz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/wBZtz+5OM4hz1xvk67B5mlXO2/j3w5dalDZQ3spa4uGtobg2cwtppRnKJOU8pmyrDAY5II60dbB0uaEs+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweYSz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5lC58deHbTVX0+e+kEsdwttJKtrK0EUzY2xvOFMasdy/KWB5HqK6GjpcOtjNln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzCWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPM0qKAObvLzXE8VWsUNnp7Zsrto431N08za67SV2/9ccny32+bJ8y7QLjSln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzCeXHiqxi8zG6yuW8vzMbsPBzt8wZxnr5bYz95M4k0qAM2WfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMJZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8zSqC9vbXTbGa81C4itbaBS8s0zhERR3JPAFF7asCpLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmEs+uDzPJ07T3xu8vffuu7/AFm3P7k4ziHPXG+TrsHmP0TW9P8AEei22raNcfabG6UtDLsZNwBI6MARyD1FV9K8U6NresanpelXy3N5pTql5GqMBEzZAG4ja3KsDgnBBBwadnewdLkss+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweYSz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5kUXinRpvFk3hqG+V9Xht/tEtsqMdiZXktjaD8ynbnOGBxg1r0ulwM2WfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMzfEd5rkGnBobPT1/023WNn1N4t2bghQTtTG7EII3N/rJBtl2CObpKzdel8rTom8zys3tqu7zNmc3EYxnzE65xjcc5xtkz5bABLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmEs+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweZpUUAZss+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweYSz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5l+eeK2t5J7iRIoYlLySOwVUUDJJJ6ACsbR/GOi65qLWFhPcLdrCLgQXdlNbO8RON6CVF3rnjK5AyPUUeQdLlqWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMJZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8ylZ+N9BvtVh0+3upxNcM628ktnNHDcFckiKZkEcnAJ+VjkAkZFE/jfQbbVRYT3UySG4Fr55s5vs4mPAj8/Z5QbPGN2c8deKNw2Lss+uDzPJ07T3xu8vffuu7/AFm3P7k4ziHPXG+TrsHmEs+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweZpUUAZss+uDzPJ07T3xu8vffuu7/AFm3P7k4ziHPXG+TrsHmZugXmuS+FdNlhs9PuN1lG0cj6m7eZ8j7SW2y5ziHJ8yT/WSfM+wGXpKzfDkvneFdKl8zzd9lC3meZ5m/KDnd5km7Pr5j5/vN1IASz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/wBZtz+5OM4hz1xvk67B5mlRQBmyz64PM8nTtPfG7y99+67v9Ztz+5OM4hz1xvk67B5hLPrg8zydO098bvL337ru/wBZtz+5OM4hz1xvk67B5lKfxvoNtqosJ7qZJDcC1882c32cTHgR+fs8oNnjG7OeOvFJrHjbR9BkuV1NNUjS1TfNPHo13LCigbi3mpEUwB1OeOc9KV1a47O9i9LPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmEs+uDzPJ07T3xu8vffuu7/AFm3P7k4ziHPXG+TrsHmVLnxjpVrHbyNFq00dzAs8T2ujXc6lGGRkxxEKf8AZOCO4q9omtWHiLRrfVdImaeyuVLRSNE8ZYZIztYAjkdxVWYhks+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweYSz64PM8nTtPfG7y99+67v8AWbc/uTjOIc9cb5OuweZpUUgObsLzXG1HXVhs9Pm8q92xq+pvx/o4Kgja+zP7kkbUx5sh2ttEk+lLPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmGly+ZqOsr5m/y71V2+Zu2f6PCcY8xtvXONsfXO058x9KgDNln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzCWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPM0qzNZ8Q6boKwf2lNIJLlisEFvBJPNKQMnbHGrO2BySBx3oAWWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMJZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8yK+8VaPpfhptf1W7bT9OVdzSXsLwOPby3UPuOOFxk9gc0+78R6VY6BFrV1dhLCZI3ik8ti0m/GwKgG5mbIwoGSTjFADpZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8wln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzE0XxFpmvi4GmzSGS1cJPBcW8lvNCSNw3RyKrrkHIJGD2rToAzZZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8zNvLzXE8VWsUNnp7Zsrto431N08za67SV2/9ccny32+bJ8y7QLjpKzZ5ceKrGLzMbrK5by/Mxuw8HO3zBnGevltjP3kziQAJZ9cHmeTp2nvjd5e+/dd3+s25/cnGcQ5643yddg8wln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzNKigDNln1weZ5Onae+N3l77913f6zbn9ycZxDnrjfJ12DzCWfXB5nk6dp743eXvv3Xd/rNuf3JxnEOeuN8nXYPMk1jWrDQdP+2arceTDvWNcIzvI7HCoiKCzsT0VQSfSqNt4y0G50e+1MX/kWunEreG7hkt3tyADh45FV1JBBGRzkYzmgC1LPrg8zydO098bvL337ru/1m3P7k4ziHPXG+TrsHmEs+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweZTsPGmi6lJdRWz3q3FpALmS1n024hnMRJAdInjDuMgj5QeeOtMsvHGiX2s22lR/2lBe3Su0Ed5pN1beYEGWIaWNRxkd+49aAL8s+uDzPJ07T3xu8vffuu7/Wbc/uTjOIc9cb5OuweYSz64PM8nTtPfG7y99+67v8AWbc/uTjOIc9cb5OuweZpUUAeE/tRSXz/AAysheW9vFENaj8torhpGb93cjkFFx8gjPU8sw6KGb3avEv2q/8Aklmm/wDYai/9ET17bQAUUUUAFfPv7NH/ACTXUP8AsLyf+iYa+gq+ff2aP+Sa6h/2F5P/AETDXyXF/wDyK36o6MP8Z7DRRRX42egFFFFAHF63Y3F/8UdOjtdUu9MZdIuGMtosTMw86Lg+ajjH0GeOtbketQ2esLot3LJLOsMPlysu552feCSqKAuPLyWwFG7txWxWRceGrK48RprgaaLUERIhLGVB8tSxMZ45Vt/IPopGCAa7vb06kVCqrKMbK297337feQ07uS/rS36GvRRRXCWFFFFAHn/xX+94I/7G6w/9nr0ivN/iv97wR/2N1h/7PXpFfr3Cf/Irj6s8vFfxAooor6o5Qrj7aytbH4siOxtobaNtFkkZIYwgLNcAsxA7knJPeuwrFXwZ4XXUBfr4b0gXgl84XAsYvMEmc7923O7POeuaFpJP1/KwPWLXp+dzaooooAKKKKAKGhS+d4d02XzPN32kTeZ5nmb8oOd3mSbs+vmPn+83U36oaFL53h3TZfM83faRN5nmeZvyg53eZJuz6+Y+f7zdTfoe4wooooEcf44srVLrQ71LaFbqTWrON5xGA7KGYhS3UgEnA9zXYVk6l4V8Pa1dC61jQdMv7gKEEt1ZxyvtHQZYE45PFaVvbwWdrFbWkMcEEKBI4olCqigYAAHAAHahaRt53/L/ACB6u/l/n/mSUUUUAFUNOl8y+1VfM3+Xdqu3zN2z9xEcY8xtvXONsfXO058x79UNOl8y+1VfM3+Xdqu3zN2z9xEcY8xtvXONsfXO058xwZfooooEFZHiLxBF4f09ZPJe7vLhvKs7KI/vLmU9FX0Hct0UAk9K16z9V8P6NroiGt6TY6kIc+X9stkl2ZxnG4HGcD8qBq3UqeENDl8PeHIrS7kjku5JJLm6eJcIZZXLvtH90FsD2ArbqnpmkabotqbbR9PtdPgLFzFawLEpY98KAM8DmrlN6sXqFFFFIChNLjxFZxeZjdaTt5fmY3YeHnb5gzjPXy2xn7yZxJfqhNLjxFZxeZjdaTt5fmY3YeHnb5gzjPXy2xn7yZxJfoGFFFFAivf3At7N2+1QWsj4jiluBlBIx2oCNy7ssQNoIJ6A81yOiC8tPihfwa1PDf6hc6XHItzaoYY4YkkIEfkksVJZ2bcXO7kADbz2F3aW1/aSWt9bxXNvKu2SGZA6OPQqeCKr6XomlaHC8Oi6ZZ6dFI250tLdIlY9MkKBk01o7/1/X/DDe1v6/r/hy9RRRSEFUNZl8qxjbzPKzd2y7vM2ZzOgxnzE65xjcc5xtkz5bX6oazL5VjG3meVm7tl3eZszmdBjPmJ1zjG45zjbJny2FuMv0UUUCCiiigDz2WKbwb/Yj+H9fuNR0/UdUEI0+dYJEdJmZ3aJ0RXyuS+SzDaDXoVZlj4a0LTNQkv9N0XTrS8lyJLi3tEjkfJycsBk5PJrTp9LDe9wooopCCqGhS+d4d02XzPN32kTeZ5nmb8oOd3mSbs+vmPn+83U36oaFL53h3TZfM83faRN5nmeZvyg53eZJuz6+Y+f7zdSdBl+iiigQV5hrlpqur+JvFZ8M6lHpKW0EUGpxzup+1nyw4ZSVJg/dkp5nzA8/ICoavT6y9S8M6DrN0l1rGiadf3EahUlurSOV1AOQAWBIGST+NL+v67+hUXYZ4Su7a+8G6PdWFq1pazWULQ27NuMSFBhc98Dv3rXooqpO7bISsrBRRRSGUNOl8y+1VfM3+Xdqu3zN2z9xEcY8xtvXONsfXO058x79UNOl8y+1VfM3+Xdqu3zN2z9xEcY8xtvXONsfXO058x79DGFFFFAjj7aytbH4siOxtobaNtFkkZIYwgLNcAsxA7knJPeqPj+a7k0OTUjqNje6Fa3kLvYW6GOaZo5VHl+fvZSRIPuCMElduQea6RfBnhddQF+vhvSBeCXzhcCxi8wSZzv3bc7s8565qb/AIRnQf7Y/tb+xNO/tLdv+2/ZI/O3YxnfjdnHGc046KPl/ncb3b7/AOVjUByKKKKQgqhNLjxFZxeZjdaTt5fmY3YeHnb5gzjPXy2xn7yZxJfqhNLjxFZxeZjdaTt5fmY3YeHnb5gzjPXy2xn7yZxIIZfooooEFch41uG12OTwZpYEl1qMW2+lxlbG2bhnb/aYZVF7nnoprr6xr/wf4a1W9e81Tw7pN7dSY3z3FjHI7YGBlmUk8ACjrqNO2pjfEjTrNPAN9OLWEz21usUMxjBeNDImVDdQDgZHfArsqyr7wt4f1OG3i1LQtNvI7VPLt0uLOOQQrx8qgj5RwOB6Crthp9lpVklnpdnBZWsedkFvEsaLk5OFUADkk09xbFiiiikBT1OXyoLdvM8rN7aru8zZnM6DGfMTrnGNxznG2TPlt0tc1qcvlQW7eZ5Wb21Xd5mzOZ0GM+YnXOMbjnONsmfLbpa2hsaR2CiiirKM3V5b1/Ks9G1PT7LUJMyKt5bm43xrgMRGssZ4LL82SBnGORXnFh/a83gC/wBF0bTrrUZjrk9pq13Z3UO+ZGYvPLHvaNQW3FNoOUJPLFefStW0HSNfhjh13SrHUoo23Il5bJMqNjGQGBwas2lnbafZxWlhbxWttCoSKGFAiIo6AKOAPpSt3/rVf5Wt1Hfa39b/AOe55/8ACq4c6n4vthol1pkEesZRZmhKxYt4VEWI5G5AAPGVwRznIHo1Q29la2jzva20MD3EnmzNHGFMr4A3NjqcADJ5wBU1Ve6XovwRNrNhRRRSGZvhyXzvCulS+Z5u+yhbzPM8zflBzu8yTdn18x8/3m6nSrN8OS+d4V0qXzPN32ULeZ5nmb8oOd3mSbs+vmPn+83U6VABWV4n02x1nw1e6Zqt01paXiCF5kdUZdxAGCwIySQBkHk1q1DeWdtqFnLaX9tDdW0y7ZYZ4w6OvoVPBFJjRxVvd3th4yv/AAzq2vS6rpj6O15Lc3aQRy2XzbMM0aIm1l3EZXI2NyRUdgl94N8U+GfD1lrt1rGmXtvLCLa8jg8y2jhjBSVXijQleiHduyWXn16/TfD+jaNZy2mj6TY2FtMS0kNrbJEjkjBJVQAeOKZpHhrQtAaVtB0XTtMMwAlNlaJDvx0ztAzjJ6+tUtP69fyuS1/X3f5GnRRRSGFZuly+ZqOsr5m/y71V2+Zu2f6PCcY8xtvXONsfXO058x9Ks3S5fM1HWV8zf5d6q7fM3bP9HhOMeY23rnG2Prnac+Y4BpUUUUAI7bEZiCcDOB1NeJaYL2DQvDevSXaXHhKfV45LLQ/NXzrZpZQsX74L+98tyzeVxt5Bd9gr26sm38K+HrXWG1a10HTIdSdmdr2OzjWYs33iXA3ZOTk55zQtJX/r+vPoD1i1/X9fmeb+NNG1/QfAXiLRLdNKuLHV7yVrKd7p0ujJcSbxEIRGVd95IBEg4wccEV65GCsahuoABrNg8MaDa6y+r22iabDqbli97HaRrMxbqS4G457881qULSKQPV3/AK1CiiigDNnlx4qsYvMxusrlvL8zG7Dwc7fMGcZ6+W2M/eTOJNKs2eXHiqxi8zG6yuW8vzMbsPBzt8wZxnr5bYz95M4k0qACoLyxtNQgEN/aw3UQdZBHPGHUMpyrYPcEAg9iKnqrqWl2GsWL2Wr2Ntf2rkFoLqFZUYg5GVYEHB5oA4Pw5PrMHwRjPhm0a71RjPHAqNGCha4cGT52VTtBLYJGSMZGaxvCE17onjTxPZ6L4T1JJbbRbMQW11cWwLSKJyu91mYZkYn5hnncWxxn03SPDeh+H/N/sHRtP0zzseb9itUh8zGcbtoGcZPX1NXEsrWK8mu4raFLmdVSWdYwHkVc7QzdSBk4z0yaLaNB0t/W6f6HkfhZb/S/itotvfeH9UivZtHu3vrid7XMssk8LST4SdsICAoAywG0AEAkexVCbK1a+S9a2hN2kZiWcxjzFQkEqG6gEgHHTgVNTv7qXa/5ti6t/wBbBWbr0vladE3meVm9tV3eZszm4jGM+YnXOMbjnONsmfLbSrN16XytOibzPKze2q7vM2ZzcRjGfMTrnGNxznG2TPlshmlRRRQA13SKNpJGVEUFmZjgADqSa4zQifFfjL/hLhH5Wk2NrJZaY7jDXYdlaS49ozsVU9RuboRXY3FvDd20ttdwxzwTIUkikUMrqRgqQeCCO1ZOneC/C+j3yXuk+G9IsbqMEJPbWEUbrkYOGVQRxxQt7g9rHK+I5r3+3/C+rX2pWGq6RJqyDT7awjMLbpUZY5S5eQThVZjhRGCCW6DFHxEmvJdBl1Q6np994ftL2CSTT7ZDHPO8cygx/aN7KSJR9wRgkrs3A5NdfY+FfD2l6k+o6boOmWd9Ju33VvZxxytuOWy4AJyevrR/wivh7+2v7Y/sHTP7U3b/ALd9jj8/djGfMxuzjjOaFpb1v+X37b/5A9b/ANd/u/ruaoORmiiigArN8OS+d4V0qXzPN32ULeZ5nmb8oOd3mSbs+vmPn+83U6VZvhyXzvCulS+Z5u+yhbzPM8zflBzu8yTdn18x8/3m6kA0qKKKAPO/iJNeS6DLqh1PT77w/aXsEkmn2yGOed45lBj+0b2UkSj7gjBJXZuBya0fHzHWH0nwhATnWp915jqlnFh5c/7x2R/9tK3v+EV8Pf21/bH9g6Z/am7f9u+xx+fuxjPmY3ZxxnNXvsNp/aAv/ssP2wReSLjyx5nl5zs3dduecdM0LZet/wCv62B7u39f1+ZznxA1Cez8MLpmkt5Wo6xMmm2e3gxmThnGOyRh3/4DXQaXp1to+k2mm2MYjtrSFYYlHZVGB/KnzWNpcXdvdT2sMtxbbjBM8YLxbhhtpPK5HBx1qehdfP8Ar/P7w7f1/XQKKKKAM3S5fM1HWV8zf5d6q7fM3bP9HhOMeY23rnG2Prnac+Y+lWbpcvmajrK+Zv8ALvVXb5m7Z/o8JxjzG29c42x9c7TnzH0qACvPdXtLy9+NSQR61daOraCDbyW0cLPIwnPmKvmo4wAYywAz93kDr6FVDVtB0jX4Y4dd0qx1KKNtyJeWyTKjYxkBgcGl1T/rZr9R9Gv63T/Q4zTLt/FHwlutR15LXUbq0jvktr7yFxL5fmRLcIOillGcrgcnGAaq3jCLQfhdPOyrapd2qyF+gdrORY//AB8gD3Iru9R8PaLrFlDZ6vpFhf2sBBigurZJUjIGBtVgQOOOO1R2/hbw/aaTPpVpoWmwadcHdNZxWcawynjlkAweg6jsKa0bfp+F/wA7iev4/j/kYOmMlx8Z9dltMNHb6RaW9yy9BN5krhSfUIwOPRh689nVTTNJ07RbMWejafa6fbBiwgtYViQE9TtUAZq3Rskv67hu2/62sFZs8uPFVjF5mN1lct5fmY3YeDnb5gzjPXy2xn7yZxJpVmzy48VWMXmY3WVy3l+Zjdh4OdvmDOM9fLbGfvJnEgBpUUUUAc74v0O/1ZNKu9Ha2N9pN+t5FDdsUimG1kZGZVYr8rkhgpwQOK851S6mmk8e6hr1nbNDOmn6cV06/JjiuQ7KCZ2jGChkiZm2Hb0w2OfXNU0fTNcs/smtadaajbbg/k3cCypuHQ7WBGeetEOkabb6R/ZVvp9rFp3ltF9jSBVh2HOV2AYwcnIx3pW0a/rp/l+o77f11ucL4bg1fSficln4t1CLW9SutILWt7AohEEUbxiRGhA6u7BvMyckYCoBitPw3/xUPjvWvEbfNa2JOkacexCENcSD6yYTI/55V0WkeHdE0BZV0LR7DTBNgyiytUh346Z2gZxk9fWrVnY2mnWq2un2sNrboSVhgjCIuTk4A4GSSfxqr7eV/wAf+Bp577k9/l+H/BS/InooopDPEv2q/wDklmm/9hqL/wBET17bXiX7Vf8AySzTf+w1F/6Inr22gAooooAK+Vfgb8N/CnjHwReah4j0r7ZdR6i8CSfaZY8II42AwjAdWPPXmvqqvn39mj/kmuof9heT/wBEw18vxTXq0Mtc6MnF3WqbT/A3oJOdmdB/wov4c/8AQu/+T1x/8co/4UX8Of8AoXf/ACeuP/jldzf3senabc3s4ZoraF5nCDLEKCTjPfivP4vjh4cla326Xr4W8i32T/2cxF44AzHFg/MwJwf4cjr0NfmeHxOc4lOVGrUkl2lL/M7JRpx3SJ/+FF/Dn/oXf/J64/8AjlH/AAov4c/9C7/5PXH/AMcq3F8V/DsnhGTX3S+iWO7NibGS3xdG5/54hAfve2frii0+K/h6fRdXv76LUNKk0dVa7sdQtjFcIG+58mTncSAOe4zitPaZ5r79TR2+KW+i792vvQWpaaIqf8KL+HP/AELv/k9cf/HKP+FF/Dn/AKF3/wAnrj/45XOQ/Eae9+JOo6hFDrFhZWPhaa6bS9SjaH96kgIfy8lTlcYYdjVW+8ReI9F8C+AYl8UtpU+uO0l9qd8qT7A4DjPm8ADdjGRjAruVLOOaMXiZJu28pdpSe19kuid7qxF6fRf0kn+p1v8Awov4c/8AQu/+T1x/8co/4UX8Of8AoXf/ACeuP/jldL4Qa4fw3C914kg8TOzuRqVvFHGkg3EYAjJXjGOD2pvi7xhpvgrTLe/1hLhoLi6S1Bt495VmBIJGc4+U9Mn2ryvr2aSrewp15yd7aSlr99n96TNFGDV7HOf8KL+HP/Qu/wDk9cf/AByj/hRfw5/6F3/yeuP/AI5UGp+NYvGngHxVFoS6xour6TbGV4bhDbXMTBTIh+Uk4baRjPI7c12fhbVjr3hHSdVddr3lnFMw9GZQSPzrWtic2oU+epXmnezXNLTRNdeq2ElTbskuv4HknxB+FHgvQ28Lf2Xo3kfb/EVpZXP+lTN5kL7ty/M5xnA5GD712v8Awoj4b/8AQuf+T1x/8cqL4r/e8Ef9jdYf+z16RX6NwziK1fLlOrNyd3q22/xODEpRnZHnn/CiPhv/ANC5/wCT1x/8co/4UR8N/wDoXP8AyeuP/jleh0V9JdnNdnnn/CiPhv8A9C5/5PXH/wAco/4UR8N/+hc/8nrj/wCOV6HXCaR4x1+6+LNx4Z1XTLSxshpjX0AWQyTnEoQF2B2jPJ2gHHHNNNt2DW1yv/woj4b/APQuf+T1x/8AHKP+FEfDf/oXP/J64/8Ajleh0UrsLs88/wCFEfDf/oXP/J64/wDjlH/CiPhv/wBC5/5PXH/xyvQ6KLsLs8x0n4JfDm/0WyvH8Pxu1xbxylor6fYxZQcrtndcc8Ydx6M3U2/+FEfDf/oXP/J64/8AjldpoUvneHdNl8zzd9pE3meZ5m/KDnd5km7Pr5j5/vN1N+m27hdnnn/CiPhv/wBC5/5PXH/xyj/hRHw3/wChc/8AJ64/+OV6HRSuwuzzz/hRHw3/AOhc/wDJ64/+OUf8KI+G/wD0Ln/k9cf/AByrHjjxjr/hvxBoVvYaZaf2ZqGpwWM11cyFnfzDyI0UjGAD8zd+x613dO7tcHdOx55/woj4b/8AQuf+T1x/8co/4UR8N/8AoXP/ACeuP/jleh0UrsLs88/4UR8N/wDoXP8AyeuP/jlVLP4JfDm4u9Qibw/GwtrgRKEvp8qDFG+GxOxzlyeQhwR8pGHf06qGnS+Zfaqvmb/Lu1Xb5m7Z+4iOMeY23rnG2Prnac+Y7uwuzi/+FEfDf/oXP/J64/8AjlH/AAoj4b/9C5/5PXH/AMcr0Oildhdnnn/CiPhv/wBC5/5PXH/xyj/hRHw3/wChc/8AJ64/+OV6HXPeK7jxbHHbxeC7PS5Zn3NNcapK6xxAYwNqfMxbJ56DHPWjmY1dnO/8KI+G/wD0Ln/k9cf/AByj/hRHw3/6Fz/yeuP/AI5Wv8NfF11428FQavqFrFbXPmyQyrCxMbMhwWXPOD9T9TXWU3dOwrs88/4UR8N/+hc/8nrj/wCOUf8ACiPhv/0Ln/k9cf8AxyvQ6KV2F2eYyfBL4cprVtZjw/GFlt5ZSpvp95KNGAR+/DYG85wjDkZZOA9v/hRHw3/6Fz/yeuP/AI5XaTS48RWcXmY3Wk7eX5mN2Hh52+YM4z18tsZ+8mcSX6d2F2eef8KI+G//AELn/k9cf/HKP+FEfDf/AKFz/wAnrj/45XodFK7C7PPP+FEfDf8A6Fz/AMnrj/45R/woj4b/APQuf+T1x/8AHK6Lx14qXwX4Nvtba3Ny8AVYoQceZIzBVBPYZPNYHhjxd4qTxunhjx1Y6XFcXVib20n0x5NhAIDIwfJ3DOcjjjv1ppt7f11/IbulcZ/woj4b/wDQuf8Ak9cf/HKP+FEfDf8A6Fz/AMnrj/45XodFK7Fdnnn/AAoj4b/9C5/5PXH/AMcqpqfwS+HNlaJKnh+NC1xDFmS+nxh5VQj5p0GSGwOSc4wrnCN6dVDWZfKsY28zys3dsu7zNmczoMZ8xOucY3HOcbZM+WzTdwuzi/8AhRHw3/6Fz/yeuP8A45R/woj4b/8AQuf+T1x/8cr0Oildhdnnn/CiPhv/ANC5/wCT1x/8co/4UR8N/wDoXP8AyeuP/jleh0UczC7PPP8AhRHw3/6Fz/yeuP8A45R/woj4b/8AQuf+T1x/8cqsPGvjbSfHWhab4o0nR4bDXpZIoIrOeR7i3KgH52Pyt1/hGPf19Mp62vcbunY88/4UR8N/+hc/8nrj/wCOUf8ACiPhv/0Ln/k9cf8AxyvQ6KV2K7PPP+FEfDf/AKFz/wAnrj/45VTSfgl8Ob/RbK8fw/G7XFvHKWivp9jFlByu2d1xzxh3HozdT6dVDQpfO8O6bL5nm77SJvM8zzN+UHO7zJN2fXzHz/ebqXd2C7OL/wCFEfDf/oXP/J64/wDjlH/CiPhv/wBC5/5PXH/xyvQ6KV2F2eef8KI+G/8A0Ln/AJPXH/xyj/hRHw3/AOhc/wDJ64/+OV6HXnXxE8WeNvCcF7rOmaZoraDp/l+YbuaQ3FyGKglAuFTBYr82TxnB6Ucz7jSb0Q7/AIUR8N/+hc/8nrj/AOOUf8KI+G//AELn/k9cf/HK7yxuftun291sMfnxLJsPVcgHH61PTfMnZkqV1dHnn/CiPhv/ANC5/wCT1x/8co/4UR8N/wDoXP8AyeuP/jleh0Ursd2eY2fwS+HNxd6hE3h+NhbXAiUJfT5UGKN8NidjnLk8hDgj5SMO9v8A4UR8N/8AoXP/ACeuP/jldpp0vmX2qr5m/wAu7Vdvmbtn7iI4x5jbeucbY+udpz5j36d2F2eef8KI+G//AELn/k9cf/HKP+FEfDf/AKFz/wAnrj/45XodFK7C7PPP+FEfDf8A6Fz/AMnrj/45R/woj4b/APQuf+T1x/8AHK3vHuu6z4d8K3eo6Bp0F5NbwyTO9zLtihVF3EkD5mJxgAY9yKv+FdUn1zwhpGq3axpPe2UVxIsQIUM6BiACScZPqaabab7A7q3mcl/woj4b/wDQuf8Ak9cf/HKP+FEfDf8A6Fz/AMnrj/45XodFK7C7PPP+FEfDf/oXP/J64/8AjlVJPgl8OU1q2sx4fjCy28spU30+8lGjAI/fhsDec4RhyMsnAf06qE0uPEVnF5mN1pO3l+Zjdh4edvmDOM9fLbGfvJnEjuwuzi/+FEfDf/oXP/J64/8AjlH/AAoj4b/9C5/5PXH/AMcr0Oildhdnnn/CiPhv/wBC5/5PXH/xyj/hRHw3/wChc/8AJ64/+OV6HXPeOvFS+C/Bt9rbW5uXgCrFCDjzJGYKoJ7DJ5o5mNXbsc7/AMKI+G//AELn/k9cf/HKP+FEfDf/AKFz/wAnrj/45T/DHi7xUnjdPDHjqx0uK4urE3tpPpjybCAQGRg+TuGc5HHHfrXoFN3XUV2eef8ACiPhv/0Ln/k9cf8Axyj/AIUR8N/+hc/8nrj/AOOV6HRSuwuzzO++CPw4tIoXHh6Nd91BCTJfT4IeVEI+adBkhsDknOMK5wjbn/DPnwx/6Fn/AMn7n/45XSanL5UFu3meVm9tV3eZszmdBjPmJ1zjG45zjbJny26WtYaouOx5t/wz58Mf+hZ/8n7n/wCOUf8ADPnwx/6Fn/yfuf8A45XpNFWUebf8M+fDH/oWf/J+5/8AjlH/AAz58Mf+hZ/8n7n/AOOV6TXn+jeNvEV38Ybnwtq+lWdhYDS2v7cLIZLg4lEYLsDsGeTtAOOPmoWrt/WgdLlb/hnz4Y/9Cz/5P3P/AMco/wCGfPhj/wBCz/5P3P8A8cr0migDzb/hnz4Y/wDQs/8Ak/c//HKP+GfPhj/0LP8A5P3P/wAcr0migDynRPgR8M9R0DT72Xw5HI9zaxzM8V/PsYsoJK7Z3XHPGHcejN1N3/hnz4Y/9Cz/AOT9z/8AHK7fw5L53hXSpfM83fZQt5nmeZvyg53eZJuz6+Y+f7zdTpUAebf8M+fDH/oWf/J+5/8AjlH/AAz58Mf+hZ/8n7n/AOOV6TRQB5t/wz58Mf8AoWf/ACfuf/jlH/DPnwx/6Fn/AMn7n/45Vnx7428ReF/Efh+20/SrP+y9R1S3sJru6kLO/mnkRopG3AB+Zj1/hI5r0Chaq/yB6Ox5t/wz58Mf+hZ/8n7n/wCOUf8ADPnwx/6Fn/yfuf8A45XpNFAHm3/DPnwx/wChZ/8AJ+5/+OVSsPgR8M7q91OJ/DkbC1ulhUJfz5UGGN8NidjnLk/MEOCPlIw7+rVm6XL5mo6yvmb/AC71V2+Zu2f6PCcY8xtvXONsfXO058xwDiP+GfPhj/0LP/k/c/8Axyj/AIZ8+GP/AELP/k/c/wDxyvSaKAPNv+GfPhj/ANCz/wCT9z/8co/4Z8+GP/Qs/wDk/c//AByvSa5zxfceMYoraLwNY6TNNJvaa41WZ1ihAxhdqfMxbJ5yAMc9aTdhrU5n/hnz4Y/9Cz/5P3P/AMco/wCGfPhj/wBCz/5P3P8A8crZ+F/jK78d+BbfWdRtIrW682SCVYGJjZkbBZc84Ppk/U12FU1YR5t/wz58Mf8AoWf/ACfuf/jlH/DPnwx/6Fn/AMn7n/45XpNFIDymX4EfDNNftLIeHIwk1rPMUN/PvJRogCP34bA8w5wjDkZZOA93/hnz4Y/9Cz/5P3P/AMcrt55ceKrGLzMbrK5by/Mxuw8HO3zBnGevltjP3kziTSoA82/4Z8+GP/Qs/wDk/c//AByj/hnz4Y/9Cz/5P3P/AMcr0migDzb/AIZ8+GP/AELP/k/c/wDxyj/hnz4Y/wDQs/8Ak/c//HK6Xx/4uTwN4Iv9ea2N09uFWGAHHmSOwVQT2GSM+1c74V8Z+Lk8eJ4V8f2GkxXN5YG+s7jSnk2EKwDRsHydwznI4475zQtXb+tr/kD0V/67DP8Ahnz4Y/8AQs/+T9z/APHKP+GfPhj/ANCz/wCT9z/8cr0migDzb/hnz4Y/9Cz/AOT9z/8AHKpat8CPhnY2UcsfhyNC11bwkyX8+MPMiEfNOgyQxA5JyRhXOEb1as3XpfK06JvM8rN7aru8zZnNxGMZ8xOucY3HOcbZM+WwBxH/AAz58Mf+hZ/8n7n/AOOUf8M+fDH/AKFn/wAn7n/45XpNFAHm3/DPnwx/6Fn/AMn7n/45R/wz58Mf+hZ/8n7n/wCOV6TQenFAHm3/AAz58Mf+hZ/8n7n/AOOUf8M+fDH/AKFn/wAn7n/45VUeOvHej+P/AA/pnizR9Eg07xBLJFbw2U8klzbFQD+8Y/I3XnaMc9Rjn1OjpcHo7Hm3/DPnwx/6Fn/yfuf/AI5R/wAM+fDH/oWf/J+5/wDjlek0UAebf8M+fDH/AKFn/wAn7n/45VLRPgR8M9R0DT72Xw5HI9zaxzM8V/PsYsoJK7Z3XHPGHcejN1Pq1ZvhyXzvCulS+Z5u+yhbzPM8zflBzu8yTdn18x8/3m6kA4j/AIZ8+GP/AELP/k/c/wDxyj/hnz4Y/wDQs/8Ak/c//HK9JooA82/4Z8+GP/Qs/wDk/c//AByj/hnz4Y/9Cz/5P3P/AMcr0mvM/iV4w8d+D7e+1vStK0NvD2m+WZTeTyG4ugxUExhcKmCxX5snjOD0pNpbjSb2H/8ADPnwx/6Fn/yfuf8A45R/wz58Mf8AoWf/ACfuf/jleg2F19u022u/LMfnxJLsbqu4A4/WrFU007MlNNXR5t/wz58Mf+hZ/wDJ+5/+OUf8M+fDH/oWf/J+5/8Ajlek0UhnlNh8CPhndXupxP4cjYWt0sKhL+fKgwxvhsTsc5cn5ghwR8pGHe7/AMM+fDH/AKFn/wAn7n/45Xb6XL5mo6yvmb/LvVXb5m7Z/o8JxjzG29c42x9c7TnzH0qAPNv+GfPhj/0LP/k/c/8Axyj/AIZ8+GP/AELP/k/c/wDxyvSaKAPNv+GfPhj/ANCz/wCT9z/8co/4Z8+GP/Qs/wDk/c//AByug+IXiDW/DXhG81Lw7ptvez28Mk0j3Uu2KFEXcSQPmcnGAox7kVo+EtWn17wXo2r3iRpcX9jDcSrECEDOgYgAknGT3JoWt/L9QelvM47/AIZ8+GP/AELP/k/c/wDxyj/hnz4Y/wDQs/8Ak/c//HK9JooA82/4Z8+GP/Qs/wDk/c//AByqUvwI+Gaa/aWQ8ORhJrWeYob+feSjRAEfvw2B5hzhGHIyycB/VqzZ5ceKrGLzMbrK5by/Mxuw8HO3zBnGevltjP3kziQA4j/hnz4Y/wDQs/8Ak/c//HKP+GfPhj/0LP8A5P3P/wAcr0migDzb/hnz4Y/9Cz/5P3P/AMco/wCGfPhj/wBCz/5P3P8A8cr0mub8f+Lk8DeCL/XmtjdPbhVhgBx5kjsFUE9hkjPtSbsNK7sc1/wz58Mf+hZ/8n7n/wCOUf8ADPnwx/6Fn/yfuf8A45T/AAr4z8XJ48Twr4/sNJiubywN9Z3GlPJsIVgGjYPk7hnORxx3zmvRqfS5Nzzb/hnz4Y/9Cz/5P3P/AMco/wCGfPhj/wBCz/5P3P8A8cr0migZ8yftAfC3wd4I8A2WpeGNH+w3cupxwPJ9qmkyhilYjDuR1VecZ4r6brxL9qv/AJJZpv8A2Gov/RE9e20AFFFFABXz7+zR/wAk11D/ALC8n/omGvoKvkH4QfF/QPAHhG60rWbTUp5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data-image-state=\"image-loaded\" width=\"649\" height=\"201\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.9px; text-align: left; transform-origin: 384px 18.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129px 7px; transform-origin: 129px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI have used Pisano period in the solutions of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56050-easy-sequences-73-emergence-of-fibonacci-insects\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 56050. Easy Sequences 73: Emergence of Fibonacci Insects\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56065-easy-sequences-74-fibonacci-bank-account\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 56065. Easy Sequences 74: Fibonacci Bank Account\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 18.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 9.45px; text-align: left; transform-origin: 384px 9.45px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.5px 7px; transform-origin: 258.5px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn this problem, we are asked to simply output the Pisano period of given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = pisanoPi(n)\r\n y = x;\r\nend","test_suite":"%%\r\nn = 1:10;\r\np_correct = [1 3 8 6 20 24 16 12 24 60];\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 1234;\r\np_correct = 1236;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = [1111 2222 3333 4444 5555 6666 7777 8888 9999];\r\np_correct = [50 150 200 150 100 600 400 300 600];\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 1000000;\r\np_correct = 1500000;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 19531250;\r\np_correct = 117187500;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 102334155;\r\np_correct = 80;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 123456789;\r\np_correct = 6862416;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 4807526976;\r\np_correct = 96;\r\nassert(isequal(pisanoPi(n),p_correct))\r\n%%\r\nn = 1000:2000;\r\np = pisanoPi(n);\r\ns = floor([mean(p) mode(p) median(p) std(p)]);\r\ns_correct = [1153 240 768 1124];\r\nassert(isequal(s,s_correct))\r\n%%\r\nfiletext = fileread('pisanoPi.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-10-06T12:23:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2022-10-06T10:06:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-05T08:50:04.000Z","updated_at":"2026-03-22T12:27:15.000Z","published_at":"2022-10-05T14:00:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pisano_period\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePisano period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e of an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eis the period in which the sequence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFibonacci numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emodulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e repeats. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example it is not hard to show that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi(4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"201\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"649\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI have used Pisano period in the solutions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56050-easy-sequences-73-emergence-of-fibonacci-insects\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 56050. Easy Sequences 73: Emergence of Fibonacci Insects\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56065-easy-sequences-74-fibonacci-bank-account\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 56065. Easy Sequences 74: Fibonacci Bank Account\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn this problem, we are asked to simply output the Pisano period of given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" 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Recurrence Equations - Generalised Fibonacci-like sequences","description":"This problem is inspired by problems \u003chttp://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci 2187\u003e, \u003chttp://uk.mathworks.com/matlabcentral/cody/problems/3092-return-fibonacci-sequence-do-not-use-loop-and-condition 3092\u003e and \u003chttp://uk.mathworks.com/matlabcentral/cody/?term=tag%3A%22fibonacci%22 other problems\u003e based on Fibonacci sequence.\r\n\r\nI haven't seen here many problems based on other recursive sequences such as \u003chttp://oeis.org/A000032 Lucas numbers\u003e, \u003chttp://oeis.org/A000129 Pell numbers\u003e, \u003chttp://oeis.org/A000931 Padovan sequence\u003e or \u003chttp://oeis.org/A000073 Tribonacci numbers\u003e so this is a problem about them all.\r\n\r\nYour function input will be _N_, _Init_ and _Rules_. _Init_ and _Rules_ represent initial values of sequence and a kernel which denotes recurrence relation:\r\n\r\n Init : [ A1 A2 ... Ak]\r\n Rules : [ Ck ... C2 C1]\r\n \r\n function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)\r\n and f(1) = A1, f(2) = A2, ..., f(k) = Ak,\r\n\r\n_Init_ and _Rules_ have the same length, _N_ may be a single number or a vector. Your function should return values of _f(N)_. Example:\r\n\r\n % Fibonacci sequence: f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)\r\n \u003e\u003e Init = [1 1];\r\n \u003e\u003e Rules = [1 1];\r\n \u003e\u003e N = 1:10;\r\n \u003e\u003e fibonacci = recurrence_seq(N,Init,Rules),\r\n fibonacci = \r\n 1 1 2 3 5 8 13 21 34 55\r\n \r\n \r\n \r\n\r\nOther info:\r\n\r\n* Different approaches may lead to solutions which won't be able to compute _f(n)_ for _n_ being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for _n\u003c1_.\r\n* Please, try to avoid unnecessary things like strings, _ans_, etc. ","description_html":"\u003cp\u003eThis problem is inspired by problems \u003ca href = \"http://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci\"\u003e2187\u003c/a\u003e, \u003ca href = \"http://uk.mathworks.com/matlabcentral/cody/problems/3092-return-fibonacci-sequence-do-not-use-loop-and-condition\"\u003e3092\u003c/a\u003e and \u003ca href = \"http://uk.mathworks.com/matlabcentral/cody/?term=tag%3A%22fibonacci%22\"\u003eother problems\u003c/a\u003e based on Fibonacci sequence.\u003c/p\u003e\u003cp\u003eI haven't seen here many problems based on other recursive sequences such as \u003ca href = \"http://oeis.org/A000032\"\u003eLucas numbers\u003c/a\u003e, \u003ca href = \"http://oeis.org/A000129\"\u003ePell numbers\u003c/a\u003e, \u003ca href = \"http://oeis.org/A000931\"\u003ePadovan sequence\u003c/a\u003e or \u003ca href = \"http://oeis.org/A000073\"\u003eTribonacci numbers\u003c/a\u003e so this is a problem about them all.\u003c/p\u003e\u003cp\u003eYour function input will be \u003ci\u003eN\u003c/i\u003e, \u003ci\u003eInit\u003c/i\u003e and \u003ci\u003eRules\u003c/i\u003e. \u003ci\u003eInit\u003c/i\u003e and \u003ci\u003eRules\u003c/i\u003e represent initial values of sequence and a kernel which denotes recurrence relation:\u003c/p\u003e\u003cpre\u003e Init : [ A1 A2 ... Ak]\r\n Rules : [ Ck ... C2 C1]\u003c/pre\u003e\u003cpre\u003e function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)\r\n and f(1) = A1, f(2) = A2, ..., f(k) = Ak,\u003c/pre\u003e\u003cp\u003e\u003ci\u003eInit\u003c/i\u003e and \u003ci\u003eRules\u003c/i\u003e have the same length, \u003ci\u003eN\u003c/i\u003e may be a single number or a vector. Your function should return values of \u003ci\u003ef(N)\u003c/i\u003e. Example:\u003c/p\u003e\u003cpre\u003e % Fibonacci sequence: f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)\r\n \u0026gt;\u0026gt; Init = [1 1];\r\n \u0026gt;\u0026gt; Rules = [1 1];\r\n \u0026gt;\u0026gt; N = 1:10;\r\n \u0026gt;\u0026gt; fibonacci = recurrence_seq(N,Init,Rules),\r\n fibonacci = \r\n 1 1 2 3 5 8 13 21 34 55\u003c/pre\u003e\u003cp\u003eOther info:\u003c/p\u003e\u003cul\u003e\u003cli\u003eDifferent approaches may lead to solutions which won't be able to compute \u003ci\u003ef(n)\u003c/i\u003e for \u003ci\u003en\u003c/i\u003e being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for \u003ci\u003en\u0026lt;1\u003c/i\u003e.\u003c/li\u003e\u003cli\u003ePlease, try to avoid unnecessary things like strings, \u003ci\u003eans\u003c/i\u003e, etc.\u003c/li\u003e\u003c/ul\u003e","function_template":"function values = recurrence_seq(N, Init, Rules)\r\n values = N;\r\n values(N\u003c1) = NaN;\r\n\r\n\r\n\r\nend","test_suite":"%% Fibonacci\r\nInit = [1,1];\r\nRules = [1,1];\r\nN = 1:10;\r\nvalues_correct = [1 1 2 3 5 8 13 21 34 55];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Fibonacci - shifted\r\nInit = [2,3];\r\nRules = [1,1];\r\nN = 1:10;\r\nvalues_correct = [2, 3, 5, 8, 13, 21, 34, 55, 89, 144];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Fibonacci - negative n\r\nInit = [1,1];\r\nRules = [1,1];\r\nN = -5:5;\r\nvalues_correct = [5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5];\r\nvalues_accepted = [nan, nan, nan, nan, nan, nan, 1, 1, 2, 3, 5];\r\nvalues = recurrence_seq(N, Init, Rules);\r\nassert(isequal(values,values_correct)||isequaln(values,values_accepted))\r\n%% Lucas numbers\r\nInit = [1,3];\r\nRules = [1,1];\r\nN = 1:10;\r\nvalues_correct = [1, 3, 4, 7, 11, 18, 29, 47, 76, 123];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Padovan sequence\r\nInit = [1, 1, 1];\r\nRules = [1, 1, 0];\r\nN = 4:21;\r\nvalues_correct = [2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Pell numbers\r\nInit = [0, 1];\r\nRules = [1, 2];\r\nN = 4:3:19;\r\nvalues_correct = [5, 70, 985, 13860, 195025, 2744210];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% 3^n-2^n sequence\r\nInit = [3-2, 9-4];\r\nRules = [-6 5];\r\nN = 1:10;\r\nvalues_correct = [1, 5, 19, 65, 211, 665, 2059, 6305, 19171, 58025];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Perrin sequence\r\nInit = [3, 0, 2];\r\nRules = [1, 1, 0];\r\nN = [28:38, 10:-1:1];\r\nvalues_correct = [1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 12, 10, 7, 5, 5, 2, 3, 2, 0, 3];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% \r\nInit = [3, 0, 2]; % Perrin init\r\nRules = [1, 1, 1]; % Tribonacci rules\r\nN = [1:15];\r\nvalues_correct = [3, 0, 2, 5, 7, 14, 26, 47, 87, 160, 294, 541, 995, 1830, 3366];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Tribonacci\r\nInit = [0, 0, 1];\r\nRules = [1, 1, 1];\r\nN = [1:23];\r\nvalues_correct = [0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Tetranacci\r\nInit = [0, 0, 0, 1];\r\nRules = [1, 1, 1, 1];\r\nN = [20:23];\r\nvalues_correct = [20569, 39648, 76424, 147312];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Heptanacci\r\nInit = [0, 0, 0, 0, 0, 0, 1];\r\nRules = [1, 1, 1, 1, 1, 1, 1];\r\nN = [7:15, 19];\r\nvalues_correct = [1, 1, 2, 4, 8, 16, 32, 64, 127, 2000];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, -1];\r\nRules = [1, -1];\r\nN = 1:10;\r\nvalues_correct = [1, -1, 2, -3, 5, -8, 13, -21, 34, -55];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, -1];\r\nRules = [-1, 1];\r\nN = 1:10;\r\nvalues_correct = [1, -1, -2, -1, 1, 2, 1, -1, -2, -1];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, -1];\r\nRules = [1, 1];\r\nN = 1:10;\r\nvalues_correct = [1, -1, 0, -1, -1, -2, -3, -5, -8, -13];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, 1];\r\nRules = [2, -1];\r\nN = 1:10;\r\nvalues_correct = ones(1,10);\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\nInit = [1, 2];\r\nRules = [2, -1];\r\nN = 1:10;\r\nvalues_correct = [1, 2, 0, 4, -4, 12, -20, 44, -84, 172];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% Jacobsthal numbers\r\nInit = [0, 1];\r\nRules = [2, 1];\r\nN = 1:10;\r\nvalues_correct = [0, 1, 1, 3, 5, 11, 21, 43, 85, 171];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%% A028242\r\nInit = [1, 0, 2];\r\nRules = [-1 1 1];\r\nN = 1:20;\r\nvalues_correct = [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9];\r\nassert(isequal(recurrence_seq(N, Init, Rules),values_correct))\r\n%%\r\n\r\n","published":true,"deleted":false,"likes_count":18,"comments_count":3,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":414,"test_suite_updated_at":"2015-04-02T15:23:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-04-02T14:52:53.000Z","updated_at":"2026-03-26T04:58:55.000Z","published_at":"2015-04-02T14:54:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is inspired by problems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2187\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://uk.mathworks.com/matlabcentral/cody/problems/3092-return-fibonacci-sequence-do-not-use-loop-and-condition\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e3092\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://uk.mathworks.com/matlabcentral/cody/?term=tag%3A%22fibonacci%22\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eother problems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e based on Fibonacci sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI haven't seen here many problems based on other recursive sequences such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000032\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLucas numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000129\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePell numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000931\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePadovan sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A000073\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTribonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e so this is a problem about them all.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function input will be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRules\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRules\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e represent initial values of sequence and a kernel which denotes recurrence relation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Init : [ A1 A2 ... Ak]\\n Rules : [ Ck ... C2 C1]\\n\\n function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)\\n and f(1) = A1, f(2) = A2, ..., f(k) = Ak,]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRules\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e have the same length,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e may be a single number or a vector. Your function should return values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(N)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % Fibonacci sequence: f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)\\n \u003e\u003e Init = [1 1];\\n \u003e\u003e Rules = [1 1];\\n \u003e\u003e N = 1:10;\\n \u003e\u003e fibonacci = recurrence_seq(N,Init,Rules),\\n fibonacci = \\n 1 1 2 3 5 8 13 21 34 55]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOther info:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDifferent approaches may lead to solutions which won't be able to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026lt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease, try to avoid unnecessary things like strings,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eans\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52562,"title":"Easy Sequences 6: Coefficient sums of derivatives","description":"Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: etc. The total sum of this sequence converge to .\r\nFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, . Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 98px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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YCAwEBgIDFSJgf8D3Giv49mFrO8AAAAASUVORK5CYII=\" width=\"163\" height=\"20\" style=\"width: 163px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and its first-order derivative \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"35\" style=\"width: 129.5px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The sums of the coefficients of P and P', are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"120\" height=\"18\" style=\"width: 120px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"108\" height=\"18\" style=\"width: 108px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"18\" style=\"width: 90px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e etc. The total sum of this sequence converge to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJKADAAQAAAABAAAAJAAAAAAqDuP8AAACUElEQVRYCe2WT0tWQRTGrwVZQRGYiwhpVQgZSbRp4cLy3bmxPkCt8iO4zhZt/ABGBEbbWrboCxS4UIsUiWphtIhIzEQLsvo915mXc+fOa9BBV/fAc+f8mfOcw9y5c6coGmlWoFmBvV2Brn/QHyU+Cs6BM+ArWAJPwCbYTTy5Wd5xvJ/BL/AcPAZvwB8gfwt0Ek9ulvMmXhVeBQNmhlb0DlDsOxgEqXhyU67SPshzHajoROmpPg5gLgLF71dDhSe3pBJ5KhdwHAvOD2kQ+zd4FfxDSdyTW1LlGjptilw0ulVPBUPNWfHkWp6Krib0OoRvwBbBLPT1/ASKPwJWPLmWp6bHr0lF34I+M2MKXX5t+LPGH1VPbuSojVfw/AAqHIvfRn8Y7HeM50FOPLk5vrbvBlp8NbExjdPgcHtWXvHk5hmDd5jRNiNdh+JIiO82eHKzvNq82rRqQr8J29g2tl5hJ/HkZjmP430B1MQMOALuATUSG5N+HaTiyU252vYDNBXWj7S77d15VV9CTPFPSVxTPbnKr8klPDrwVHCyFi0KxTdCXHPGzBxPbkmTO6kvE+kKRWZNsajOoej6EcWeRZ7cki/X0IlYiVGHX06eGaf2UhRPbsmRa+hlZGfsN7pVV4yxbHRPrqGpqocw14H2x2ugK0Uqd3EovgZ6TNCTa2jq6jVcW0BFn4KTIMotlHiC60ROxZObclXsq1gLQE1pn7wH2lOy50ELdJL/zo1fUydi+XXp0pfUCz4C/f11cUvvQrhq4smtkTWOZgWaFWhWYD9W4C/P++GDxZTKPgAAAABJRU5ErkJggg==\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"19\" style=\"width: 98.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function totSum = tot_dCoefSum(coef)\r\n y = x;\r\nend","test_suite":"%%\r\ncs = [5 6 -7 -8];\r\nts = '88';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [3 15 -2 1];\r\nts = '120';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [-7 22 43 6 -75 3 1 0 -80 10 5];\r\nts = '-42698751';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = 1:25;\r\nts = '1836856501837772435875025';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([2,-1],1,15);\r\nts = '47298214022376392514505945712317';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [ones(1,20) zeros(1,10)];\r\nts = '24893912605687593731774059567276';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([-2,-25,1],1,10);\r\nts = '-68761759219969440143678420163128';\r\nassert(isequal(tot_dCoefSum(cs),ts))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2021-08-17T17:53:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-16T19:00:56.000Z","updated_at":"2025-11-30T19:39:34.000Z","published_at":"2021-08-17T12:43:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\\\\left(x\\\\right)=5x^3+6x^2-7x-8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and its first-order derivative \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dP}{dx}=15x^2+12x-7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The sums of the coefficients of P and P', are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 + 6 - 7 - 8 = -4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e15+12-7= 20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-4,\\\\ 20,\\\\ 42, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e etc. The total sum of this sequence converge to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e88\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 6\\\\ -7\\\\ -8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree 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