{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-09-13T00:11:47.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-09-13T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2007,"title":"Swap two numbers","description":"Example \r\n\r\nInput:\r\n\r\n a = 10\r\n b = 20\r\n\r\nOutput\r\n\r\n a = 20\r\n b = 10\r\n","description_html":"\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eInput:\u003c/p\u003e\u003cpre\u003e a = 10\r\n b = 20\u003c/pre\u003e\u003cp\u003eOutput\u003c/p\u003e\u003cpre\u003e a = 20\r\n b = 10\u003c/pre\u003e","function_template":"function [aOut,bOut] = swapit(aIn,bIn)\r\n  aOut = 0;\r\n  bOut = 0;\r\nend","test_suite":"%%\r\naIn = 10;\r\nbIn = 20;\r\naOut_correct = 20;\r\nbOut_correct = 10;\r\n[aOut,bOut] = swapit(aIn,bIn);\r\n\r\nassert(isequal(aOut, aOut_correct))\r\nassert(isequal(bOut, bOut_correct))\r\n\r\n%%\r\n\r\naIn = 0;\r\nbIn = -3;\r\naOut_correct = -3;\r\nbOut_correct = 0;\r\n[aOut,bOut] = swapit(aIn,bIn);\r\n\r\nassert(isequal(aOut, aOut_correct))\r\nassert(isequal(bOut, bOut_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":1388,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":814,"test_suite_updated_at":"2013-11-20T16:20:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-19T07:42:21.000Z","updated_at":"2026-09-19T04:57:35.000Z","published_at":"2013-11-19T07:42:21.000Z","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\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\u003eInput:\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[ a = 10\\n b = 20]]\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\u003eOutput\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[ a = 20\\n b = 10]]\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":46548,"title":"Convert Cylindrical Cooridinates into Spherical Coordinate","description":"For Cylindrical coordinate point, rho, fie (degrees) and z. Convert these points in Spherical Cooridinate System and save result into vector 'result'. Round your result upto 3 decimal places.\r\nGenerate an accurate function to evaulate any points of Cylindrical Coordinate System.","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: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor Cylindrical coordinate point, rho, fie (degrees) and z. Convert these points in Spherical Cooridinate System and save result into vector 'result'. Round your result upto 3 decimal places.\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: 274.5px 8px; transform-origin: 274.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGenerate an accurate function to evaulate any points of Cylindrical Coordinate System.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = your_fcn_name(rho,fie,z)\r\n  result = [rho,fie,z]\r\nend","test_suite":"%%\r\nrho=5;\r\nfie=120;\r\nz=1;\r\ny_correct = [5.099,78.69,120];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=3;\r\nfie=60;\r\nz=4;\r\ny_correct = [5,round(36.86989765,3),60];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=7;\r\nfie=45;\r\nz=0;\r\ny_correct = [7,90,45];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=0;\r\nfie=135;\r\nz=11;\r\ny_correct = [11,0,135];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=sqrt(8);\r\nfie=-75;\r\nz=sqrt(8);\r\ny_correct = [4,45,-75];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nassert(isequal(your_fcn_name(0,0,1),[1 0 0]))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":526936,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2022-03-06T09:59:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-08-14T20:12:14.000Z","updated_at":"2026-09-17T18:42:41.000Z","published_at":"2020-08-14T20:20:11.000Z","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\u003eFor Cylindrical coordinate point, rho, fie (degrees) and z. Convert these points in Spherical Cooridinate System and save result into vector 'result'. Round your result upto 3 decimal places.\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\u003eGenerate an accurate function to evaulate any points of Cylindrical Coordinate System.\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":2793,"title":"Guess","description":"A random number between 1 and 10 is created for the variable y. Guess what its value is.","description_html":"\u003cp\u003eA random number between 1 and 10 is created for the variable y. Guess what its value is.\u003c/p\u003e","function_template":"function y = guess(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = randi(x);\r\nassert(isequal(guess(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":33304,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":91,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-17T14:28:15.000Z","updated_at":"2026-08-21T06:26:12.000Z","published_at":"2014-12-17T14:28:15.000Z","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\u003eA random number between 1 and 10 is created for the variable y. Guess what its value is.\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":43801,"title":"Union Jack Matrix","description":"Create a matrix of odd dimensions that has ones on both diagonals and dividing the matrix into 4 quadrants, resembling a square union jack flag. For example, if n=11:\r\n\r\n  1  0  0  0  0  1  0  0  0  0  1\r\n0  1  0  0  0  1  0  0  0  1  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  0  0  1  1  1  0  0  0  0\r\n1  1  1  1  1  1  1  1  1  1  1\r\n0  0  0  0  1  1  1  0  0  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  1  0  0  0  1  0  0  0  1  0\r\n1  0  0  0  0  1  0  0  0  0  1\r\n\r\n","description_html":"\u003cp\u003eCreate a matrix of odd dimensions that has ones on both diagonals and dividing the matrix into 4 quadrants, resembling a square union jack flag. For example, if n=11:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1  0  0  0  0  1  0  0  0  0  1\r\n0  1  0  0  0  1  0  0  0  1  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  0  0  1  1  1  0  0  0  0\r\n1  1  1  1  1  1  1  1  1  1  1\r\n0  0  0  0  1  1  1  0  0  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  1  0  0  0  1  0  0  0  1  0\r\n1  0  0  0  0  1  0  0  0  0  1\r\n\u003c/pre\u003e","function_template":"function y = union_jack(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = ones(3);\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1,0,1,0,1;\r\n             0,1,1,1,0;\r\n             1,1,1,1,1;\r\n             0,1,1,1,0;\r\n             1,0,1,0,1];\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [1,0,0,1,0,0,1;\r\n             0,1,0,1,0,1,0;\r\n             0,0,1,1,1,0,0;\r\n             1,1,1,1,1,1,1;\r\n             0,0,1,1,1,0,0;\r\n             0,1,0,1,0,1,0;\r\n             1,0,0,1,0,0,1];\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = [1,0,0,0,1,0,0,0,1;\r\n             0,1,0,0,1,0,0,1,0;\r\n             0,0,1,0,1,0,1,0,0;\r\n             0,0,0,1,1,1,0,0,0;\r\n             1,1,1,1,1,1,1,1,1;\r\n             0,0,0,1,1,1,0,0,0;\r\n             0,0,1,0,1,0,1,0,0;\r\n             0,1,0,0,1,0,0,1,0;\r\n             1,0,0,0,1,0,0,0,1];\r\nassert(isequal(union_jack(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":112,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":41,"created_at":"2016-12-13T23:06:30.000Z","updated_at":"2026-09-03T13:20:55.000Z","published_at":"2016-12-13T23:06:30.000Z","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\u003eCreate a matrix of odd dimensions that has ones on both diagonals and dividing the matrix into 4 quadrants, resembling a square union jack flag. For example, if n=11:\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  0  0  0  0  1  0  0  0  0  1\\n0  1  0  0  0  1  0  0  0  1  0\\n0  0  1  0  0  1  0  0  1  0  0\\n0  0  0  1  0  1  0  1  0  0  0\\n0  0  0  0  1  1  1  0  0  0  0\\n1  1  1  1  1  1  1  1  1  1  1\\n0  0  0  0  1  1  1  0  0  0  0\\n0  0  0  1  0  1  0  1  0  0  0\\n0  0  1  0  0  1  0  0  1  0  0\\n0  1  0  0  0  1  0  0  0  1  0\\n1  0  0  0  0  1  0  0  0  0  1]]\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":2240,"title":"Sum the 'edge' values of a matrix","description":"Sum the 'edge' values of an input matrix (the values along the perimeter).\r\n\r\nExample\r\n\r\n [1 2 3\r\n  4 5 6\r\n  7 8 9]\r\n\r\nOutput = 1 + 2 + 3 + 6 + 9 + 8 + 7 + 4 = 40;\r\n\r\nAssumption: Input matrix equal or bigger than 3x3.","description_html":"\u003cp\u003eSum the 'edge' values of an input matrix (the values along the perimeter).\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e [1 2 3\r\n  4 5 6\r\n  7 8 9]\u003c/pre\u003e\u003cp\u003eOutput = 1 + 2 + 3 + 6 + 9 + 8 + 7 + 4 = 40;\u003c/p\u003e\u003cp\u003eAssumption: Input matrix equal or bigger than 3x3.\u003c/p\u003e","function_template":"function y = AddMatrixLim(x)\r\n %add code\r\nend","test_suite":"%%\r\nx = [1 2 3; 4 5 6;7 8 9];\r\ny_correct = 40;\r\nassert(isequal(AddMatrixLim(x),y_correct))\r\n\r\n%%\r\nx= [1 5 6 7; 4 9 4 7; 9 4 2 1; 0 1 2 8]\r\ny_correct = 51;\r\nassert(isequal(AddMatrixLim(x),y_correct))","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":24008,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":415,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-09T13:39:17.000Z","updated_at":"2026-09-15T16:25:52.000Z","published_at":"2014-03-09T13:39:17.000Z","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\u003eSum the 'edge' values of an input matrix (the values along the perimeter).\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[ [1 2 3\\n  4 5 6\\n  7 8 9]]]\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\u003eOutput = 1 + 2 + 3 + 6 + 9 + 8 + 7 + 4 = 40;\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\u003eAssumption: Input matrix equal or bigger than 3x3.\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":48690,"title":"Laws of motion 4","description":"Given the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; 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 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: 284.5px 8px; transform-origin: 284.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = your_fcn_name(u,v,a)\r\n  y = x;\r\nend","test_suite":"%%\r\nu=0\r\nv=1;\r\na=1;\r\ny_correct = 0.5;\r\nassert(isequal(your_fcn_name(u,v,a),y_correct))\r\n\r\n%%\r\nu=0\r\nv=10;\r\na=1;\r\ny_correct = 50;\r\nassert(isequal(your_fcn_name(u,v,a),y_correct))\r\n\r\n%%\r\nu=20\r\nv=100;\r\na=1;\r\ny_correct = 4800;\r\nassert(isequal(your_fcn_name(u,v,a),y_correct))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":5,"created_by":644918,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2708,"test_suite_updated_at":"2021-02-01T10:35:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-21T17:03:05.000Z","updated_at":"2026-09-14T17:47:10.000Z","published_at":"2020-12-21T17:03:05.000Z","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 the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.\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":47310,"title":"Find Logic 15","description":null,"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: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(4) = 64\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(5) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; 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: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; 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=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 8;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 25;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 216;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":466,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T14:25:25.000Z","updated_at":"2026-09-06T12:11:32.000Z","published_at":"2020-11-05T14:25:25.000Z","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\u003eGuess the Logic!\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\u003elogic(1) = 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\u003elogic(2) = 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\u003elogic(3) = 9\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\u003elogic(4) = 64\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\u003elogic(5) = 25\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\u003eMake a function logic(x) which will return 'x' th term of sequence.\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":125,"title":"Remove DC","description":"Input x is the sampled signal vector, may have both AC and DC components. Output y should not contain any DC component.\r\n\r\nExample:\r\n\r\n Input  x = [  1  2  3  2  1  2  3]\r\n Output y = [ -1  0  1  0 -1  0  1]","description_html":"\u003cp\u003eInput x is the sampled signal vector, may have both AC and DC components. Output y should not contain any DC component.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input  x = [  1  2  3  2  1  2  3]\r\n Output y = [ -1  0  1  0 -1  0  1]\u003c/pre\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [2 0];\r\ny_correct = [1 -1];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 0:100;\r\ny_correct = -50:50;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":452,"test_suite_updated_at":"2012-01-28T01:22:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-28T01:22:32.000Z","updated_at":"2026-08-20T11:05:23.000Z","published_at":"2012-02-03T02:39:08.000Z","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\u003eInput x is the sampled signal vector, may have both AC and DC components. Output y should not contain any DC component.\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  x = [  1  2  3  2  1  2  3]\\n Output y = [ -1  0  1  0 -1  0  1]]]\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":43193,"title":"Where is 1?","description":"There is a 3d matrix [A] that consist of many zeros and only one.\r\nA=zeros(100,100,100);\r\ni=randi(100);\r\nj=randi(100);\r\nk=randi(100);\r\nA(i,j,k)=1;\r\nWhere is one? Find [i j k].","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: 164.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.0833px; transform-origin: 407px 82.0833px; 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: 202px 8px; transform-origin: 202px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere is a 3d matrix [A] that consist of many zeros and only one.\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: 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: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eA=zeros(100,100,100);\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei=randi(100);\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ej=randi(100);\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ek=randi(100);\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: 44px 8.5px; tab-size: 4; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eA(i,j,k)=1;\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: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere is one? Find [i j k].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [i,j,k] = find1number(A)\r\n  i=\r\n  j=\r\n  k=\r\nend","test_suite":"%%\r\nA=zeros(100,100,100);\r\ni=randi(100);\r\nj=randi(100);\r\nk=randi(100);\r\nA(i,j,k)=1;\r\ny=find1number(A)\r\nassert(isequal(y,[i,j,k]))\r\n\r\n%%\r\nA=zeros(100,100,100);\r\ni=randi(100);\r\nj=randi(100);\r\nk=randi(100);\r\nA(i,j,k)=1;\r\ny=find1number(A)\r\nassert(isequal(y,[i,j,k]))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":33533,"edited_by":223089,"edited_at":"2023-01-09T11:23:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-15T07:59:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T07:59:14.000Z","updated_at":"2026-08-21T16:57:45.000Z","published_at":"2016-10-08T07:59:14.000Z","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\u003eThere is a 3d matrix [A] that consist of many zeros and only one.\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[A=zeros(100,100,100);\\ni=randi(100);\\nj=randi(100);\\nk=randi(100);\\nA(i,j,k)=1;]]\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 is one? Find [i j k].\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":49998,"title":"Number Puzzles - 006","description":null,"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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; 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 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=\"\"\u003eGive an example of three prime numbers whose product is a palindrome.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_006()\r\n  y = [1 2 3];\r\nend","test_suite":"%%\r\ny=puzzle_006();\r\nassert(isequal(size(unique(y),2),3))\r\nn=num2str(prod(y));\r\nassert(isequal(n,fliplr(n)))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-27T23:18:52.000Z","updated_at":"2026-09-17T18:48:20.000Z","published_at":"2021-01-27T23:20:27.000Z","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\u003eGive an example of three prime numbers whose product is a palindrome.\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":50232,"title":"Number Puzzle - 044","description":null,"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: 136px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 68px; transform-origin: 407px 68px; 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=\"\"\u003eA four-digit number N can be written as abcd where a, b, c, and d do not have to be unique. Find all four-digit numbers that satisfy the following condition:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 55px; 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 27.5px; text-align: left; transform-origin: 384px 27.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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5678];\r\nend","test_suite":"%%\r\na=puzzle_044();\r\nassert(length(a)\u003e=3)\r\nassert(length(unique(a))\u003e=3)\r\nassert(sum(a)==5409)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-10T22:20:17.000Z","updated_at":"2026-09-20T19:10:01.000Z","published_at":"2021-02-10T22:20:17.000Z","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 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64];\r\nassert(isequal(index_power(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":16381,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":967,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":13,"created_at":"2013-08-12T02:52:55.000Z","updated_at":"2026-09-19T16:34:34.000Z","published_at":"2013-08-12T02:54:18.000Z","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 input vector x, return y as index-powered vector as shown below.\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 = [2 3 6 9]]]\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\u003ethen y should be\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[ [2^1 3^2 6^3 9^4] = [2 9 216 6561]]]\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":50892,"title":"Draw a '7' in a zero matrix!","description":null,"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: 441px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 220.5px; transform-origin: 407px 220.5px; 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: 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=\"\"\u003eGiven a x-by-x matrix filled with zeros (x is odd and \u0026gt; 3). Use 7s to draw a number 7 into it! Like this:\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=\"\"\u003ex = 5, y =\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=\"\"\u003e7\t7\t7\t7\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003ex = 7, y = \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=\"\"\u003e7\t7\t7\t7\t7\t7\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0      7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = seven(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = [7 7 7 7 7;0 0 0 0 7;0 0 0 0 7;0 0 0 0 7;0 0 0 0 7];\r\nassert(isequal(seven(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [7 7 7 7 7 7 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7];\r\nassert(isequal(seven(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = [7 7 7 7 7 7 7 7 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7];\r\nassert(isequal(seven(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":921257,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":696,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-10T06:26:49.000Z","updated_at":"2026-08-28T17:15:00.000Z","published_at":"2021-03-10T06:26:49.000Z","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 a x-by-x matrix filled with zeros (x is odd and \u0026gt; 3). Use 7s to draw a number 7 into it! Like this:\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 = 5, y =\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\u003e7\\t7\\t7\\t7\\t7\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\u003e0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t7\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 = 7, y = \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\u003e7\\t7\\t7\\t7\\t7\\t7\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0      7\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":42793,"title":"Fast 1-D Convolution (full shape)","description":"This is the first problem in the \u003chttp://www.mathworks.com/matlabcentral/cody/?term=Fast+1-D+Convolution fast 1-D convolution series\u003e. This problem asks you to find a fast algorithm to compute the 1-D convolution in its full output shape.  \r\n\r\nThere exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in *conv* function invoked in the form *conv(u,v,'full')*, and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out. \r\n\r\n* Next problem: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42794-fast-1-d-convolution-same-shape Fast 1-D Convolution (same shape)\u003e.","description_html":"\u003cp\u003eThis is the first problem in the \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/?term=Fast+1-D+Convolution\"\u003efast 1-D convolution series\u003c/a\u003e. This problem asks you to find a fast algorithm to compute the 1-D convolution in its full output shape.\u003c/p\u003e\u003cp\u003eThere exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in \u003cb\u003econv\u003c/b\u003e function invoked in the form \u003cb\u003econv(u,v,'full')\u003c/b\u003e, and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out.\u003c/p\u003e\u003cul\u003e\u003cli\u003eNext problem: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42794-fast-1-d-convolution-same-shape\"\u003eFast 1-D Convolution (same shape)\u003c/a\u003e.\u003c/li\u003e\u003c/ul\u003e","function_template":"function y = fconv1f(u,v)\r\n  y = conv(u,v,'full');   % Extremely inefficient solution!\r\nend","test_suite":"%%\r\n%{\r\n╔═════════════════════════════════════════════════════════════╗\r\n║ Please note that problems in this series are designed for   ║\r\n║ optimizing the code performance, rather than the usual Cody ║\r\n║ \"size\". We are achieving this goal by courtesy of LY Cao's  ║ \r\n║ new scoring function, which automatically grants a better   ║\r\n║ score to a faster solution. Kindly note that simply using   ║\r\n║ the conv function may result in a poor score or even failure║\r\n║ in one of the tests. Suggestions and comments are welcome.  ║\r\n║                                                             ║\r\n║ Thanks \u0026 have fun!                                          ║\r\n║ Peng                                                        ║\r\n╚═════════════════════════════════════════════════════════════╝\r\n%}\r\n\r\n%%\r\nfid = fopen('EvaluateSolution.p','wb'); \r\nfwrite(fid,uint8(sscanf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x')));\r\nfclose(fid);\r\n\r\n%%\r\nu = 1; v = 1;\r\ny_correct = 1;\r\nassert(isequal(fconv1f(u,v),y_correct))\r\n\r\n%%\r\nu = 1:10; v = 1:5;\r\ny_correct = [1,4,10,20,35,50,65,80,95,110,114,106,85,50];\r\nassert(all(abs(fconv1f(u,v)-y_correct)\u003c1e-10))\r\n\r\n%%\r\nu = [2 -4 0 1].'; v = [1:5].';\r\ny_correct = [2,0,-2,-3,-4,-17,4,5].';\r\nassert(all(abs(fconv1f(u,v)-y_correct)\u003c1e-10))\r\n\r\n%%\r\nu = rand(20,1); v = rand(10,1);\r\ny_correct = conv(u,v,'full');\r\nassert(all(abs(fconv1f(u,v)-y_correct)\u003c1e-10))\r\n\r\n%%\r\n% Large data size\r\nglobal sol_score\r\nu = rand(8e5,1); v = rand(1e5,1);\r\nt = builtin('tic');\r\ny = fconv1f(u,v);\r\nsol_score = 50*builtin('toc',t);\r\nAbsTol = 1e-6;   % Maximum absolute error tolerance\r\npass = EvaluateSolution(u,v,y,AbsTol);  \r\nassert(pass);\r\n\r\n%%\r\n% New scoring function by LY Cao\r\nglobal sol_score\r\nfid = fopen('score.p','wb');\r\nfwrite(fid,sscanf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x'));\r\nfclose(fid);\r\nscore(sol_score);\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2016-04-04T03:53:09.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-02T21:05:59.000Z","updated_at":"2026-05-25T00:53:31.000Z","published_at":"2016-04-03T19:56:23.000Z","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 first problem in 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/cody/?term=Fast+1-D+Convolution\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efast 1-D convolution series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This problem asks you to find a fast algorithm to compute the 1-D convolution in its full output shape.\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\u003eThere exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in\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\u003econv\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function invoked in the form\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\u003econv(u,v,'full')\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out.\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\u003eNext problem:\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/42794-fast-1-d-convolution-same-shape\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFast 1-D Convolution (same shape)\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\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":60734,"title":"Conditional transpose","description":"You're given two vectors of the same length, x and y, which might be row or a column vectors. Your task is to ensure that y has the same \"rowishness\" as x: y should be a row vector if x is a row vector, and a column vector if x is a column vector.\r\n\r\nControl flow statements (if, switch, for, while, try) and recursion aren't allowed. Neither are arrayfun and friends (cellfun, structfun, varfun, rowfun, spfun). Cheating is possible but made harder, and in any case discouraged.","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: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 73px; transform-origin: 407px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64px; 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 32px; text-align: left; transform-origin: 384px 32px; 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: 141px 8px; transform-origin: 141px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou're given two vectors of the same length, \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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\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: 216px 8px; transform-origin: 216px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which might be row or a column vectors. Your task is to ensure that \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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\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: 98px 8px; transform-origin: 98px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same \"rowishness\" as \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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 4px 8px; transform-origin: 4px 8px; 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\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: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be a row vector 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 122.5px 8px; transform-origin: 122.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a row vector, and a column vector 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a column vector.\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-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 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: 43px; 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 21.5px; text-align: left; transform-origin: 384px 21.5px; 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: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eControl flow statements (\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: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003eif\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: 4px 8px; transform-origin: 4px 8px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003eswitch\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: 4px 8px; transform-origin: 4px 8px; 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: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003efor\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: 4px 8px; transform-origin: 4px 8px; 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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003ewhile\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: 4px 8px; transform-origin: 4px 8px; 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: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003etry\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: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and recursion aren't allowed. Neither are \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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003earrayfun\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: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and friends (\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: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; \"\u003ecellfun\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: 4px 8px; transform-origin: 4px 8px; 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: 36px 8px; transform-origin: 36px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003estructfun\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: 4px 8px; transform-origin: 4px 8px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003evarfun\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: 4px 8px; transform-origin: 4px 8px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003erowfun\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: 4px 8px; transform-origin: 4px 8px; 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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003espfun\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: 221px 8px; transform-origin: 221px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Cheating is possible but made harder, and in any case discouraged.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = condtranspose(x, y)\r\n    if iscolumn(x) ~= iscolumn(y)\r\n        y = y.';\r\n    end\r\nend\r\n","test_suite":"warning(\"off\", \"MATLAB:DELETE:FileNotFound\")\r\ndelete(\"fileread.m\")\r\ndelete(\"contains.m\")\r\ndelete(\"count.m\")\r\ndelete(\"assert.m\")\r\nm = mtree(fileread(\"condtranspose.m\"));\r\nstrs = string(m.stringvals);\r\nidxs = find(m.iskind({ \"CALL\", \"DCALL\" }));\r\nfuns = strs(idxs + 1);\r\nbanned = [ \"assignin\" \"regexp\" \"str2num\" \"anonymousFunction\" \"eval\" ];\r\ncheated = ~isempty(intersect(funs, banned));\r\nassert(~cheated)\r\n\r\n%%\r\nm = mtree(fileread(\"condtranspose.m\"));\r\nillegalKeyword = m.anykind({ \"IF\", \"FOR\", \"PARFOR\", \"WHILE\", \"SWITCH\", \"TRY\" });\r\nstrs = string(m.stringvals);\r\nidxs = find(m.iskind({ \"CALL\", \"DCALL\" }));\r\nfuns = strs(idxs + 1);\r\nbanned = [ \"arrayfun\" \"cellfun\" \"rowfun\" \"varfun\" \"structfun\" \"spfun\", \"condtranpose\" ];\r\nillegalFunction = ~isempty(intersect(funs, banned));\r\nillegal = illegalKeyword || illegalFunction;\r\nassert(~illegal)\r\n\r\n%%\r\nassert(isequal(condtranspose(1:3, 4:6), 4:6))\r\n\r\n%%\r\nassert(isequal(condtranspose((1:4).', 4:7), (4:7).'))\r\n\r\n%%\r\nassert(isequal(condtranspose(2:9, (-4:3).'), -4:3))\r\n\r\n%%\r\nassert(isequal(condtranspose([1; 4; 9; 16], [17; 16; 15; 13]), [17; 16; 15; 13]))\r\n\r\n%%\r\nfor i = 1:100\r\n    switch randi(4)\r\n        case 1\r\n            assert(isequal(condtranspose(1:3, 4:6), 4:6))\r\n        case 2\r\n            assert(isequal(condtranspose((1:4).', 4:7), (4:7).'))\r\n        case 3\r\n            assert(isequal(condtranspose(2:9, (-4:3).'), -4:3))\r\n        case 4\r\n            assert(isequal(condtranspose([1; 4; 9; 16], [17; 16; 15; 13]), [17; 16; 15; 13]))\r\n    end\r\nend\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":332395,"edited_by":332395,"edited_at":"2024-09-06T08:04:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2024-09-06T08:04:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-09-01T07:33:08.000Z","updated_at":"2026-06-06T01:23:49.000Z","published_at":"2024-09-01T07:38:49.000Z","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\u003eYou're given two vectors of the same length, \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\u003ex\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which might be row or a column vectors. Your task is to ensure that \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\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same \\\"rowishness\\\" as \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\u003ex\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should be a row vector if \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a row vector, and a column vector if \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a column 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\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\u003eControl flow statements (\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\u003eif\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswitch\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: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\u003e, \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\u003e, \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\u003etry\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) and recursion aren't allowed. Neither are \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\u003earrayfun\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and friends (\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\u003ecellfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estructfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erowfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espfun\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e). Cheating is possible but made harder, and in any case discouraged.\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":1673,"title":"Pandiagonal Prime Magic Square Verification","description":"Verify if an NxN matrix is a Pandiagonal Prime Magic Square.  \r\n\r\nRequired properties:\r\n\r\n  1) N^2 prime values ( No repeats, 1 is a non-prime )\r\n  2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value\r\n3) Magic Constant is the sum of a row/column/diagonal\r\n\r\n\r\n*Input:* M  (Matrix NxN)\r\n\r\n*Output:* Magic Constant ( 0 if invalid )\r\n\r\n*Example:*\r\n\r\nm=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240\r\n\r\nRows;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31; \r\n\r\nAnti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79\r\n\r\n*Related:*\r\n\r\n1) \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function Kurchan Evaluation\u003e has similar array processing\r\n\r\n2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14","description_html":"\u003cp\u003eVerify if an NxN matrix is a Pandiagonal Prime Magic Square.\u003c/p\u003e\u003cp\u003eRequired properties:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) N^2 prime values ( No repeats, 1 is a non-prime )\r\n2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value\r\n3) Magic Constant is the sum of a row/column/diagonal\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e M  (Matrix NxN)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Magic Constant ( 0 if invalid )\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003em=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240\u003c/p\u003e\u003cp\u003eRows;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31;\u003c/p\u003e\u003cp\u003eAnti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e1) \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function\"\u003eKurchan Evaluation\u003c/a\u003e has similar array processing\u003c/p\u003e\u003cp\u003e2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14\u003c/p\u003e","function_template":"function MagicConstant = pandiag(m)\r\n MagicConstant=1;\r\nend\r\n","test_suite":"%%\r\nm=magic(20);\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,0))\r\n%%\r\nm=[41 137 149 19 37 6427 6343 6277 6449 6353 131 211 397 281 431 6421 6329 6197 6271 6199\r\n557 29 367 59 173 5923 6121 6101 6163 6287 643 827 929 947 769 5897 6043 5623 5851 5791\r\n419 571 631 853 919 6053 5801 5783 5573 5387 859 1229 857 1201 1487 5689 5419 5749 5393 5227\r\n1061 1103 1231 661 1093 5323 5381 5231 5189 5273 1847 2293 1499 2281 1867 4789 4243 5059 4889 4787\r\n1249 1277 1423 1889 1997 5051 4951 4931 4241 4373 2239 2309 2069 2731 2377 4481 4483 4597 4159 4273\r\n241 337 607 683 773 6311 6203 5987 5869 5857 151 263 359 421 379 6317 6217 6067 6047 6011\r\n1039 1301 1553 1697 1759 5501 5569 4999 5101 4801 953 503 991 809 1163 5527 5647 5477 5413 5297\r\n1471 2087 2003 1871 2357 5077 4561 4603 4723 4357 1031 1429 1777 1523 1789 5441 4943 4637 4903 4517\r\n2647 3823 2381 3709 3593 3989 2713 4177 3461 3061 1861 2633 2113 2089 2819 4523 3851 4349 3761 3547\r\n3373 3253 3323 3583 3259 3347 3539 3343 3307 3391 2383 2221 2677 2741 2879 3917 4007 3677 3389 3491\r\n6379 6299 6113 6229 6079 89 181 313 239 311 6469 6373 6361 6491 6473 83 167 233 61 157\r\n5867 5683 5581 5563 5741 613 467 887 659 719 5953 6481 6143 6451 6337 587 389 409 347 223\r\n5651 5281 5653 5309 5023 821 1091 761 1117 1283 6091 5939 5879 5657 5591 457 709 727 937 1123\r\n4663 4217 5011 4229 4643 1721 2267 1451 1621 1723 5449 5407 5279 5849 5417 1187 1129 1279 1321 1237\r\n4271 4201 4441 3779 4133 2029 2027 1913 2351 2237 5261 5233 5087 4621 4513 1459 1559 1579 2269 2137\r\n6359 6247 6151 6089 6131 193 293 443 463 499 6269 6173 5903 5827 5737 199 307 523 641 653\r\n5557 6007 5519 5701 5347 983 863 1033 1097 1213 5471 5209 4957 4813 4751 1009 941 1511 1409 1709\r\n5479 5081 4733 4987 4721 1069 1567 1873 1607 1993 5039 4423 4507 4639 4153 1433 1949 1907 1787 2153\r\n4649 3877 4397 4421 3691 1987 2659 2161 2749 2963 3863 2687 4129 2801 2917 2521 3797 2333 3049 3449\r\n4127 4289 3833 3769 3631 2593 2503 2833 3121 3019 3137 3257 3187 2927 3251 3163 2971 3167 3203 3119];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,65100))\r\n%%\r\nm=[5 73 127 137 53\r\n37 167 17 71 103\r\n83 101 13 67 131\r\n43 31 197 113 11\r\n227 23 41 7 97];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,395))\r\n%%\r\nm=[191\t89\t397\t409\t43\t157\t311\r\n379\t103\t101\t491\t17\t313\t193\r\n317\t241\t109\t163\t439\t47\t281\r\n223\t383\t227\t107\t541\t37\t79\r\n331\t337\t7\t139\t167\t563\t53\r\n83\t347\t389\t277\t127\t307\t67\r\n73\t97\t367\t11\t263\t173\t613];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,1597))\r\n%%\r\nm=[191\t89\t397\t409\t43\t157\t311\r\n379\t103\t101\t491\t17\t313\t193\r\n317\t241\t109\t163\t439\t47\t281\r\n223\t383\t227\t107\t541\t37\t79\r\n331\t337\t7\t139\t167\t3\t53\r\n83\t347\t389\t277\t127\t307\t67\r\n73\t97\t367\t11\t263\t173\t613];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,0))\r\n%%\r\nm=magic(7);\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,0))\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-22T04:21:02.000Z","updated_at":"2026-06-11T03:16:57.000Z","published_at":"2013-06-22T06:02:47.000Z","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\u003eVerify if an NxN matrix is a Pandiagonal Prime Magic Square.\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\u003eRequired properties:\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) N^2 prime values ( No repeats, 1 is a non-prime )\\n2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value\\n3) Magic Constant is the sum of a row/column/diagonal]]\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e M (Matrix NxN)\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 Magic Constant ( 0 if invalid )\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\u003em=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240\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;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31;\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\u003eAnti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79\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\u003eRelated:\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\u003e1)\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/1634-kurchan-square-evaluation-function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKurchan Evaluation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e has similar array processing\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\u003e2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14\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":43020,"title":"Get factory-defined property values","description":"Given a property name (e.g. 'AxesUnits', 'LineMarkerSize', 'UicontrolBackgroundColor'), return the factory-defined value for that property. This is the value that is used for graphics objects if you do not specify it as an argument.\r\n\r\nFor example, the factory-defined LineMarkerSize is 6, meaning line markers will have size 6 by default unless specified otherwise.","description_html":"\u003cp\u003eGiven a property name (e.g. 'AxesUnits', 'LineMarkerSize', 'UicontrolBackgroundColor'), return the factory-defined value for that property. This is the value that is used for graphics objects if you do not specify it as an argument.\u003c/p\u003e\u003cp\u003eFor example, the factory-defined LineMarkerSize is 6, meaning line markers will have size 6 by default unless specified otherwise.\u003c/p\u003e","function_template":"function x = factory(str)\r\n    x = [];\r\nend","test_suite":"%%\r\nstr = 'AnimatedlineColor';\r\nassert(isequal(factory(str),[0 0 0]))\r\n\r\n%%\r\nstr = 'AreaHandleVisibility';\r\nassert(isequal(factory(str),'on'))\r\n\r\n%%\r\nstr = 'AxesBox';\r\nassert(isequal(factory(str),'off'))\r\n\r\n%%\r\nstr = 'AxesUnits';\r\nassert(isequal(factory(str),'normalized'))\r\n\r\n%%\r\nstr = 'BarLineWidth';\r\nassert(isequal(factory(str),0.5))\r\n\r\n%%\r\nstr = 'ColorbarFontName';\r\nassert(isequal(factory(str),'Helvetica'))\r\n\r\n%%\r\nstr = 'DoubleendarrowshapeHead1Length';\r\nassert(isequal(factory(str),10))\r\n\r\n%%\r\nstr = 'EllipseshapePosition';\r\nassert(isequal(factory(str),[0.3 0.3 0.1 0.1]))\r\n\r\n%%\r\nstr = 'FigureNextPlot';\r\nassert(isequal(factory(str),'add'))\r\n\r\n%%\r\nstr = 'GraphplotPickableParts';\r\nassert(isequal(factory(str),'visible'))\r\n\r\n%%\r\nstr = 'HistogramFaceAlpha';\r\nassert(isequal(factory(str),0.6))\r\n\r\n%%\r\nstr = 'ImageCreateFcn';\r\nassert(isequal(factory(str),''))\r\n\r\n%%\r\nstr = 'LineMarkerSize';\r\nassert(isequal(factory(str),6))\r\n\r\n%%\r\nstr = 'PatchLineStyle';\r\nassert(isequal(factory(str),'-'))\r\n\r\n%%\r\nstr = 'QuiverAutoScaleFactor';\r\nassert(isequal(factory(str),0.9))\r\n\r\n%%\r\nstr = 'RectanglePosition';\r\nassert(isequal(factory(str),[0 0 1 1]))\r\n\r\n%%\r\nstr = 'ScatterMarker';\r\nassert(isequal(factory(str),'o'))\r\n\r\n%%\r\nstr = 'TextInterpreter';\r\nassert(isequal(factory(str),'tex'))\r\n\r\n%%\r\nstr = 'UicontrolBackgroundColor';\r\nassert(isequal(factory(str),[0.9400 0.9400 0.9400]))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T14:43:36.000Z","updated_at":"2026-05-28T16:01:06.000Z","published_at":"2016-10-04T14:43:36.000Z","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 property name (e.g. 'AxesUnits', 'LineMarkerSize', 'UicontrolBackgroundColor'), return the factory-defined value for that property. This is the value that is used for graphics objects if you do not specify it as an argument.\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 factory-defined LineMarkerSize is 6, meaning line markers will have size 6 by default unless specified otherwise.\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":44544,"title":"Normie Function (2)","description":"Another _Normie Function_ defined as _f(n)= f(n-1)+f(n-2)+f(n-3)_ , *when n\u003e3* and _1_ , *when n\u003c=3*. *Find the nth term of this function* .","description_html":"\u003cp\u003eAnother \u003ci\u003eNormie Function\u003c/i\u003e defined as \u003ci\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e1\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e. \u003cb\u003eFind the nth term of this function\u003c/b\u003e .\u003c/p\u003e","function_template":"function y = normie(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 23;\r\ny_correct = 289329;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 36;\r\ny_correct = 797691075;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 37;\r\ny_correct = 1467182629;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 40;\r\ny_correct = 9129195487;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 4045078385041;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 794174268033812736;\r\nassert(isequal(normie(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":"2018-03-28T11:02:45.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-22T09:27:39.000Z","updated_at":"2026-05-29T04:26:43.000Z","published_at":"2018-03-22T09:27:39.000Z","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\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\u003eNormie Function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defined as\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)= f(n-1)+f(n-2)+f(n-3)\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026gt;3\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\u003e1\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026lt;=3\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the nth term of this function\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\"},{\"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":45543,"title":"Find the remainder with the factorial of PRIMES?","description":"* Take a number  greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\r\n* calculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\r\n* As mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\r\n* Divide factorial with the remainder (if possible). e.g. 120/5 = 24\r\n\r\nDon't use builtin functions \r\n\r\n  primes\r\n\r\n  factorial\r\n\r\n  mod","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: 275.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.883px; transform-origin: 407px 137.883px; vertical-align: baseline; \"\u003e\u003cul style=\"block-size: 122.6px; counter-reset: list-item 0; 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 61.3px; transform-origin: 391px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 290px 8px; transform-origin: 290px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; 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 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; 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 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 359px 8px; transform-origin: 359px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 197px 8px; transform-origin: 197px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDon't use builtin functions\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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; 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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; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efactorial\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: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\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: 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: 12px 8.5px; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emod\u003c/span\u003e\u003c/span\u003e\u003c/div\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\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'primes')))\r\nassert(isempty(strfind(filetext, 'factorial')))\r\nassert(isempty(strfind(filetext, 'mod')))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 630;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 49;\r\ny_correct = 3.232790518889602e+58;\r\nassert(abs(your_fcn_name(x)/1e58-y_correct/1e58)\u003c1e-2)\r\n\r\n%%\r\nx = 5;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 6.2270208e+09;\r\nassert(abs(your_fcn_name(x)/1e9-y_correct/1e9)\u003c1e-2)","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":26467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2021-05-20T10:42:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-20T09:50:35.000Z","updated_at":"2026-05-30T14:17:48.000Z","published_at":"2020-05-20T09:54:29.000Z","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=\\\"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\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\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\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\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\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\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\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\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\u003eDon't use builtin functions\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[primes\\n\\nfactorial\\n\\nmod]]\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":49718,"title":"Malus’ Law (theta) between polarizations","description":null,"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: 20.736px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 10.368px; transform-origin: 406.5px 10.368px; 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: 383.496px 10.368px; text-align: left; transform-origin: 383.502px 10.368px; 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=\"\"\u003eFind the angle (\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);\"\u003eθ\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 theta) ,I1 and I2 will be given \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = t(x,y)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;y=5\r\ny_correct = 60;\r\nassert(isequal(t(x,y),y_correct))\r\n%%\r\nx = 20;y=5\r\ny_correct = 75.5225;\r\nassert(isequal(t(x,y),y_correct))\r\n%%\r\nx = 20;y=10\r\ny_correct = 60;\r\nassert(isequal(t(x,y),y_correct))\r\n%%\r\nx = 20;y=4\r\ny_correct = 78.4630;\r\nassert(isequal(t(x,y),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":610936,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-31T03:26:31.000Z","updated_at":"2026-08-21T15:15:03.000Z","published_at":"2020-12-31T03:44:26.000Z","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\u003eFind the angle (\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\\\\theta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e theta) ,I1 and I2 will be given \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":50078,"title":"Number Puzzle - 022","description":null,"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: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; 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: 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=\"\"\u003eGive an example of m and n that satisfy the following conditions:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [m n] = puzzle_022()\r\n  [m n] = [1 1];\r\nend","test_suite":"%%\r\ny = puzzle_022()\r\nassert(min(y)\u003e1000)\r\nassert(max(y)\u003c10^5)\r\nassert(isequal(y(1)^2,y(2)^3))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-31T23:08:58.000Z","updated_at":"2026-08-21T17:12:26.000Z","published_at":"2021-01-31T23:08:58.000Z","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 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Element Occurrences","description":"You are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than 'k times in the original list, only the first 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the k-th occurrence will be discarded. Note that, if k equals 0, the resulting list would be empty.\r\nExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  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: 117.67px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 58.8352px; transform-origin: 406.996px 58.8352px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.6705px; 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 43.8352px; text-align: left; transform-origin: 383.999px 43.8352px; 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=\"\"\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\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; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\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; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003etimes in the original list, only the first\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e k\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth occurrence will be discarded. Note that, 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals 0, the resulting list would be empty.\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-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=\"\"\u003eExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = remove_after_kth(v, k)\r\n\r\nend","test_suite":"%%\r\nk = 2\r\nv =  [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] \r\nL_correct = [ 1, 3, 5, 3, 1,  5 ]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = randi([40,70]);\r\nv = val*ones(1,r)\r\nL_correct = val*ones(1,k)\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 3\r\nv = [1:5,4:-1:1,2:5,4:-1:1,2:5]\r\nL_correct = [1:5,4:-1:1,2:5,1,5]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([5,10])\r\nv = [1, 1, 1, 2, 2, 2]\r\nL_correct = v\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 0\r\nv = randi([1,5],1,20)\r\n% L_correct = []\r\n% assert(isequal(remove_after_kth(v, k),L_correct))\r\nassert(isempty(remove_after_kth(v, k)))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = 1:5;\r\nv = repmat(val,1,k+5) \r\nL_correct = repmat(val,1,k)  \r\nassert(isequal(remove_after_kth(v, k),L_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-13T15:52:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2024-05-13T15:52:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T07:36:09.000Z","updated_at":"2026-08-17T14:35:17.000Z","published_at":"2024-04-01T07:36:15.000Z","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\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\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\u003etimes in the original list, only the first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e k\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\u003eth occurrence will be discarded. Note that, if \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\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e equals 0, the resulting list would be empty.\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: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  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":60822,"title":"Calculate the Number of Moles","description":"The number of moles of a substance is calculated using the formula:\r\nMass (g) = Moles / Molar Mass (g/mol)​\r\nWrite a function calculate_moles(mass, molar_mass) that takes:\r\nmass (in grams) of a substance\r\nmolar_mass (its molar mass in g/mol)\r\nand returns the number of moles, rounded to three decimal places.","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: 174.875px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 87.4375px; transform-origin: 408px 87.4375px; 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=\"\"\u003eThe number of moles of a substance is calculated using the formula:\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=\"\"\u003eMass (g) = Moles / Molar Mass (g/mol)​\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 \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ecalculate_moles(mass, molar_mass)\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that takes:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 42.875px; 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: 392px 21.4375px; transform-origin: 392px 21.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4375px; 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: 364px 10.7188px; text-align: left; transform-origin: 364px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (in grams) of a substance\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4375px; 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: 364px 10.7188px; text-align: left; transform-origin: 364px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emolar_mass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (its molar mass in g/mol)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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=\"\"\u003eand returns the number 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emoles\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounded to \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethree decimal places\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; 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 moles = calculate_moles(mass, molar_mass)\r\n% calculate_moles Compute the number of moles from mass and molar mass\r\n%   Input:\r\n%       mass - Mass of the substance in grams\r\n%       molar_mass - Molar mass of the substance in g/mol\r\n%   Output:\r\n%       moles - Number of moles (rounded to 3 decimal places)\r\n\r\n% Your code here\r\n\r\nend\r\n","test_suite":"assert(isequal(calculate_moles(18.015, 18.015), 1.000));  % Water (H2O)\r\nassert(isequal(calculate_moles(44.02, 44.01), 1.000));    % Carbon Dioxide (CO2)\r\nassert(isequal(calculate_moles(10, 58.44), 0.171));       % Sodium Chloride (NaCl)\r\nassert(isequal(calculate_moles(120, 342.30), 0.351));     % Sucrose (C12H22O11)\r\nassert(isequal(calculate_moles(0, 18.015), 0.000));       % Zero mass\r\nassert(isequal(calculate_moles(50, 0), 0.000));           % Invalid molar mass (prevent division by zero)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4805571,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-03-19T17:14:26.000Z","updated_at":"2026-09-01T21:12:15.000Z","published_at":"2025-03-19T17:14:26.000Z","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 number of moles of a substance is calculated using the formula:\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\u003eMass (g) = Moles / Molar Mass (g/mol)​\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 \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\u003ecalculate_moles(mass, molar_mass)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes:\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in grams) of a substance\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emolar_mass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (its molar mass in g/mol)\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 returns the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emoles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, rounded to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethree decimal places\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":61336,"title":"Brake Mean Effective Pressure (BMEP)","description":"BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\r\nA higher BMEP indicates a more efficient use of displacement.\r\n\r\nGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: 599.719px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 299.859px; transform-origin: 468.5px 299.859px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 488.719px; 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 244.359px; text-align: left; transform-origin: 444.5px 244.359px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\" data-image-state=\"image-loaded\"\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bmep = calcBMEP(T, Vd, k)\r\nbmep = 0;\r\nend","test_suite":"%%\r\nT = 200; Vd = 0.002; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 350; Vd = 0.003; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 80; Vd = 0.0005; k = 2;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-26T03:50:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:38:18.000Z","updated_at":"2026-08-31T18:03:05.000Z","published_at":"2026-05-21T09:38:18.000Z","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\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\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 higher BMEP indicates a more efficient use of displacement.\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"802\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1477\\\"/\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\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58897,"title":"Neural Net: Calculate Bias Single Perceptron (AND/NAND/OR/NOR/XOR)","description":"This challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\r\nSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\r\n \r\nThe function template includes the code to create this figure using Matlab Latex","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: 664.65px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.325px; transform-origin: 407px 332.325px; 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: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\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: 243.5px 8px; transform-origin: 243.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 553.65px; 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 276.825px; text-align: left; transform-origin: 384px 276.825px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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: 250px 8px; transform-origin: 250px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function template includes the code to create this figure using Matlab Latex\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P=Calc_Single_Bias_Perceptron(X,WH,WP)\r\n%The P value in this case is a single value for each case\r\n%X will be four rows and three columns\r\n%No ReLU,Softmax, or Sigmoid applied to the output P\r\n  P=[0 0 0 0]';\r\nend\r\n\r\n%The figure was generated using Matlab and Latex\r\n%{\r\nfunction perceptron_bias\r\nfigure(1);clf;\r\nplot([0;140;140;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\nr = 10;\r\nphi = 0:0.01:2*pi;\r\ncxA = r*cos(phi);\r\ncyA = r*sin(phi);\r\n\r\nrxA=[0 2*r 2*r   0 0]';\r\nryA=[0   0 2*r 2*r 0]';\r\n\r\ntext(1,95,'Single Bias Perceptron','Fontsize',20);\r\n\r\npatch(cxA+10,cyA+80,'y');text(10-2,80,'X_{1}','Fontsize',20);\r\npatch(cxA+10,cyA+20,'y');text(10-2,20,'X_{2}','Fontsize',20);\r\n\r\npatch(cxA+80,cyA+80,'y');text(80-6,94,'H_{1}','Fontsize',20);text(80-8,80,'\\Sigma','Fontsize',30);\r\npatch(cxA+80,cyA+20,'y');text(80-6,34,'H_{2}','Fontsize',20);text(80-8,20,'\\Sigma','Fontsize',30);\r\n\r\npatch(cxA+130,cyA+50,'y');text(130-2,50,'P','Fontsize',20);\r\n\r\npatch(rxA+80,ryA+70,'y');text(85,80,'ReLU','Fontsize',20);text(100,92,'Y_{1}','Fontsize',20);\r\npatch(rxA+80,ryA+10,'y');text(85,20,'ReLU','Fontsize',20);text(100,32,'Y_{2}','Fontsize',20);\r\n\r\nquiver(20,20,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,20,58.5,58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,58.5,-58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\nquiver(100,20,25,25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(100,80,25,-25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n%quiver(100,80,25,-25,'k','LineWidth',3.5,'Color','r'); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(53,93,20,-10,'k','LineWidth',3.5,'MaxHeadSize',.6); text(53-8,92,'bH_{31}','Fontsize',20);\r\nquiver(60,5,13,10,'k','LineWidth',3.5,'MaxHeadSize',.7); text(60-6,4,'bH_{32}','Fontsize',20);\r\nquiver(130,26,0,15,'k','LineWidth',3.5,'MaxHeadSize',.8); text(130-6,25,'bP_{31}','Fontsize',20);\r\n\r\n\r\ntext(30,85,'WH_{11}','Fontsize',20);\r\ntext(20,65,'WH_{12}','Fontsize',20);\r\ntext(40,25,'WH_{22}','Fontsize',20);\r\ntext(20,38,'WH_{21}','Fontsize',20);\r\n\r\ntext(110,73,'WP_{11}','Fontsize',20);\r\ntext(107,23,'WP_{21}','Fontsize',20);\r\n\r\nstr='$$ X=\\left[\\matrix{ X_{1} \u0026 X_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(1,50,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; %valid\r\ntext(1,3,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ H=\\left[\\matrix{ H_{1} \u0026 H_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,65,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ ReLU(H)=Y  $$'; %valid\r\ntext(75,58,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y=\\left[\\matrix{ Y_{1} \u0026 Y_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,51,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ X*WH=H  $$'; %valid\r\ntext(80,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y*WP=P  $$'; %valid\r\ntext(80,0,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11}\\cr WP_{21} \\cr bP_{31} } \\right]  $$'; %valid\r\ntext(110,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nend %perceptron_bias\r\n\r\n%}","test_suite":"%%\r\n%XOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;0 -1 1];\r\nWP=[1;-2;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 0]')\r\nassert(valid)\r\n%%\r\n%AND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[.5;.5;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 0 0 1]')\r\nassert(valid)\r\n%%\r\n%NAND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[-.5;-.5;1];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 1 1 0]')\r\nassert(valid)\r\n%%\r\n%OR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 -.5 0;-.5 1 0;0 0 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 1]')\r\nassert(valid)\r\n%%\r\n%NOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[-1 -1 0;-1 -1 0;0.5 .5 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 0 0 0]')\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-21T05:50:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-21T04:23:55.000Z","updated_at":"2026-09-03T10:14:08.000Z","published_at":"2023-08-21T05:50:47.000Z","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 challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\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\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"930\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1303\\\"/\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\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 function template includes the code to create this figure using Matlab 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.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average (variable kernel length)","description":"Find the moving average in a vector. The kernel length is a variable.\r\nFor example \r\n\r\n x = 1:10\r\n kernel_length = 2 \r\n\r\nwould result in\r\n\r\n [ 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 ]\r\n\r\nand\r\n\r\n x = 1:10\r\n kernel_length = 3 \r\n\r\nwould result in\r\n\r\n [ 2 3 4 5 6 7 8 9 ]\r\n","description_html":"\u003cp\u003eFind the moving average in a vector. The kernel length is a variable.\r\nFor example\u003c/p\u003e\u003cpre\u003e x = 1:10\r\n kernel_length = 2 \u003c/pre\u003e\u003cp\u003ewould result in\u003c/p\u003e\u003cpre\u003e [ 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 ]\u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e x = 1:10\r\n kernel_length = 3 \u003c/pre\u003e\u003cp\u003ewould result in\u003c/p\u003e\u003cpre\u003e [ 2 3 4 5 6 7 8 9 ]\u003c/pre\u003e","function_template":"function y = moving_avg(x,kernel_length)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1:10;\r\nkernel_length=4\r\ny_correct = [  2.5000    3.5000    4.5000    5.5000    6.5000    7.5000    8.5000];\r\nassert(isequal(moving_avg(x,kernel_length),y_correct))\r\n\r\n%%\r\n\r\nx = 10:20;\r\nkernel_length=5\r\ny_correct = [  12.0000   13.0000   14.0000   15.0000   16.0000   17.0000   18.0000];\r\nassert(isequal(moving_avg(x,kernel_length),y_correct))\r\n\r\n%%\r\nx = ones(1,10);\r\nkernel_length=5\r\ny_correct = ones(1,6);\r\nassert(isequal(moving_avg(x,kernel_length),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1023,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":139,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-15T03:02:53.000Z","updated_at":"2026-09-10T12:09:17.000Z","published_at":"2013-03-15T03:02:52.000Z","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\u003eFind the moving average in a vector. The kernel length is a variable. 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 = 1:10\\n kernel_length = 2]]\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\u003ewould result in\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[ [ 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 ]]]\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\u003eand\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 = 1:10\\n kernel_length = 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\u003ewould result in\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[ [ 2 3 4 5 6 7 8 9 ]]]\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":61413,"title":"Title","description":"Make a plot for x and add title \"My Plot\".\r\nNOTICE: YOU CAN NOT USE ans INSTEAD OF [y ax]!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; 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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a plot for \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ex \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand add title \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eMy Plot\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; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eNOTICE: YOU CAN NOT USE ans INSTEAD OF [y ax]!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y ax] = makeTitle(x)\r\n  \r\nend","test_suite":"%%\r\nx = [1:50];\r\ny = makeTitle(x)\r\nassert(isequal(y.YData,x))\r\nax = y.Parent;\r\nassert(strcmp(ax.Title.String, 'My Plot'));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-17T19:12:43.000Z","updated_at":"2026-09-14T04:56:20.000Z","published_at":"2026-06-17T19:12:43.000Z","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:rPr/\u003e\u003cw:t\u003eMake a plot for \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\u003ex \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand add title \\\"\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\u003eMy Plot\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\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\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTICE: YOU CAN NOT USE ans INSTEAD OF [y ax]!\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":57595,"title":"MATLAB 101: Find alternating sum","description":"Given an array, find alternating sum i.e. – y = x (1) – x (2) + x (3) – x (4) + x (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: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 10.4972px; transform-origin: 406.996px 10.5043px; 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: 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 an array, find alternating sum i.e. – y = x (1) – x (2) + x (3) – x (4) + x (5) - …\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 = [2,5,4,6,1];\r\ny_correct = -4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = repmat([1,0],1,20);\r\ny_correct = 20;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1:100;\r\ny_correct = -50;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1000:23:1000000;\r\ny_correct = 500491;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":2294940,"edited_at":"2026-06-13T16:23:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-20T10:52:03.000Z","updated_at":"2026-09-18T03:45:44.000Z","published_at":"2023-01-20T10:52:03.000Z","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 an array, find alternating sum i.e. – y = x (1) – x (2) + x (3) – x (4) + x (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":42438,"title":"row removal ","description":"Consider a matrix and remove the first row of the matrix.\r\n","description_html":"\u003cp\u003eConsider a matrix and remove the first row of the matrix.\u003c/p\u003e","function_template":"function y = remove_row(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx  = [ 1, 2, 3; 3, 5, 9; 1, 8, 0 ]\r\ny_correct  = [3, 5, 9; 1, 8, 0]\r\nassert(isequal(remove_row(x),y_correct))\r\n\r\n%%\r\nx  = [ 3, 5; 1, 0 ]\r\ny_correct  = [1, 0]\r\nassert(isequal(remove_row(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":43484,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":414,"test_suite_updated_at":"2015-07-14T21:03:19.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-06-29T06:48:13.000Z","updated_at":"2026-09-05T18:23:56.000Z","published_at":"2015-06-29T06:48:13.000Z","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\u003eConsider a matrix and remove the first row of the matrix.\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":49082,"title":"Energy Conversion 1","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; 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 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: 239px 8px; transform-origin: 239px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an energy in the unit of BTU (British Thermal Unit), convert it to Joule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = convert_stuff(x)\r\n  y = x+273.15;\r\nend","test_suite":"%%\r\nx = 123;\r\ny_correct = 129772.38;\r\nassert(abs(convert_stuff(x)-y_correct)\u003c1e-4)\r\n\r\n%%\r\nx = 0.015;\r\ny_correct = 15.8259;\r\nassert(abs(convert_stuff(x)-y_correct)\u003c1e-4)\r\n\r\n%%\r\nx = 66.3;\r\ny_correct = 69950.478;\r\nassert(abs(convert_stuff(x)-y_correct)\u003c1e-4)","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1079,"test_suite_updated_at":"2021-03-22T11:36:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T22:07:55.000Z","updated_at":"2026-08-25T15:48:09.000Z","published_at":"2020-12-22T22:07:55.000Z","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 an energy in the unit of BTU (British Thermal Unit), convert it to Joule.\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":120,"title":"radius of a spherical planet","description":"You just measured its surface area, that is the input.","description_html":"\u003cp\u003eYou just measured its surface area, that is the input.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 4*pi;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 400*pi;\r\ny_correct = 10;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 40000*pi;\r\ny_correct = 100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = -4*pi;\r\ny_correct = 1i;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":19,"comments_count":9,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4603,"test_suite_updated_at":"2012-02-15T16:29:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-27T21:02:01.000Z","updated_at":"2026-09-21T14:31:03.000Z","published_at":"2012-02-15T16:45:42.000Z","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\u003eYou just measured its surface area, that is the 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":45803,"title":"SatCom #7: Thermal Noise in a Receiver ","description":"Satellite and Space Engineering - Problem #7\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\r\nYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\r\nYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\r\nHint: See https://en.wikipedia.org/wiki/Noise_figure#General - but don't forget to convert to dB!\r\nExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","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: 294px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 147px; transform-origin: 407px 147px; 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: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #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: 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: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\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: 359.5px 8px; transform-origin: 359.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\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: 334.5px 8px; transform-origin: 334.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\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: 209px 8px; transform-origin: 209px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\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: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: See\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=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Noise_figure#General\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Noise_figure#General\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: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - but don't forget to convert to dB!\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: 354px 8px; transform-origin: 354px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function power = thermal_noise_power(Bandwidth, Noise_Temp)\r\n  power = Bandwidth+Noise_Temp;\r\nend","test_suite":"%%\r\nBandwidth = 2e6;\r\nNoise_Temp = 200;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -142.5786;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\nBandwidth = 20e6;\r\nNoise_Temp = 120;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -134.7971;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\nBandwidth = 1;\r\nNoise_Temp = 290;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -203.9752;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\ns=fileread('thermal_noise_power.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":3,"created_by":437780,"edited_by":223089,"edited_at":"2023-03-01T17:32:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":"2023-03-01T17:32:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-09T20:05:50.000Z","updated_at":"2026-08-25T14:54:37.000Z","published_at":"2020-09-25T16:48:19.000Z","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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\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\u003eDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\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\u003eYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\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\u003eYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\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\u003eHint: See\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/Noise_figure#General\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Noise_figure#General\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e - but don't forget to convert to dB!\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: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\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":640,"title":"Getting logical indexes","description":"This is a basic MATLAB operation.  It is for instructional purposes.\r\n\r\n---\r\n\r\nLogical indexing works like this.\r\n\r\n  thresh = 4;\r\n  vec    = [1 2 3 4 5 6 7 8];\r\n  \r\n  vi     = (vec \u003e thresh)\r\n  \r\n  vi =\r\n  \r\n       0     0     0     0     1     1     1     1\r\n\r\nOnce you have this TRUE FALSE vector (I call it vi: Valid Indices)\r\n\r\nIt can be used to get the values out:\r\n\r\n  big = vec(vi)\r\n  \r\n  big =\r\n  \r\n       5     6     7     8\r\n\r\nGiven a vector, vec, and a value, v, return a binary vector that represents the indices where vector, vec, is equal to scalar, v.\r\n\r\nNote, this works just as well with scalars and matrices.\r\n\r\n----\r\n\r\nTo get the indices where this comparison is true, see this \u003chttp://www.mathworks.com/matlabcentral/cody/problems/645-getting-the-indices-from-a-vector Cody problem\u003e.","description_html":"\u003cp\u003eThis is a basic MATLAB operation.  It is for instructional purposes.\u003c/p\u003e\u003cp\u003e---\u003c/p\u003e\u003cp\u003eLogical indexing works like this.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ethresh = 4;\r\nvec    = [1 2 3 4 5 6 7 8];\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003evi     = (vec \u003e thresh)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003evi =\r\n\u003c/pre\u003e\u003cpre\u003e       0     0     0     0     1     1     1     1\u003c/pre\u003e\u003cp\u003eOnce you have this TRUE FALSE vector (I call it vi: Valid Indices)\u003c/p\u003e\u003cp\u003eIt can be used to get the values out:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ebig = vec(vi)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ebig =\r\n\u003c/pre\u003e\u003cpre\u003e       5     6     7     8\u003c/pre\u003e\u003cp\u003eGiven a vector, vec, and a value, v, return a binary vector that represents the indices where vector, vec, is equal to scalar, v.\u003c/p\u003e\u003cp\u003eNote, this works just as well with scalars and matrices.\u003c/p\u003e\u003cp\u003e----\u003c/p\u003e\u003cp\u003eTo get the indices where this comparison is true, see this \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/645-getting-the-indices-from-a-vector\"\u003eCody problem\u003c/a\u003e.\u003c/p\u003e","function_template":"function vi = binaryEqualsVector(vec, v)\r\n  vi = true;\r\nend","test_suite":"%%\r\nvec = [1 2 3 3 2 1];\r\nv = 2;\r\ny_correct = [false true false false true false];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n\r\n%%\r\nvec = [1 2 3 4 5 6];\r\nv = 0;\r\ny_correct = [false false false false false false];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n\r\n%%\r\nvec = [1 1 1 1 1];\r\nv = 1;\r\ny_correct = [true true true true true];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n\r\n%%\r\nvec = 'abcdef';\r\nv = 'a';\r\ny_correct = [true false false false false false];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":0,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1197,"test_suite_updated_at":"2012-04-30T18:48:13.000Z","rescore_all_solutions":false,"group_id":12,"created_at":"2012-04-30T18:46:03.000Z","updated_at":"2026-09-15T12:13:09.000Z","published_at":"2012-04-30T18:48:13.000Z","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 a basic MATLAB operation. It is for instructional purposes.\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\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\u003eLogical indexing works like this.\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[thresh = 4;\\nvec    = [1 2 3 4 5 6 7 8];\\n\\nvi     = (vec \u003e thresh)\\n\\nvi =\\n\\n       0     0     0     0     1     1     1     1]]\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\u003eOnce you have this TRUE FALSE vector (I call it vi: Valid Indices)\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\u003eIt can be used to get the values out:\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[big = vec(vi)\\n\\nbig =\\n\\n       5     6     7     8]]\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, vec, and a value, v, return a binary vector that represents the indices where vector, vec, is equal to scalar, 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\u003eNote, this works just as well with scalars and matrices.\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\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\u003eTo get the indices where this comparison is true, see this\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/645-getting-the-indices-from-a-vector\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody problem\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\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":2779,"title":"Rule of mixtures (composites) - weighted bound","description":"The \u003chttp://en.wikipedia.org/wiki/Rule_of_mixtures rule of mixtures\u003e is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:\r\n\r\n* Ef: elastic modulus of the fiber material\r\n* Em: elastic modulus of the matrix material\r\n* ff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)\r\n\r\nBased on these values, the lower-bound estimate of elastic modulus is calculated by:\r\n\r\nEc = 1 / (ff / Ef + (1 – ff) / Em).\r\n\r\nOn the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:\r\n\r\nEc = ff * Ef + (1 – ff) * Em.\r\n\r\nWrite a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)\r\n","description_html":"\u003cp\u003eThe \u003ca href = \"http://en.wikipedia.org/wiki/Rule_of_mixtures\"\u003erule of mixtures\u003c/a\u003e is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:\u003c/p\u003e\u003cul\u003e\u003cli\u003eEf: elastic modulus of the fiber material\u003c/li\u003e\u003cli\u003eEm: elastic modulus of the matrix material\u003c/li\u003e\u003cli\u003eff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eBased on these values, the lower-bound estimate of elastic modulus is calculated by:\u003c/p\u003e\u003cp\u003eEc = 1 / (ff / Ef + (1 – ff) / Em).\u003c/p\u003e\u003cp\u003eOn the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:\u003c/p\u003e\u003cp\u003eEc = ff * Ef + (1 – ff) * Em.\u003c/p\u003e\u003cp\u003eWrite a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)\u003c/p\u003e","function_template":"function [Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt)\r\n Ec = 1;\r\nend","test_suite":"%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 19.5240) \u003c 1e-4)\r\n\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 25.3493) \u003c 1e-4)\r\n\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 31.1747) \u003c 1e-4)\r\n\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 14.5455) \u003c 1e-4)\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 17.5303) \u003c 1e-4)\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 20.5152) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 87.4186) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 160.6124) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 233.8062) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 48.4330) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 85.1220) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 121.8110) \u003c 1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":99,"test_suite_updated_at":"2014-12-16T23:05:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-16T04:22:51.000Z","updated_at":"2026-06-22T03:08:37.000Z","published_at":"2014-12-16T04:22:51.000Z","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\",\"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://en.wikipedia.org/wiki/Rule_of_mixtures\\\"\u003e\u003cw:r\u003e\u003cw:t\u003erule of mixtures\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:\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\u003eEf: elastic modulus of the fiber material\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\u003eEm: elastic modulus of the matrix material\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\u003eff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)\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\u003eBased on these values, the lower-bound estimate of elastic modulus is calculated 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:t\u003eEc = 1 / (ff / Ef + (1 – ff) / Em).\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 other hand, the upper-bound (linear) estimate of elastic modulus is calculated 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:t\u003eEc = ff * Ef + (1 – ff) * Em.\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\u003eWrite a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)\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":45446,"title":"Create logarithmically spaced values (★)","description":"Given three numbers a,b,n with b\u003ea, create a vector y with n logarithmic spaced values between 10^a and 10^b.\r\nThus, if a = -2, b = 3 and n = 6, then \r\n\r\n  y = [10^-2 10^-1 10^0 10^1 10^2 10^3] = [0.01 0.1 1.0 10.0 100.0 1000.0]  ","description_html":"\u003cp\u003eGiven three numbers a,b,n with b\u0026gt;a, create a vector y with n logarithmic spaced values between 10^a and 10^b.\r\nThus, if a = -2, b = 3 and n = 6, then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey = [10^-2 10^-1 10^0 10^1 10^2 10^3] = [0.01 0.1 1.0 10.0 100.0 1000.0]  \r\n\u003c/pre\u003e","function_template":"function y = logarithmic_spacing(a,b,n)\r\n  y = 1;\r\nend","test_suite":"%%\r\na = -2; b = 3; n = 6;\r\ny_correct = [0.01 0.1 1.0 10.0 100.0 1000.0];\r\nassert(isequal(y_correct,logarithmic_spacing(a,b,n)))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":118,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-12T21:20:54.000Z","updated_at":"2026-05-30T05:51:27.000Z","published_at":"2020-04-12T21:20:54.000Z","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 three numbers a,b,n with b\u0026gt;a, create a vector y with n logarithmic spaced values between 10^a and 10^b. Thus, if a = -2, b = 3 and n = 6, 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[y = [10^-2 10^-1 10^0 10^1 10^2 10^3] = [0.01 0.1 1.0 10.0 100.0 1000.0]]]\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":51755,"title":"Make the first letter of a sentence Capital.","description":"In this problem you will be given a string of 2 or 3 lines. Your work is to make the first letters of every line Capital. You will not be given a string with any names. You have to keep all the spaces, symbols as they are given, except the first letter of the sentence.\r\nHappy coding!!!","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: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem you will be given a string of 2 or 3 lines. Your work is to make the first letters of every line Capital. You will not be given a string with any names. You have to keep all the spaces, symbols as they are given, except the first letter of the sentence.\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: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHappy coding!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = making_capital(x)\r\n\r\nend","test_suite":"%%\r\nx = 'hello everyone. how are you? its a nice day for walk';\r\ny_correct = 'Hello everyone. How are you? Its a nice day for walk';\r\nassert(isequal(making_capital(x),y_correct))\r\n\r\n%%\r\nx = 'long long day ago there was a king. he was very kind to his people. people loved him very much';\r\ny_correct = 'Long long day ago there was a king. He was very kind to his people. People loved him very much';\r\nassert(isequal(making_capital(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1022097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2021-07-16T06:51:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-12T16:33:03.000Z","updated_at":"2026-07-24T15:16:07.000Z","published_at":"2021-05-17T06:20:52.000Z","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\u003eIn this problem you will be given a string of 2 or 3 lines. Your work is to make the first letters of every line Capital. You will not be given a string with any names. You have to keep all the spaces, symbols as they are given, except the first letter of the sentence.\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\u003eHappy coding!!!\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":43608,"title":"Namespace","description":"Create a set of n variable names 'a_1',...,'a_n'\r\n\r\nThe result should be a column oriented cell array of strings.\r\n\r\nExample input:\r\n\r\n  n=5\r\n\r\nExample output: \r\n\r\n  {'a_1';'a_2';'a_3';'a_4';'a_5'}","description_html":"\u003cp\u003eCreate a set of n variable names 'a_1',...,'a_n'\u003c/p\u003e\u003cp\u003eThe result should be a column oriented cell array of strings.\u003c/p\u003e\u003cp\u003eExample input:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003en=5\r\n\u003c/pre\u003e\u003cp\u003eExample output:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e{'a_1';'a_2';'a_3';'a_4';'a_5'}\r\n\u003c/pre\u003e","function_template":"function varnames = your_fcn_name(n)\r\n  varnames = {};\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = {'a_1';'a_2';'a_3';'a_4';'a_5';'a_6';'a_7';'a_8';'a_9';'a_10'};\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = {'a_1';'a_2';'a_3';'a_4';'a_5';'a_6'};\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":29461,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2016-12-05T18:26:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T15:52:10.000Z","updated_at":"2026-07-26T02:06:35.000Z","published_at":"2016-10-24T15:52:10.000Z","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\u003eCreate a set of n variable names 'a_1',...,'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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe result should be a column oriented cell array of strings.\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 input:\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]]\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\u003eExample output:\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[{'a_1';'a_2';'a_3';'a_4';'a_5'}]]\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":2012,"title":"Tony's trick for duplicating an mx1 vector n times","description":"Without using repmat, or for loop, or concatenation, create a function to duplicate a vector, v, a specified number of times, n. v can be numeric or character. n may be 0.\r\n\r\nExamples\r\n\r\nIf\r\n\r\n v = 5;\r\n n = 3;\r\n\r\nthen return v1:\r\n\r\n v1 = [5 5 5] \r\n\r\nIf a 2d matrix is supplied then the vector v will be the first column.\r\n\r\n V = magic(4);\r\n n = 4;\r\n\r\nthen v and v1 are returned as shown below.\r\n\r\n v = [16 5 9 4]'\r\n v1 = [16 16 16 16; 5 5 5 5; 9 9 9 9; 4 4 4 4] \r\n\r\nHint: use indexing\r\n","description_html":"\u003cp\u003eWithout using repmat, or for loop, or concatenation, create a function to duplicate a vector, v, a specified number of times, n. v can be numeric or character. n may be 0.\u003c/p\u003e\u003cp\u003eExamples\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre\u003e v = 5;\r\n n = 3;\u003c/pre\u003e\u003cp\u003ethen return v1:\u003c/p\u003e\u003cpre\u003e v1 = [5 5 5] \u003c/pre\u003e\u003cp\u003eIf a 2d matrix is supplied then the vector v will be the first column.\u003c/p\u003e\u003cpre\u003e V = magic(4);\r\n n = 4;\u003c/pre\u003e\u003cp\u003ethen v and v1 are returned as shown below.\u003c/p\u003e\u003cpre\u003e v = [16 5 9 4]'\r\n v1 = [16 16 16 16; 5 5 5 5; 9 9 9 9; 4 4 4 4] \u003c/pre\u003e\u003cp\u003eHint: use indexing\u003c/p\u003e","function_template":"function v1 = reproduce_nv(v,n)\r\n  v1 = v;\r\nend","test_suite":"%%\r\nx=magic(3);\r\nn=3;\r\ny_correct=[8 8 8; 3 3 3; 4 4 4];\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n%%\r\nx=magic(10);\r\nn=19;\r\ny_correct=repmat(x(:,1),1,19);\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n%% \r\nx=1;\r\nn=0;\r\ny_correct=linspace(x,x,n); %arbitrary way to get the soln\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n%%\r\nx='1';\r\nn=7;\r\ny_correct=['1' '1' '1' '1' '1' '1' '1'];\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":17471,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-23T08:42:47.000Z","updated_at":"2026-09-03T20:43:41.000Z","published_at":"2013-11-23T08:48:28.000Z","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\u003eWithout using repmat, or for loop, or concatenation, create a function to duplicate a vector, v, a specified number of times, n. v can be numeric or character. n may be 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\u003eExamples\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\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[ v = 5;\\n n = 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\u003ethen return v1:\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[ v1 = [5 5 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\u003eIf a 2d matrix is supplied then the vector v will be the first column.\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[ V = magic(4);\\n n = 4;]]\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\u003ethen v and v1 are returned as shown below.\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[ v = [16 5 9 4]'\\n v1 = [16 16 16 16; 5 5 5 5; 9 9 9 9; 4 4 4 4]]]\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\u003eHint: use indexing\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":61020,"title":"The Case of the Missing Prototype - Count the Fingerprints Found at the Lab Door to Begin Your Investigation","description":"You arrive at the Innovation Lab where the secret prototype was stolen. The door has been dusted for fingerprints, and a technician provides you with a binary vector prints.\r\nHere, 1 represents a fingerprint found and 0 means a clean spot.\r\nYour first task as Detective Alex Verma is to count the total number of fingerprints discovered at the scene. Every fingerprint brings you one step closer to the truth.\r\nReturn a single number — the count of 1s in prints.","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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 153px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 76.5px; transform-origin: 408px 76.5px; 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: 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=\"\"\u003eYou arrive at 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eInnovation Lab\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003esecret prototype\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e was stolen. The door has been dusted for fingerprints, and a technician provides you with a binary vector \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eprints\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; 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: 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=\"\"\u003eHere, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e represents 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e fingerprint found\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e0\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e means 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eclean spot\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; unicode-bidi: normal; \"\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; 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=\"\"\u003eYour first task as Detective Alex Verma is to \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecount the total 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of fingerprints discovered at the scene. Every fingerprint brings you one step closer to the truth.\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=\"\"\u003eReturn a single number — 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecount 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003es\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eprints\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; 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 count = countFingerprints(prints)\r\n  y = x;\r\nend","test_suite":"%%\r\nprints = [1 0 1 1 0 0 1];\r\nprints_correct = 4;\r\nassert(isequal(countFingerprints(prints),prints_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4953963,"edited_by":4953963,"edited_at":"2025-10-20T15:41:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-20T15:39:33.000Z","updated_at":"2026-09-12T23:32:44.000Z","published_at":"2025-10-20T15:41:28.000Z","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\u003eYou arrive at the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInnovation Lab\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esecret prototype\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e was stolen. The door has been dusted for fingerprints, and a technician provides you with a binary vector \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\u003eprints\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\u003eHere, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e represents a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e fingerprint found\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:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eclean spot\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\u003eYour first task as Detective Alex Verma is to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecount the total number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of fingerprints discovered at the scene. Every fingerprint brings you one step closer to the truth.\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\u003eReturn a single number — the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecount of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in \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\u003eprints\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":50048,"title":"Number Puzzles - 016","description":null,"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: 413px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.5px; transform-origin: 407px 206.5px; 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=\"\"\u003eA smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 332px; 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 166px; text-align: left; transform-origin: 384px 166px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\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=\"\"\u003eThe Sudoko board in this problem has \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-weight: 700; \"\u003ethree\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 numbers not in the right position. Please help fixing it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_016(x)\r\n  y = ones(6);\r\nend","test_suite":"%%\r\nx = [4\t1\t6\t5\t3\t4\r\n2\t3\t5\t6\t1\t4\r\n5\t3\t2\t1\t4\t3\r\n3\t4\t1\t2\t6\t5\r\n1\t2\t3\t4\t5\t6\r\n6\t5\t4\t6\t2\t1];\r\ny=puzzle_016(x);\r\nassert(unique(sum(y,1))==21)\r\nassert(unique(sum(y,2))==21)\r\nassert(length(unique(y-x))==4)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"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":"2021-01-29T16:07:44.000Z","updated_at":"2026-09-20T18:41:20.000Z","published_at":"2021-01-29T16:07:44.000Z","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 smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"326\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"377\\\"/\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\u003eThe Sudoko board in this problem has \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 numbers not in the right position. Please help fixing 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Puzzles - 015","description":null,"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: 413px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.5px; transform-origin: 407px 206.5px; 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=\"\"\u003eA smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 332px; 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 166px; text-align: left; transform-origin: 384px 166px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\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=\"\"\u003eThe Sudoko board in this problem has two numbers not in the right position. Please help fixing it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_015(x)\r\n  y = min(floor(rand(6).*6)+1,6);\r\nend","test_suite":"%%\r\nx = [1\t2\t3\t4\t5\t6\r\n6\t5\t1\t3\t2\t1\r\n5\t6\t2\t1\t4\t3\r\n3\t4\t1\t2\t6\t5\r\n4\t1\t6\t5\t3\t2\r\n2\t4\t5\t6\t1\t4];\r\ny=puzzle_015(x);\r\nassert(unique(sum(y,1))==21)\r\nassert(unique(sum(y,2))==21)\r\nassert(length(unique(y-x))==3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"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":"2021-01-29T16:01:59.000Z","updated_at":"2026-09-20T18:37:44.000Z","published_at":"2021-01-29T16:01:59.000Z","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 smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"326\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"377\\\"/\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\u003eThe Sudoko board in this problem has two numbers not in the right position. Please help fixing 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roots of unity","description":"First, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\r\n\r\n\u003chttps://en.wikipedia.org/wiki/Root_of_unity\u003e\r\n\r\nSecond, raise each root to the power pi (.^pi).\r\n\r\nThird, sum the resulting numbers and use that as the output. \r\n","description_html":"\u003cp\u003eFirst, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Root_of_unity\"\u003ehttps://en.wikipedia.org/wiki/Root_of_unity\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSecond, raise each root to the power pi (.^pi).\u003c/p\u003e\u003cp\u003eThird, sum the resulting numbers and use that as the output.\u003c/p\u003e","function_template":"function y = your_fcn_name(n)\r\n  y = 0;\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct =  -0.467800202134647;\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 50;\r\ny_correct = -2.151544927902936 - 0.430301217000093i\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 7;\r\ny_correct =   -0.435928596902380\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n\r\n%%\r\nn = 70;\r\ny_correct =   -3.031653804728051 - 0.430301217000095i\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":65480,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-08-01T00:25:42.000Z","updated_at":"2026-02-24T14:03:00.000Z","published_at":"2016-08-01T00:25:42.000Z","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\u003eFirst, find the n nth roots of unity. eg if n = 6, find the n distinct (complex) numbers such that n^6 = 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\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Root_of_unity\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Root_of_unity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\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\u003eSecond, raise each root to the power pi (.^pi).\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\u003eThird, sum the resulting numbers and use that as the output.\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":45448,"title":"Vector raised to a power, element-wise (★)","description":"Given a vector A and a number x, raise each element of the vector to the power of x. Thus, if A = [2 5 7 1] and x = 0.5, then \r\n\r\n  y = [2^0.5 5^0.5 7^0.5 1^0.5] = [1.4142 2.2361 2.6458 1.0000]","description_html":"\u003cp\u003eGiven a vector A and a number x, raise each element of the vector to the power of x. Thus, if A = [2 5 7 1] and x = 0.5, then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey = [2^0.5 5^0.5 7^0.5 1^0.5] = [1.4142 2.2361 2.6458 1.0000]\r\n\u003c/pre\u003e","function_template":"function y = raise_vector(A,x)\r\n  y = 1;\r\nend","test_suite":"%%\r\nA = [1 2 3 4]; x = 2;\r\ny_correct = [1 4 9 16];\r\nassert(isequal(raise_vector(A,x),y_correct))\r\n%%\r\nA = [81 16 1296]; x = 0.25;\r\ny_correct = [3 2 6];\r\nassert(isequal(raise_vector(A,x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":134,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-12T21:41:15.000Z","updated_at":"2026-05-30T05:51:33.000Z","published_at":"2020-04-12T21:41:15.000Z","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 A and a number x, raise each element of the vector to the power of x. Thus, if A = [2 5 7 1] and x = 0.5, 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[y = [2^0.5 5^0.5 7^0.5 1^0.5] = [1.4142 2.2361 2.6458 1.0000]]]\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":2120,"title":"Rounding off numbers to n decimals","description":"Inspired by a mistake in one of the problems I created, I created this problem where you have to round off a floating point number to n decimals. There are 2 inputs to the function: x: floating point number and n: number of decimals which need to match with the given solutions.","description_html":"\u003cp\u003eInspired by a mistake in one of the problems I created, I created this problem where you have to round off a floating point number to n decimals. There are 2 inputs to the function: x: floating point number and n: number of decimals which need to match with the given solutions.\u003c/p\u003e","function_template":"function y = myround(x,n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\nn=1;\r\ny_correct = 1;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = pi;\r\nn=5;\r\ny_correct = 3.14159;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = 0.5*sqrt(2);\r\nn=6;\r\ny_correct = 0.707107;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = exp(1);\r\nn=9;\r\ny_correct = 2.718281828;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = 0.00123456;\r\nn=6;\r\ny_correct = 0.001235;\r\nassert(isequal(myround(x,n),y_correct))\r\n","published":true,"deleted":false,"likes_count":24,"comments_count":3,"created_by":20079,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5810,"test_suite_updated_at":"2014-01-15T04:17:27.000Z","rescore_all_solutions":false,"group_id":38,"created_at":"2014-01-15T04:03:48.000Z","updated_at":"2026-09-19T05:06:03.000Z","published_at":"2014-01-15T04:14:20.000Z","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\u003eInspired by a mistake in one of the problems I created, I created this problem where you have to round off a floating point number to n decimals. There are 2 inputs to the function: x: floating point number and n: number of decimals which need to match with the given solutions.\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":61381,"title":"Switch-Case-Otherwise","description":"You should make random numbers to 10, by 3 rows and 3 columns.\r\nCases from 1 to 3, b = true.\r\nOtherwise, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 40.5px; transform-origin: 401px 40.5px; 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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCases from 1 to 3, b = true.\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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eOtherwise, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = CASE(a)\r\n  \r\nend","test_suite":"%%\r\na = 6;\r\nb = false;\r\nassert(isequal(CASE(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":124,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:39:29.000Z","updated_at":"2026-08-30T15:03:24.000Z","published_at":"2026-05-31T07:39:29.000Z","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:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\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\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCases from 1 to 3, b = true.\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\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOtherwise, b = false.\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":195,"title":"Program an exclusive OR operation with logical operators","description":"Program an exclusive or operation *without* using the MATLAB function xor.\r\n\r\nUse logical operators like |, \u0026, ~, ... instead.\r\n\r\nExamples:\r\n  \r\n  myXOR(1,1)\r\n    \r\n  ans = 0\r\n         \r\n    \r\n  myXOR(1,0)\r\n    \r\n  ans = 1\r\n    \r\n    \r\n  myXOR(0,1)\r\n    \r\n  ans = 1\r\n    \r\n         \r\n  myXOR(0,0)\r\n    \r\n  ans = 0","description_html":"\u003cp\u003eProgram an exclusive or operation \u003cb\u003ewithout\u003c/b\u003e using the MATLAB function xor.\u003c/p\u003e\u003cp\u003eUse logical operators like |, \u0026, ~, ... instead.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(1,1)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 0\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(1,0)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 1\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(0,1)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 1\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(0,0)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 0\r\n\u003c/pre\u003e","function_template":"function y = myXOR(a,b)\r\n  y=0;\r\nend","test_suite":"%%\r\na=0;b=0;\r\nres=0;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=1;b=1;\r\nres=0;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=1;b=0;\r\nres=1;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=0;b=1;\r\nres=1;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=[0 0 1 1];b=[1 0 1 0];\r\nres=[1 0 0 1];\r\nassert(isequal(myXOR(a,b),res))","published":true,"deleted":false,"likes_count":9,"comments_count":0,"created_by":564,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":803,"test_suite_updated_at":"2012-01-31T07:59:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T07:59:29.000Z","updated_at":"2026-08-14T04:17:49.000Z","published_at":"2012-01-31T08:03:50.000Z","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\u003eProgram an exclusive or operation\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\u003ewithout\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e using the MATLAB function xor.\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 logical operators like\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, \u0026amp;, ~, ... instead.\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[myXOR(1,1)\\n\\nans = 0\\n\\nmyXOR(1,0)\\n\\nans = 1\\n\\nmyXOR(0,1)\\n\\nans = 1\\n\\nmyXOR(0,0)\\n\\nans = 0]]\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":51820,"title":"Count unique orderings of vertices of a polygon","description":"Cody Problem 2671 asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\r\nHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \r\nWrite a function to determine the unique orderings of vertices of a polygon with  sides. \r\n","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: 356.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 178.458px; transform-origin: 407px 178.458px; 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2671\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 2671\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: 294.433px 7.91667px; transform-origin: 294.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\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: 383.133px 7.91667px; transform-origin: 383.133px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \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: 245.317px 7.91667px; transform-origin: 245.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the unique orderings of vertices of a polygon with \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: 22.1667px 7.91667px; transform-origin: 22.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 182.917px; 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 91.4583px; text-align: left; transform-origin: 384px 91.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 262px;height: 177px\" 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data-image-state=\"image-loaded\" width=\"262\" height=\"177\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polyVert(n)\r\n  y = nchoosek(2*n,n);\r\nend","test_suite":"%% Rectangle\r\nassert(isequal(polyVert(4),3))\r\n\r\n%% Triangle\r\nassert(isequal(polyVert(3),1))\r\n\r\n%% Heptagon\r\nassert(isequal(polyVert(7),360))\r\n\r\n%% Dodecagon\r\nassert(isequal(polyVert(12),19958400))\r\n\r\n%% Heptadecagon\r\nassert(isequal(polyVert(17),10461394944000))\r\n\r\n%% \r\nd = num2str(polyVert(19))-'0';\r\np = polyval(d(1:3:end),4);\r\np_correct = 3760;\r\nassert(isequal(p,p_correct))\r\n\r\n%% \r\nd = num2str(polyVert(15));\r\ns = polyVert(str2num(d(4)))+polyVert(str2num(d(6:7)));\r\ns_correct = 3113512920;\r\nassert(isequal(s,s_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":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-27T04:52:02.000Z","updated_at":"2026-05-25T05:51:39.000Z","published_at":"2021-05-27T04:56:25.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2671\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2671\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\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\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \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 unique orderings of vertices of a polygon with \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\u003e sides. \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 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hydraulic geometry relations","description":"Hydraulic geometry relations express the velocity , width , and depth  of a river as a function of the discharge (or flow) , which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\r\n\r\nwhere the coefficients have the appropriate dimensions. \r\nWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., ) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. ","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: 200px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100px; transform-origin: 407px 100px; 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-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=\"\"\u003eHydraulic geometry relations express the velocity \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, width \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);\"\u003eB\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and depth \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);\"\u003eH\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a river as a function of the discharge (or flow) \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);\"\u003eQ\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; 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 13px; text-align: left; transform-origin: 384px 13px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203.5\" height=\"26\" alt=\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\" style=\"width: 203.5px; height: 26px;\"\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-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=\"\"\u003ewhere the coefficients have the appropriate dimensions. \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-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 two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" alt=\"Q = VBH\" style=\"width: 63px; 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [anew,enew] = hydraulicGeometry(a,e)\r\n  anew = 1.1*a;\r\n  enew = 1.1*e;\r\nend","test_suite":"%\r\na = [NaN 7.2 0.27];\r\ne = [NaN 0.5 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5144 7.2 0.27];\r\nenew_correct = [0.2 0.5 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.5 NaN 0.3];\r\ne = [0.25 NaN 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5 6.6667 0.3];\r\nenew_correct = [0.25 0.45 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.45 7 NaN];\r\ne = [0.23 0.48 NaN];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.45 7 0.3175];\r\nenew_correct = [0.23 0.48 0.29];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.8 5 NaN];\r\ne = [NaN 0.3 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.8 5 0.25];\r\nenew_correct = [0.3 0.3 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.6 4 NaN];\r\ne = [0.1 NaN 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.6 4 0.4167];\r\nenew_correct = [0.1 0.5 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [NaN 4.6 0.8];\r\ne = [0.15 NaN 0.37];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.2717 4.6 0.8];\r\nenew_correct = [0.15 0.48 0.37];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-14T15:47:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-12-14T15:46:55.000Z","updated_at":"2026-06-06T01:59:06.000Z","published_at":"2024-12-14T15:47:02.000Z","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\u003eHydraulic geometry relations express the velocity \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=\\\"V\\\"/\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:t\u003e, width \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=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and depth \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=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a river as a function of the discharge (or flow) \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=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = a_1 Q^{e_1}, B = a_2 Q^{e_2}, H = a_3 Q^{e_3}\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\u003ewhere the coefficients have the appropriate dimensions. \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 two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \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=\\\"Q = VBH\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = VBH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \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":57615,"title":"About jokes (and compression)","description":"An argument can be made about jokes. The shorter they are, the funnier. Further explained here: https://en.wikipedia.org/wiki/Humour#Formula.Thus, jokes are data compression made art.\r\nYou will be given a single text for the whole problem. Your goal is to make it shorter so it would take less space. \r\nWrite a function that takes no argument. It always returns the same character array. You will find that exact array in the Test Suite. However, the content of your MATLAB file must be shorter than the source material. The number of characters you type counts and you must save at least 25%.\r\n\r\nFind patterns and/or useful documentation on your own. There are multiple ways to go about it. I know you will come up with a great one-liner. Have fun!","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: 225px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.5px; transform-origin: 407px 112.5px; 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=\"\"\u003eAn argument can be made about jokes. The shorter they are, the funnier. Further explained here: \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/dQw4w9WgXcQ\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Humour#Formula\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.Thus, jokes are \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Data_compression\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edata compression\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 made art.\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=\"\"\u003eYou will be given a single text for the whole problem. Your goal is to make it shorter so it would take less space. \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efunction\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 that takes \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; \"\u003eno argument.\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 It always \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; \"\u003ereturns the same character array.\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 You will find that exact array in the Test Suite. However, the content of your MATLAB file must be shorter than the source material. \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=\"text-decoration: underline; text-decoration-line: underline; \"\u003eThe number of characters you type counts and you must save at least 25%.\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: 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=\"\"\u003eFind patterns and/or useful documentation on your own. There are multiple ways to go about it. I know you will come up with a great one-liner. Have fun!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function never_gonna_give_you_up = roll()\r\n    % Did I mention Cody does not like running jokes?\r\n    never_gonna_give_you_up = ['We''re no strangers to love' ,char(10),...\r\n    'You know the rules and so do I (do I)' ,char(10),...\r\n    'A full commitment''s what I''m thinking of' ,char(10),...\r\n    'You wouldn''t get this from any other guy' ,char(10),...\r\n    'I just wanna tell you how I''m feeling' ,char(10),...\r\n    'Gotta make you understand' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'We''ve known each other for so long' ,char(10),...\r\n    'Your heart''s been aching, but you''re too shy to say it (say it)' ,char(10),...\r\n    'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n    'We know the game and we''re gonna play it' ,char(10),...\r\n    'And if you ask me how I''m feeling' ,char(10),...\r\n    'Don''t tell me you''re too blind to see' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'We''ve known each other for so long' ,char(10),...\r\n    'Your heart''s been aching, but you''re too shy to say it (to say it)' ,char(10),...\r\n    'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n    'We know the game and we''re gonna play it' ,char(10),...\r\n    'I just wanna tell you how I''m feeling' ,char(10),...\r\n    'Gotta make you understand' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you']\r\nend","test_suite":"RICK = ['We''re no strangers to love' ,char(10),...\r\n'You know the rules and so do I (do I)' ,char(10),...\r\n'A full commitment''s what I''m thinking of' ,char(10),...\r\n'You wouldn''t get this from any other guy' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'And if you ask me how I''m feeling' ,char(10),...\r\n'Don''t tell me you''re too blind to see' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (to say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you'];\r\n\r\n%% Hint :)\r\nRICK = ['We''re no strangers to love' ,char(10),...\r\n'You know the rules and so do I (do I)' ,char(10),...\r\n'A full commitment''s what I''m thinking of' ,char(10),...\r\n'You wouldn''t get this from any other guy' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'And if you ask me how I''m feeling' ,char(10),...\r\n'Don''t tell me you''re too blind to see' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (to say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you'];\r\ndisplay(RICK);\r\nroll();\r\n\r\n%% Content\r\nroll_ = roll();\r\ndisplay(roll_)\r\nassert(ischar(roll_), 'Output is not a char array.');\r\nassert(isequal(RICK, roll_), 'Text output does not match.');\r\n\r\n%% Compression\r\nfiletext = fileread('roll.m');\r\ndisplay(filetext);\r\nl0 = length(RICK);\r\nl1 = length(filetext);\r\nfprintf('\\nOriginal size:%d, Your file:%d\\n', [l0 l1]);\r\nassert(l0 \u003e l1, 'Your file should contain less characters than the original text.');\r\nspaceSaving = ceil(100*(1-l1/l0));\r\nfprintf('\\nYou saved %d/100!\\n', spaceSaving);\r\nif spaceSaving \u003e 85\r\n    display(\"but at what cost...\");\r\nelse\r\n    assert(spaceSaving \u003e 25, 'Try to reach 25/100.');\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3019900,"edited_by":3019900,"edited_at":"2023-01-26T01:47:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-01-26T01:47:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-25T23:33:10.000Z","updated_at":"2026-06-03T23:08:56.000Z","published_at":"2023-01-26T01:43:23.000Z","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\u003eAn argument can be made about jokes. The shorter they are, the funnier. Further explained here: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/dQw4w9WgXcQ\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Humour#Formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.Thus, jokes are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Data_compression\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata compression\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e made art.\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\u003eYou will be given a single text for the whole problem. Your goal is to make it shorter so it would take less space. \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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eno argument.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e It always \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ereturns the same character array.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e You will find that exact array in the Test Suite. However, the content of your MATLAB file must be shorter than the source material. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe number of characters you type counts and you must save at least 25%.\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\u003eFind patterns and/or useful documentation on your own. There are multiple ways to go about it. I know you will come up with a great one-liner. Have fun!\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":53950,"title":"Time reverse indices","description":"Time reverse the index values as follows\r\nIndexIn = [7 1 0]    \r\nIndexOut = [7 6 0]\r\nNote that the indices are zero based and sorted from largest to smallest.\r\nYou can think of this as a time reversal of a vector:\r\n[7 1 0] --\u003e [1     1     0     0     0     0     0     1 ] \r\n[7 6 0] --\u003e [1     0     0     0     0     0     1     1 ]\r\n\r\nHere is a second example\r\n[8 4 3 2 0]  --\u003e [ 1     0     1     1     1     0     0     0     1 ]\r\n[8 6 5 4 0]  --\u003e [ 1     0     0     0     1     1     1     0     1 ]\r\n\r\nBackground of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.","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: 465px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 331.5px 232.5px; transform-origin: 331.5px 232.5px; 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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTime reverse the index values as follows\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIndexIn = [7 1 0]    \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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIndexOut = [7 6 0]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eNote that the indices are zero based and sorted from largest to smallest.\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou can think of this as a time reversal of a vector:\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[7 1 0] --\u0026gt; [1     1     0     0     0     0     0     1 ] \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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[7 6 0] --\u0026gt; [1     0     0     0     0     0     1     1 ]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHere is a second example\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[8 4 3 2 0]  --\u0026gt; [ 1     0     1     1     1     0     0     0     1 ]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[8 6 5 4 0]  --\u0026gt; [ 1     0     0     0     1     1     1     0     1 ]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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: 308.5px 52.5px; text-align: left; transform-origin: 308.5px 52.5px; 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=\"\"\u003eBackground of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function IndexOut = reverseIndices(IndexIn)\r\n  IndexOut = IndexIn;\r\nend","test_suite":"%%\r\nx = [7  1  0];\r\ny_correct = [7  6  0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [8  4  3  2  0];\r\ny_correct = [8  6  5  4  0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [9  4  0];\r\ny_correct = [9  5  0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [10   3   0];\r\ny_correct = [10   7   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [11   2   0];\r\ny_correct = [11   9   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [45   4   3   1   0];\r\ny_correct = [45  44  42  41   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [46   8   5   3   2   1   0];\r\ny_correct = [46  45  44  43  41  38   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [47   5   0];\r\ny_correct = [47  42   0];\r\nassert(isequal(reverseIndices(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":280816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-20T21:14:20.000Z","updated_at":"2026-06-11T02:46:39.000Z","published_at":"2022-01-20T21:14:20.000Z","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\u003eTime reverse the index values as follows\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\u003eIndexIn = [7 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIndexOut = [7 6 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\u003eNote that the indices are zero based and sorted from largest to smallest.\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\u003eYou can think of this as a time reversal of 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[7 1 0] --\u0026gt; [1     1     0     0     0     0     0     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\u003e[7 6 0] --\u0026gt; [1     0     0     0     0     0     1     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\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\u003eHere is a second example\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[8 4 3 2 0]  --\u0026gt; [ 1     0     1     1     1     0     0     0     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\u003e[8 6 5 4 0]  --\u0026gt; [ 1     0     0     0     1     1     1     0     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\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\u003eBackground of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.\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":{"problems":[{"id":2007,"title":"Swap two numbers","description":"Example \r\n\r\nInput:\r\n\r\n a = 10\r\n b = 20\r\n\r\nOutput\r\n\r\n a = 20\r\n b = 10\r\n","description_html":"\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eInput:\u003c/p\u003e\u003cpre\u003e a = 10\r\n b = 20\u003c/pre\u003e\u003cp\u003eOutput\u003c/p\u003e\u003cpre\u003e a = 20\r\n b = 10\u003c/pre\u003e","function_template":"function [aOut,bOut] = swapit(aIn,bIn)\r\n  aOut = 0;\r\n  bOut = 0;\r\nend","test_suite":"%%\r\naIn = 10;\r\nbIn = 20;\r\naOut_correct = 20;\r\nbOut_correct = 10;\r\n[aOut,bOut] = swapit(aIn,bIn);\r\n\r\nassert(isequal(aOut, aOut_correct))\r\nassert(isequal(bOut, bOut_correct))\r\n\r\n%%\r\n\r\naIn = 0;\r\nbIn = -3;\r\naOut_correct = -3;\r\nbOut_correct = 0;\r\n[aOut,bOut] = swapit(aIn,bIn);\r\n\r\nassert(isequal(aOut, aOut_correct))\r\nassert(isequal(bOut, bOut_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":1388,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":814,"test_suite_updated_at":"2013-11-20T16:20:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-19T07:42:21.000Z","updated_at":"2026-09-19T04:57:35.000Z","published_at":"2013-11-19T07:42:21.000Z","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\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\u003eInput:\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[ a = 10\\n b = 20]]\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\u003eOutput\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[ a = 20\\n b = 10]]\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":46548,"title":"Convert Cylindrical Cooridinates into Spherical Coordinate","description":"For Cylindrical coordinate point, rho, fie (degrees) and z. Convert these points in Spherical Cooridinate System and save result into vector 'result'. Round your result upto 3 decimal places.\r\nGenerate an accurate function to evaulate any points of Cylindrical Coordinate System.","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: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor Cylindrical coordinate point, rho, fie (degrees) and z. Convert these points in Spherical Cooridinate System and save result into vector 'result'. Round your result upto 3 decimal places.\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: 274.5px 8px; transform-origin: 274.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGenerate an accurate function to evaulate any points of Cylindrical Coordinate System.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = your_fcn_name(rho,fie,z)\r\n  result = [rho,fie,z]\r\nend","test_suite":"%%\r\nrho=5;\r\nfie=120;\r\nz=1;\r\ny_correct = [5.099,78.69,120];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=3;\r\nfie=60;\r\nz=4;\r\ny_correct = [5,round(36.86989765,3),60];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=7;\r\nfie=45;\r\nz=0;\r\ny_correct = [7,90,45];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=0;\r\nfie=135;\r\nz=11;\r\ny_correct = [11,0,135];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nrho=sqrt(8);\r\nfie=-75;\r\nz=sqrt(8);\r\ny_correct = [4,45,-75];\r\nassert(isequal(your_fcn_name(rho,fie,z),y_correct))\r\n\r\n%%\r\nassert(isequal(your_fcn_name(0,0,1),[1 0 0]))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":526936,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2022-03-06T09:59:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-08-14T20:12:14.000Z","updated_at":"2026-09-17T18:42:41.000Z","published_at":"2020-08-14T20:20:11.000Z","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\u003eFor Cylindrical coordinate point, rho, fie (degrees) and z. Convert these points in Spherical Cooridinate System and save result into vector 'result'. Round your result upto 3 decimal places.\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\u003eGenerate an accurate function to evaulate any points of Cylindrical Coordinate System.\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":2793,"title":"Guess","description":"A random number between 1 and 10 is created for the variable y. Guess what its value is.","description_html":"\u003cp\u003eA random number between 1 and 10 is created for the variable y. Guess what its value is.\u003c/p\u003e","function_template":"function y = guess(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = randi(x);\r\nassert(isequal(guess(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":33304,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":91,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-17T14:28:15.000Z","updated_at":"2026-08-21T06:26:12.000Z","published_at":"2014-12-17T14:28:15.000Z","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\u003eA random number between 1 and 10 is created for the variable y. Guess what its value is.\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":43801,"title":"Union Jack Matrix","description":"Create a matrix of odd dimensions that has ones on both diagonals and dividing the matrix into 4 quadrants, resembling a square union jack flag. For example, if n=11:\r\n\r\n  1  0  0  0  0  1  0  0  0  0  1\r\n0  1  0  0  0  1  0  0  0  1  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  0  0  1  1  1  0  0  0  0\r\n1  1  1  1  1  1  1  1  1  1  1\r\n0  0  0  0  1  1  1  0  0  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  1  0  0  0  1  0  0  0  1  0\r\n1  0  0  0  0  1  0  0  0  0  1\r\n\r\n","description_html":"\u003cp\u003eCreate a matrix of odd dimensions that has ones on both diagonals and dividing the matrix into 4 quadrants, resembling a square union jack flag. For example, if n=11:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1  0  0  0  0  1  0  0  0  0  1\r\n0  1  0  0  0  1  0  0  0  1  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  0  0  1  1  1  0  0  0  0\r\n1  1  1  1  1  1  1  1  1  1  1\r\n0  0  0  0  1  1  1  0  0  0  0\r\n0  0  0  1  0  1  0  1  0  0  0\r\n0  0  1  0  0  1  0  0  1  0  0\r\n0  1  0  0  0  1  0  0  0  1  0\r\n1  0  0  0  0  1  0  0  0  0  1\r\n\u003c/pre\u003e","function_template":"function y = union_jack(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = ones(3);\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1,0,1,0,1;\r\n             0,1,1,1,0;\r\n             1,1,1,1,1;\r\n             0,1,1,1,0;\r\n             1,0,1,0,1];\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [1,0,0,1,0,0,1;\r\n             0,1,0,1,0,1,0;\r\n             0,0,1,1,1,0,0;\r\n             1,1,1,1,1,1,1;\r\n             0,0,1,1,1,0,0;\r\n             0,1,0,1,0,1,0;\r\n             1,0,0,1,0,0,1];\r\nassert(isequal(union_jack(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = [1,0,0,0,1,0,0,0,1;\r\n             0,1,0,0,1,0,0,1,0;\r\n             0,0,1,0,1,0,1,0,0;\r\n             0,0,0,1,1,1,0,0,0;\r\n             1,1,1,1,1,1,1,1,1;\r\n             0,0,0,1,1,1,0,0,0;\r\n             0,0,1,0,1,0,1,0,0;\r\n             0,1,0,0,1,0,0,1,0;\r\n             1,0,0,0,1,0,0,0,1];\r\nassert(isequal(union_jack(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":112,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":41,"created_at":"2016-12-13T23:06:30.000Z","updated_at":"2026-09-03T13:20:55.000Z","published_at":"2016-12-13T23:06:30.000Z","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\u003eCreate a matrix of odd dimensions that has ones on both diagonals and dividing the matrix into 4 quadrants, resembling a square union jack flag. For example, if n=11:\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  0  0  0  0  1  0  0  0  0  1\\n0  1  0  0  0  1  0  0  0  1  0\\n0  0  1  0  0  1  0  0  1  0  0\\n0  0  0  1  0  1  0  1  0  0  0\\n0  0  0  0  1  1  1  0  0  0  0\\n1  1  1  1  1  1  1  1  1  1  1\\n0  0  0  0  1  1  1  0  0  0  0\\n0  0  0  1  0  1  0  1  0  0  0\\n0  0  1  0  0  1  0  0  1  0  0\\n0  1  0  0  0  1  0  0  0  1  0\\n1  0  0  0  0  1  0  0  0  0  1]]\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":2240,"title":"Sum the 'edge' values of a matrix","description":"Sum the 'edge' values of an input matrix (the values along the perimeter).\r\n\r\nExample\r\n\r\n [1 2 3\r\n  4 5 6\r\n  7 8 9]\r\n\r\nOutput = 1 + 2 + 3 + 6 + 9 + 8 + 7 + 4 = 40;\r\n\r\nAssumption: Input matrix equal or bigger than 3x3.","description_html":"\u003cp\u003eSum the 'edge' values of an input matrix (the values along the perimeter).\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e [1 2 3\r\n  4 5 6\r\n  7 8 9]\u003c/pre\u003e\u003cp\u003eOutput = 1 + 2 + 3 + 6 + 9 + 8 + 7 + 4 = 40;\u003c/p\u003e\u003cp\u003eAssumption: Input matrix equal or bigger than 3x3.\u003c/p\u003e","function_template":"function y = AddMatrixLim(x)\r\n %add code\r\nend","test_suite":"%%\r\nx = [1 2 3; 4 5 6;7 8 9];\r\ny_correct = 40;\r\nassert(isequal(AddMatrixLim(x),y_correct))\r\n\r\n%%\r\nx= [1 5 6 7; 4 9 4 7; 9 4 2 1; 0 1 2 8]\r\ny_correct = 51;\r\nassert(isequal(AddMatrixLim(x),y_correct))","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":24008,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":415,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-09T13:39:17.000Z","updated_at":"2026-09-15T16:25:52.000Z","published_at":"2014-03-09T13:39:17.000Z","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\u003eSum the 'edge' values of an input matrix (the values along the perimeter).\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[ [1 2 3\\n  4 5 6\\n  7 8 9]]]\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\u003eOutput = 1 + 2 + 3 + 6 + 9 + 8 + 7 + 4 = 40;\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\u003eAssumption: Input matrix equal or bigger than 3x3.\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":48690,"title":"Laws of motion 4","description":"Given the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; 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 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: 284.5px 8px; transform-origin: 284.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = your_fcn_name(u,v,a)\r\n  y = x;\r\nend","test_suite":"%%\r\nu=0\r\nv=1;\r\na=1;\r\ny_correct = 0.5;\r\nassert(isequal(your_fcn_name(u,v,a),y_correct))\r\n\r\n%%\r\nu=0\r\nv=10;\r\na=1;\r\ny_correct = 50;\r\nassert(isequal(your_fcn_name(u,v,a),y_correct))\r\n\r\n%%\r\nu=20\r\nv=100;\r\na=1;\r\ny_correct = 4800;\r\nassert(isequal(your_fcn_name(u,v,a),y_correct))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":5,"created_by":644918,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2708,"test_suite_updated_at":"2021-02-01T10:35:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-21T17:03:05.000Z","updated_at":"2026-09-14T17:47:10.000Z","published_at":"2020-12-21T17:03:05.000Z","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 the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.\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":47310,"title":"Find Logic 15","description":null,"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: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(4) = 64\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; 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: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; 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=\"\"\u003elogic(5) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; 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: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; 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=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 8;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 25;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 216;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":466,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T14:25:25.000Z","updated_at":"2026-09-06T12:11:32.000Z","published_at":"2020-11-05T14:25:25.000Z","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\u003eGuess the Logic!\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\u003elogic(1) = 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\u003elogic(2) = 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\u003elogic(3) = 9\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\u003elogic(4) = 64\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\u003elogic(5) = 25\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\u003eMake a function logic(x) which will return 'x' th term of sequence.\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":125,"title":"Remove DC","description":"Input x is the sampled signal vector, may have both AC and DC components. Output y should not contain any DC component.\r\n\r\nExample:\r\n\r\n Input  x = [  1  2  3  2  1  2  3]\r\n Output y = [ -1  0  1  0 -1  0  1]","description_html":"\u003cp\u003eInput x is the sampled signal vector, may have both AC and DC components. Output y should not contain any DC component.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input  x = [  1  2  3  2  1  2  3]\r\n Output y = [ -1  0  1  0 -1  0  1]\u003c/pre\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [2 0];\r\ny_correct = [1 -1];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 0:100;\r\ny_correct = -50:50;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":452,"test_suite_updated_at":"2012-01-28T01:22:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-28T01:22:32.000Z","updated_at":"2026-08-20T11:05:23.000Z","published_at":"2012-02-03T02:39:08.000Z","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\u003eInput x is the sampled signal vector, may have both AC and DC components. Output y should not contain any DC component.\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  x = [  1  2  3  2  1  2  3]\\n Output y = [ -1  0  1  0 -1  0  1]]]\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":43193,"title":"Where is 1?","description":"There is a 3d matrix [A] that consist of many zeros and only one.\r\nA=zeros(100,100,100);\r\ni=randi(100);\r\nj=randi(100);\r\nk=randi(100);\r\nA(i,j,k)=1;\r\nWhere is one? Find [i j k].","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: 164.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.0833px; transform-origin: 407px 82.0833px; 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: 202px 8px; transform-origin: 202px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere is a 3d matrix [A] that consist of many zeros and only one.\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: 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: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eA=zeros(100,100,100);\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei=randi(100);\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ej=randi(100);\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ek=randi(100);\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: 44px 8.5px; tab-size: 4; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eA(i,j,k)=1;\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: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere is one? Find [i j k].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [i,j,k] = find1number(A)\r\n  i=\r\n  j=\r\n  k=\r\nend","test_suite":"%%\r\nA=zeros(100,100,100);\r\ni=randi(100);\r\nj=randi(100);\r\nk=randi(100);\r\nA(i,j,k)=1;\r\ny=find1number(A)\r\nassert(isequal(y,[i,j,k]))\r\n\r\n%%\r\nA=zeros(100,100,100);\r\ni=randi(100);\r\nj=randi(100);\r\nk=randi(100);\r\nA(i,j,k)=1;\r\ny=find1number(A)\r\nassert(isequal(y,[i,j,k]))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":33533,"edited_by":223089,"edited_at":"2023-01-09T11:23:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-15T07:59:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T07:59:14.000Z","updated_at":"2026-08-21T16:57:45.000Z","published_at":"2016-10-08T07:59:14.000Z","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\u003eThere is a 3d matrix [A] that consist of many zeros and only one.\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[A=zeros(100,100,100);\\ni=randi(100);\\nj=randi(100);\\nk=randi(100);\\nA(i,j,k)=1;]]\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 is one? Find [i j k].\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":49998,"title":"Number Puzzles - 006","description":null,"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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; 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 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=\"\"\u003eGive an example of three prime numbers whose product is a palindrome.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_006()\r\n  y = [1 2 3];\r\nend","test_suite":"%%\r\ny=puzzle_006();\r\nassert(isequal(size(unique(y),2),3))\r\nn=num2str(prod(y));\r\nassert(isequal(n,fliplr(n)))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-27T23:18:52.000Z","updated_at":"2026-09-17T18:48:20.000Z","published_at":"2021-01-27T23:20:27.000Z","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\u003eGive an example of three prime numbers whose product is a palindrome.\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":50232,"title":"Number Puzzle - 044","description":null,"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: 136px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 68px; transform-origin: 407px 68px; 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=\"\"\u003eA four-digit number N can be written as abcd where a, b, c, and d do not have to be unique. Find all four-digit numbers that satisfy the following condition:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 55px; 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 27.5px; text-align: left; transform-origin: 384px 27.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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5678];\r\nend","test_suite":"%%\r\na=puzzle_044();\r\nassert(length(a)\u003e=3)\r\nassert(length(unique(a))\u003e=3)\r\nassert(sum(a)==5409)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-10T22:20:17.000Z","updated_at":"2026-09-20T19:10:01.000Z","published_at":"2021-02-10T22:20:17.000Z","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 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64];\r\nassert(isequal(index_power(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":16381,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":967,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":13,"created_at":"2013-08-12T02:52:55.000Z","updated_at":"2026-09-19T16:34:34.000Z","published_at":"2013-08-12T02:54:18.000Z","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 input vector x, return y as index-powered vector as shown below.\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 = [2 3 6 9]]]\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\u003ethen y should be\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[ [2^1 3^2 6^3 9^4] = [2 9 216 6561]]]\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":50892,"title":"Draw a '7' in a zero matrix!","description":null,"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: 441px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 220.5px; transform-origin: 407px 220.5px; 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: 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=\"\"\u003eGiven a x-by-x matrix filled with zeros (x is odd and \u0026gt; 3). Use 7s to draw a number 7 into it! Like this:\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=\"\"\u003ex = 5, y =\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=\"\"\u003e7\t7\t7\t7\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t7\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=\"\"\u003ex = 7, y = \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=\"\"\u003e7\t7\t7\t7\t7\t7\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0\t7\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=\"\"\u003e0\t0\t0\t0\t0\t0      7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = seven(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = [7 7 7 7 7;0 0 0 0 7;0 0 0 0 7;0 0 0 0 7;0 0 0 0 7];\r\nassert(isequal(seven(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [7 7 7 7 7 7 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7;0 0 0 0 0 0 7];\r\nassert(isequal(seven(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = [7 7 7 7 7 7 7 7 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7;0 0 0 0 0 0 0 0 7];\r\nassert(isequal(seven(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":921257,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":696,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-10T06:26:49.000Z","updated_at":"2026-08-28T17:15:00.000Z","published_at":"2021-03-10T06:26:49.000Z","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 a x-by-x matrix filled with zeros (x is odd and \u0026gt; 3). Use 7s to draw a number 7 into it! Like this:\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 = 5, y =\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\u003e7\\t7\\t7\\t7\\t7\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\u003e0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t7\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 = 7, y = \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\u003e7\\t7\\t7\\t7\\t7\\t7\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0\\t7\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\u003e0\\t0\\t0\\t0\\t0\\t0      7\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":42793,"title":"Fast 1-D Convolution (full shape)","description":"This is the first problem in the \u003chttp://www.mathworks.com/matlabcentral/cody/?term=Fast+1-D+Convolution fast 1-D convolution series\u003e. This problem asks you to find a fast algorithm to compute the 1-D convolution in its full output shape.  \r\n\r\nThere exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in *conv* function invoked in the form *conv(u,v,'full')*, and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out. \r\n\r\n* Next problem: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42794-fast-1-d-convolution-same-shape Fast 1-D Convolution (same shape)\u003e.","description_html":"\u003cp\u003eThis is the first problem in the \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/?term=Fast+1-D+Convolution\"\u003efast 1-D convolution series\u003c/a\u003e. This problem asks you to find a fast algorithm to compute the 1-D convolution in its full output shape.\u003c/p\u003e\u003cp\u003eThere exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in \u003cb\u003econv\u003c/b\u003e function invoked in the form \u003cb\u003econv(u,v,'full')\u003c/b\u003e, and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out.\u003c/p\u003e\u003cul\u003e\u003cli\u003eNext problem: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42794-fast-1-d-convolution-same-shape\"\u003eFast 1-D Convolution (same shape)\u003c/a\u003e.\u003c/li\u003e\u003c/ul\u003e","function_template":"function y = fconv1f(u,v)\r\n  y = conv(u,v,'full');   % Extremely inefficient solution!\r\nend","test_suite":"%%\r\n%{\r\n╔═════════════════════════════════════════════════════════════╗\r\n║ Please note that problems in this series are designed for   ║\r\n║ optimizing the code performance, rather than the usual Cody ║\r\n║ \"size\". We are achieving this goal by courtesy of LY Cao's  ║ \r\n║ new scoring function, which automatically grants a better   ║\r\n║ score to a faster solution. Kindly note that simply using   ║\r\n║ the conv function may result in a poor score or even failure║\r\n║ in one of the tests. Suggestions and comments are welcome.  ║\r\n║                                                             ║\r\n║ Thanks \u0026 have fun!                                          ║\r\n║ Peng                                                        ║\r\n╚═════════════════════════════════════════════════════════════╝\r\n%}\r\n\r\n%%\r\nfid = fopen('EvaluateSolution.p','wb'); \r\nfwrite(fid,uint8(sscanf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x')));\r\nfclose(fid);\r\n\r\n%%\r\nu = 1; v = 1;\r\ny_correct = 1;\r\nassert(isequal(fconv1f(u,v),y_correct))\r\n\r\n%%\r\nu = 1:10; v = 1:5;\r\ny_correct = [1,4,10,20,35,50,65,80,95,110,114,106,85,50];\r\nassert(all(abs(fconv1f(u,v)-y_correct)\u003c1e-10))\r\n\r\n%%\r\nu = [2 -4 0 1].'; v = [1:5].';\r\ny_correct = [2,0,-2,-3,-4,-17,4,5].';\r\nassert(all(abs(fconv1f(u,v)-y_correct)\u003c1e-10))\r\n\r\n%%\r\nu = rand(20,1); v = rand(10,1);\r\ny_correct = conv(u,v,'full');\r\nassert(all(abs(fconv1f(u,v)-y_correct)\u003c1e-10))\r\n\r\n%%\r\n% Large data size\r\nglobal sol_score\r\nu = rand(8e5,1); v = rand(1e5,1);\r\nt = builtin('tic');\r\ny = fconv1f(u,v);\r\nsol_score = 50*builtin('toc',t);\r\nAbsTol = 1e-6;   % Maximum absolute error tolerance\r\npass = EvaluateSolution(u,v,y,AbsTol);  \r\nassert(pass);\r\n\r\n%%\r\n% New scoring function by LY Cao\r\nglobal sol_score\r\nfid = fopen('score.p','wb');\r\nfwrite(fid,sscanf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x'));\r\nfclose(fid);\r\nscore(sol_score);\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2016-04-04T03:53:09.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-02T21:05:59.000Z","updated_at":"2026-05-25T00:53:31.000Z","published_at":"2016-04-03T19:56:23.000Z","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 first problem in 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/cody/?term=Fast+1-D+Convolution\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efast 1-D convolution series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This problem asks you to find a fast algorithm to compute the 1-D convolution in its full output shape.\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\u003eThere exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in\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\u003econv\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function invoked in the form\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\u003econv(u,v,'full')\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out.\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\u003eNext problem:\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/42794-fast-1-d-convolution-same-shape\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFast 1-D Convolution (same shape)\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\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":60734,"title":"Conditional transpose","description":"You're given two vectors of the same length, x and y, which might be row or a column vectors. Your task is to ensure that y has the same \"rowishness\" as x: y should be a row vector if x is a row vector, and a column vector if x is a column vector.\r\n\r\nControl flow statements (if, switch, for, while, try) and recursion aren't allowed. Neither are arrayfun and friends (cellfun, structfun, varfun, rowfun, spfun). Cheating is possible but made harder, and in any case discouraged.","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: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 73px; transform-origin: 407px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64px; 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 32px; text-align: left; transform-origin: 384px 32px; 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: 141px 8px; transform-origin: 141px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou're given two vectors of the same length, \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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\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: 216px 8px; transform-origin: 216px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which might be row or a column vectors. Your task is to ensure that \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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\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: 98px 8px; transform-origin: 98px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same \"rowishness\" as \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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 4px 8px; transform-origin: 4px 8px; 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ey\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: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be a row vector 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 122.5px 8px; transform-origin: 122.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a row vector, and a column vector 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\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: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a column vector.\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-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 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: 43px; 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 21.5px; text-align: left; transform-origin: 384px 21.5px; 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: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eControl flow statements (\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: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 8px 8.5px; transform-origin: 8px 8.5px; \"\u003eif\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: 4px 8px; transform-origin: 4px 8px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003eswitch\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: 4px 8px; transform-origin: 4px 8px; 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: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003efor\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: 4px 8px; transform-origin: 4px 8px; 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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003ewhile\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: 4px 8px; transform-origin: 4px 8px; 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: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003etry\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: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and recursion aren't allowed. Neither are \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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003earrayfun\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: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and friends (\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: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; \"\u003ecellfun\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: 4px 8px; transform-origin: 4px 8px; 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: 36px 8px; transform-origin: 36px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; \"\u003estructfun\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: 4px 8px; transform-origin: 4px 8px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003evarfun\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: 4px 8px; transform-origin: 4px 8px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003erowfun\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: 4px 8px; transform-origin: 4px 8px; 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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003espfun\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: 221px 8px; transform-origin: 221px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Cheating is possible but made harder, and in any case discouraged.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = condtranspose(x, y)\r\n    if iscolumn(x) ~= iscolumn(y)\r\n        y = y.';\r\n    end\r\nend\r\n","test_suite":"warning(\"off\", \"MATLAB:DELETE:FileNotFound\")\r\ndelete(\"fileread.m\")\r\ndelete(\"contains.m\")\r\ndelete(\"count.m\")\r\ndelete(\"assert.m\")\r\nm = mtree(fileread(\"condtranspose.m\"));\r\nstrs = string(m.stringvals);\r\nidxs = find(m.iskind({ \"CALL\", \"DCALL\" }));\r\nfuns = strs(idxs + 1);\r\nbanned = [ \"assignin\" \"regexp\" \"str2num\" \"anonymousFunction\" \"eval\" ];\r\ncheated = ~isempty(intersect(funs, banned));\r\nassert(~cheated)\r\n\r\n%%\r\nm = mtree(fileread(\"condtranspose.m\"));\r\nillegalKeyword = m.anykind({ \"IF\", \"FOR\", \"PARFOR\", \"WHILE\", \"SWITCH\", \"TRY\" });\r\nstrs = string(m.stringvals);\r\nidxs = find(m.iskind({ \"CALL\", \"DCALL\" }));\r\nfuns = strs(idxs + 1);\r\nbanned = [ \"arrayfun\" \"cellfun\" \"rowfun\" \"varfun\" \"structfun\" \"spfun\", \"condtranpose\" ];\r\nillegalFunction = ~isempty(intersect(funs, banned));\r\nillegal = illegalKeyword || illegalFunction;\r\nassert(~illegal)\r\n\r\n%%\r\nassert(isequal(condtranspose(1:3, 4:6), 4:6))\r\n\r\n%%\r\nassert(isequal(condtranspose((1:4).', 4:7), (4:7).'))\r\n\r\n%%\r\nassert(isequal(condtranspose(2:9, (-4:3).'), -4:3))\r\n\r\n%%\r\nassert(isequal(condtranspose([1; 4; 9; 16], [17; 16; 15; 13]), [17; 16; 15; 13]))\r\n\r\n%%\r\nfor i = 1:100\r\n    switch randi(4)\r\n        case 1\r\n            assert(isequal(condtranspose(1:3, 4:6), 4:6))\r\n        case 2\r\n            assert(isequal(condtranspose((1:4).', 4:7), (4:7).'))\r\n        case 3\r\n            assert(isequal(condtranspose(2:9, (-4:3).'), -4:3))\r\n        case 4\r\n            assert(isequal(condtranspose([1; 4; 9; 16], [17; 16; 15; 13]), [17; 16; 15; 13]))\r\n    end\r\nend\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":332395,"edited_by":332395,"edited_at":"2024-09-06T08:04:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2024-09-06T08:04:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-09-01T07:33:08.000Z","updated_at":"2026-06-06T01:23:49.000Z","published_at":"2024-09-01T07:38:49.000Z","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\u003eYou're given two vectors of the same length, \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\u003ex\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which might be row or a column vectors. Your task is to ensure that \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\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same \\\"rowishness\\\" as \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\u003ex\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should be a row vector if \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a row vector, and a column vector if \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a column 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\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\u003eControl flow statements (\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\u003eif\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswitch\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: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\u003e, \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\u003e, \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\u003etry\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) and recursion aren't allowed. Neither are \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\u003earrayfun\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and friends (\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\u003ecellfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estructfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erowfun\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espfun\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e). Cheating is possible but made harder, and in any case discouraged.\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":1673,"title":"Pandiagonal Prime Magic Square Verification","description":"Verify if an NxN matrix is a Pandiagonal Prime Magic Square.  \r\n\r\nRequired properties:\r\n\r\n  1) N^2 prime values ( No repeats, 1 is a non-prime )\r\n  2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value\r\n3) Magic Constant is the sum of a row/column/diagonal\r\n\r\n\r\n*Input:* M  (Matrix NxN)\r\n\r\n*Output:* Magic Constant ( 0 if invalid )\r\n\r\n*Example:*\r\n\r\nm=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240\r\n\r\nRows;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31; \r\n\r\nAnti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79\r\n\r\n*Related:*\r\n\r\n1) \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function Kurchan Evaluation\u003e has similar array processing\r\n\r\n2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14","description_html":"\u003cp\u003eVerify if an NxN matrix is a Pandiagonal Prime Magic Square.\u003c/p\u003e\u003cp\u003eRequired properties:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) N^2 prime values ( No repeats, 1 is a non-prime )\r\n2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value\r\n3) Magic Constant is the sum of a row/column/diagonal\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e M  (Matrix NxN)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Magic Constant ( 0 if invalid )\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003em=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240\u003c/p\u003e\u003cp\u003eRows;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31;\u003c/p\u003e\u003cp\u003eAnti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e1) \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1634-kurchan-square-evaluation-function\"\u003eKurchan Evaluation\u003c/a\u003e has similar array processing\u003c/p\u003e\u003cp\u003e2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14\u003c/p\u003e","function_template":"function MagicConstant = pandiag(m)\r\n MagicConstant=1;\r\nend\r\n","test_suite":"%%\r\nm=magic(20);\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,0))\r\n%%\r\nm=[41 137 149 19 37 6427 6343 6277 6449 6353 131 211 397 281 431 6421 6329 6197 6271 6199\r\n557 29 367 59 173 5923 6121 6101 6163 6287 643 827 929 947 769 5897 6043 5623 5851 5791\r\n419 571 631 853 919 6053 5801 5783 5573 5387 859 1229 857 1201 1487 5689 5419 5749 5393 5227\r\n1061 1103 1231 661 1093 5323 5381 5231 5189 5273 1847 2293 1499 2281 1867 4789 4243 5059 4889 4787\r\n1249 1277 1423 1889 1997 5051 4951 4931 4241 4373 2239 2309 2069 2731 2377 4481 4483 4597 4159 4273\r\n241 337 607 683 773 6311 6203 5987 5869 5857 151 263 359 421 379 6317 6217 6067 6047 6011\r\n1039 1301 1553 1697 1759 5501 5569 4999 5101 4801 953 503 991 809 1163 5527 5647 5477 5413 5297\r\n1471 2087 2003 1871 2357 5077 4561 4603 4723 4357 1031 1429 1777 1523 1789 5441 4943 4637 4903 4517\r\n2647 3823 2381 3709 3593 3989 2713 4177 3461 3061 1861 2633 2113 2089 2819 4523 3851 4349 3761 3547\r\n3373 3253 3323 3583 3259 3347 3539 3343 3307 3391 2383 2221 2677 2741 2879 3917 4007 3677 3389 3491\r\n6379 6299 6113 6229 6079 89 181 313 239 311 6469 6373 6361 6491 6473 83 167 233 61 157\r\n5867 5683 5581 5563 5741 613 467 887 659 719 5953 6481 6143 6451 6337 587 389 409 347 223\r\n5651 5281 5653 5309 5023 821 1091 761 1117 1283 6091 5939 5879 5657 5591 457 709 727 937 1123\r\n4663 4217 5011 4229 4643 1721 2267 1451 1621 1723 5449 5407 5279 5849 5417 1187 1129 1279 1321 1237\r\n4271 4201 4441 3779 4133 2029 2027 1913 2351 2237 5261 5233 5087 4621 4513 1459 1559 1579 2269 2137\r\n6359 6247 6151 6089 6131 193 293 443 463 499 6269 6173 5903 5827 5737 199 307 523 641 653\r\n5557 6007 5519 5701 5347 983 863 1033 1097 1213 5471 5209 4957 4813 4751 1009 941 1511 1409 1709\r\n5479 5081 4733 4987 4721 1069 1567 1873 1607 1993 5039 4423 4507 4639 4153 1433 1949 1907 1787 2153\r\n4649 3877 4397 4421 3691 1987 2659 2161 2749 2963 3863 2687 4129 2801 2917 2521 3797 2333 3049 3449\r\n4127 4289 3833 3769 3631 2593 2503 2833 3121 3019 3137 3257 3187 2927 3251 3163 2971 3167 3203 3119];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,65100))\r\n%%\r\nm=[5 73 127 137 53\r\n37 167 17 71 103\r\n83 101 13 67 131\r\n43 31 197 113 11\r\n227 23 41 7 97];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,395))\r\n%%\r\nm=[191\t89\t397\t409\t43\t157\t311\r\n379\t103\t101\t491\t17\t313\t193\r\n317\t241\t109\t163\t439\t47\t281\r\n223\t383\t227\t107\t541\t37\t79\r\n331\t337\t7\t139\t167\t563\t53\r\n83\t347\t389\t277\t127\t307\t67\r\n73\t97\t367\t11\t263\t173\t613];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,1597))\r\n%%\r\nm=[191\t89\t397\t409\t43\t157\t311\r\n379\t103\t101\t491\t17\t313\t193\r\n317\t241\t109\t163\t439\t47\t281\r\n223\t383\t227\t107\t541\t37\t79\r\n331\t337\t7\t139\t167\t3\t53\r\n83\t347\t389\t277\t127\t307\t67\r\n73\t97\t367\t11\t263\t173\t613];\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,0))\r\n%%\r\nm=magic(7);\r\nMagicConstant=pandiag(m);\r\nassert(isequal(MagicConstant,0))\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-22T04:21:02.000Z","updated_at":"2026-06-11T03:16:57.000Z","published_at":"2013-06-22T06:02:47.000Z","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\u003eVerify if an NxN matrix is a Pandiagonal Prime Magic Square.\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\u003eRequired properties:\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) N^2 prime values ( No repeats, 1 is a non-prime )\\n2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value\\n3) Magic Constant is the sum of a row/column/diagonal]]\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e M (Matrix NxN)\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 Magic Constant ( 0 if invalid )\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\u003em=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240\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;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31;\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\u003eAnti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79\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\u003eRelated:\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\u003e1)\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/1634-kurchan-square-evaluation-function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKurchan Evaluation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e has similar array processing\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\u003e2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14\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":43020,"title":"Get factory-defined property values","description":"Given a property name (e.g. 'AxesUnits', 'LineMarkerSize', 'UicontrolBackgroundColor'), return the factory-defined value for that property. This is the value that is used for graphics objects if you do not specify it as an argument.\r\n\r\nFor example, the factory-defined LineMarkerSize is 6, meaning line markers will have size 6 by default unless specified otherwise.","description_html":"\u003cp\u003eGiven a property name (e.g. 'AxesUnits', 'LineMarkerSize', 'UicontrolBackgroundColor'), return the factory-defined value for that property. This is the value that is used for graphics objects if you do not specify it as an argument.\u003c/p\u003e\u003cp\u003eFor example, the factory-defined LineMarkerSize is 6, meaning line markers will have size 6 by default unless specified otherwise.\u003c/p\u003e","function_template":"function x = factory(str)\r\n    x = [];\r\nend","test_suite":"%%\r\nstr = 'AnimatedlineColor';\r\nassert(isequal(factory(str),[0 0 0]))\r\n\r\n%%\r\nstr = 'AreaHandleVisibility';\r\nassert(isequal(factory(str),'on'))\r\n\r\n%%\r\nstr = 'AxesBox';\r\nassert(isequal(factory(str),'off'))\r\n\r\n%%\r\nstr = 'AxesUnits';\r\nassert(isequal(factory(str),'normalized'))\r\n\r\n%%\r\nstr = 'BarLineWidth';\r\nassert(isequal(factory(str),0.5))\r\n\r\n%%\r\nstr = 'ColorbarFontName';\r\nassert(isequal(factory(str),'Helvetica'))\r\n\r\n%%\r\nstr = 'DoubleendarrowshapeHead1Length';\r\nassert(isequal(factory(str),10))\r\n\r\n%%\r\nstr = 'EllipseshapePosition';\r\nassert(isequal(factory(str),[0.3 0.3 0.1 0.1]))\r\n\r\n%%\r\nstr = 'FigureNextPlot';\r\nassert(isequal(factory(str),'add'))\r\n\r\n%%\r\nstr = 'GraphplotPickableParts';\r\nassert(isequal(factory(str),'visible'))\r\n\r\n%%\r\nstr = 'HistogramFaceAlpha';\r\nassert(isequal(factory(str),0.6))\r\n\r\n%%\r\nstr = 'ImageCreateFcn';\r\nassert(isequal(factory(str),''))\r\n\r\n%%\r\nstr = 'LineMarkerSize';\r\nassert(isequal(factory(str),6))\r\n\r\n%%\r\nstr = 'PatchLineStyle';\r\nassert(isequal(factory(str),'-'))\r\n\r\n%%\r\nstr = 'QuiverAutoScaleFactor';\r\nassert(isequal(factory(str),0.9))\r\n\r\n%%\r\nstr = 'RectanglePosition';\r\nassert(isequal(factory(str),[0 0 1 1]))\r\n\r\n%%\r\nstr = 'ScatterMarker';\r\nassert(isequal(factory(str),'o'))\r\n\r\n%%\r\nstr = 'TextInterpreter';\r\nassert(isequal(factory(str),'tex'))\r\n\r\n%%\r\nstr = 'UicontrolBackgroundColor';\r\nassert(isequal(factory(str),[0.9400 0.9400 0.9400]))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T14:43:36.000Z","updated_at":"2026-05-28T16:01:06.000Z","published_at":"2016-10-04T14:43:36.000Z","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 property name (e.g. 'AxesUnits', 'LineMarkerSize', 'UicontrolBackgroundColor'), return the factory-defined value for that property. This is the value that is used for graphics objects if you do not specify it as an argument.\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 factory-defined LineMarkerSize is 6, meaning line markers will have size 6 by default unless specified otherwise.\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":44544,"title":"Normie Function (2)","description":"Another _Normie Function_ defined as _f(n)= f(n-1)+f(n-2)+f(n-3)_ , *when n\u003e3* and _1_ , *when n\u003c=3*. *Find the nth term of this function* .","description_html":"\u003cp\u003eAnother \u003ci\u003eNormie Function\u003c/i\u003e defined as \u003ci\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e1\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e. \u003cb\u003eFind the nth term of this function\u003c/b\u003e .\u003c/p\u003e","function_template":"function y = normie(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 23;\r\ny_correct = 289329;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 36;\r\ny_correct = 797691075;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 37;\r\ny_correct = 1467182629;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 40;\r\ny_correct = 9129195487;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 4045078385041;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 794174268033812736;\r\nassert(isequal(normie(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":"2018-03-28T11:02:45.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-22T09:27:39.000Z","updated_at":"2026-05-29T04:26:43.000Z","published_at":"2018-03-22T09:27:39.000Z","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\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\u003eNormie Function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defined as\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)= f(n-1)+f(n-2)+f(n-3)\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026gt;3\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\u003e1\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026lt;=3\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the nth term of this function\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\"},{\"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":45543,"title":"Find the remainder with the factorial of PRIMES?","description":"* Take a number  greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\r\n* calculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\r\n* As mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\r\n* Divide factorial with the remainder (if possible). e.g. 120/5 = 24\r\n\r\nDon't use builtin functions \r\n\r\n  primes\r\n\r\n  factorial\r\n\r\n  mod","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: 275.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.883px; transform-origin: 407px 137.883px; vertical-align: baseline; \"\u003e\u003cul style=\"block-size: 122.6px; counter-reset: list-item 0; 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 61.3px; transform-origin: 391px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 290px 8px; transform-origin: 290px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; 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 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; 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 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 359px 8px; transform-origin: 359px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 197px 8px; transform-origin: 197px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDon't use builtin functions\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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; 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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; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efactorial\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: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\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: 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: 12px 8.5px; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emod\u003c/span\u003e\u003c/span\u003e\u003c/div\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\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'primes')))\r\nassert(isempty(strfind(filetext, 'factorial')))\r\nassert(isempty(strfind(filetext, 'mod')))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 630;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 49;\r\ny_correct = 3.232790518889602e+58;\r\nassert(abs(your_fcn_name(x)/1e58-y_correct/1e58)\u003c1e-2)\r\n\r\n%%\r\nx = 5;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 6.2270208e+09;\r\nassert(abs(your_fcn_name(x)/1e9-y_correct/1e9)\u003c1e-2)","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":26467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2021-05-20T10:42:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-20T09:50:35.000Z","updated_at":"2026-05-30T14:17:48.000Z","published_at":"2020-05-20T09:54:29.000Z","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=\\\"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\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\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\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\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\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\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\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\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\u003eDon't use builtin functions\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[primes\\n\\nfactorial\\n\\nmod]]\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":49718,"title":"Malus’ Law (theta) between polarizations","description":null,"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: 20.736px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 10.368px; transform-origin: 406.5px 10.368px; 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: 383.496px 10.368px; text-align: left; transform-origin: 383.502px 10.368px; 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=\"\"\u003eFind the angle (\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);\"\u003eθ\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 theta) ,I1 and I2 will be given \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = t(x,y)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;y=5\r\ny_correct = 60;\r\nassert(isequal(t(x,y),y_correct))\r\n%%\r\nx = 20;y=5\r\ny_correct = 75.5225;\r\nassert(isequal(t(x,y),y_correct))\r\n%%\r\nx = 20;y=10\r\ny_correct = 60;\r\nassert(isequal(t(x,y),y_correct))\r\n%%\r\nx = 20;y=4\r\ny_correct = 78.4630;\r\nassert(isequal(t(x,y),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":610936,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-31T03:26:31.000Z","updated_at":"2026-08-21T15:15:03.000Z","published_at":"2020-12-31T03:44:26.000Z","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\u003eFind the angle (\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\\\\theta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e theta) ,I1 and I2 will be given \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":50078,"title":"Number Puzzle - 022","description":null,"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: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; 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: 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=\"\"\u003eGive an example of m and n that satisfy the following conditions:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [m n] = puzzle_022()\r\n  [m n] = [1 1];\r\nend","test_suite":"%%\r\ny = puzzle_022()\r\nassert(min(y)\u003e1000)\r\nassert(max(y)\u003c10^5)\r\nassert(isequal(y(1)^2,y(2)^3))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-31T23:08:58.000Z","updated_at":"2026-08-21T17:12:26.000Z","published_at":"2021-01-31T23:08:58.000Z","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 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Element Occurrences","description":"You are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than 'k times in the original list, only the first 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the k-th occurrence will be discarded. Note that, if k equals 0, the resulting list would be empty.\r\nExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  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: 117.67px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 58.8352px; transform-origin: 406.996px 58.8352px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.6705px; 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 43.8352px; text-align: left; transform-origin: 383.999px 43.8352px; 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=\"\"\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\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; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\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; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003etimes in the original list, only the first\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e k\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth occurrence will be discarded. Note that, 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals 0, the resulting list would be empty.\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-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=\"\"\u003eExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = remove_after_kth(v, k)\r\n\r\nend","test_suite":"%%\r\nk = 2\r\nv =  [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] \r\nL_correct = [ 1, 3, 5, 3, 1,  5 ]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = randi([40,70]);\r\nv = val*ones(1,r)\r\nL_correct = val*ones(1,k)\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 3\r\nv = [1:5,4:-1:1,2:5,4:-1:1,2:5]\r\nL_correct = [1:5,4:-1:1,2:5,1,5]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([5,10])\r\nv = [1, 1, 1, 2, 2, 2]\r\nL_correct = v\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 0\r\nv = randi([1,5],1,20)\r\n% L_correct = []\r\n% assert(isequal(remove_after_kth(v, k),L_correct))\r\nassert(isempty(remove_after_kth(v, k)))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = 1:5;\r\nv = repmat(val,1,k+5) \r\nL_correct = repmat(val,1,k)  \r\nassert(isequal(remove_after_kth(v, k),L_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-13T15:52:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2024-05-13T15:52:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T07:36:09.000Z","updated_at":"2026-08-17T14:35:17.000Z","published_at":"2024-04-01T07:36:15.000Z","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\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\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\u003etimes in the original list, only the first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e k\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\u003eth occurrence will be discarded. Note that, if \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\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e equals 0, the resulting list would be empty.\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: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  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":60822,"title":"Calculate the Number of Moles","description":"The number of moles of a substance is calculated using the formula:\r\nMass (g) = Moles / Molar Mass (g/mol)​\r\nWrite a function calculate_moles(mass, molar_mass) that takes:\r\nmass (in grams) of a substance\r\nmolar_mass (its molar mass in g/mol)\r\nand returns the number of moles, rounded to three decimal places.","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: 174.875px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 87.4375px; transform-origin: 408px 87.4375px; 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=\"\"\u003eThe number of moles of a substance is calculated using the formula:\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=\"\"\u003eMass (g) = Moles / Molar Mass (g/mol)​\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 \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ecalculate_moles(mass, molar_mass)\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that takes:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 42.875px; 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: 392px 21.4375px; transform-origin: 392px 21.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4375px; 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: 364px 10.7188px; text-align: left; transform-origin: 364px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (in grams) of a substance\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.4375px; 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: 364px 10.7188px; text-align: left; transform-origin: 364px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emolar_mass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (its molar mass in g/mol)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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=\"\"\u003eand returns the number 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emoles\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounded to \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethree decimal places\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; 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 moles = calculate_moles(mass, molar_mass)\r\n% calculate_moles Compute the number of moles from mass and molar mass\r\n%   Input:\r\n%       mass - Mass of the substance in grams\r\n%       molar_mass - Molar mass of the substance in g/mol\r\n%   Output:\r\n%       moles - Number of moles (rounded to 3 decimal places)\r\n\r\n% Your code here\r\n\r\nend\r\n","test_suite":"assert(isequal(calculate_moles(18.015, 18.015), 1.000));  % Water (H2O)\r\nassert(isequal(calculate_moles(44.02, 44.01), 1.000));    % Carbon Dioxide (CO2)\r\nassert(isequal(calculate_moles(10, 58.44), 0.171));       % Sodium Chloride (NaCl)\r\nassert(isequal(calculate_moles(120, 342.30), 0.351));     % Sucrose (C12H22O11)\r\nassert(isequal(calculate_moles(0, 18.015), 0.000));       % Zero mass\r\nassert(isequal(calculate_moles(50, 0), 0.000));           % Invalid molar mass (prevent division by zero)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4805571,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-03-19T17:14:26.000Z","updated_at":"2026-09-01T21:12:15.000Z","published_at":"2025-03-19T17:14:26.000Z","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 number of moles of a substance is calculated using the formula:\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\u003eMass (g) = Moles / Molar Mass (g/mol)​\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 \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\u003ecalculate_moles(mass, molar_mass)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes:\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in grams) of a substance\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emolar_mass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (its molar mass in g/mol)\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 returns the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emoles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, rounded to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethree decimal places\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":61336,"title":"Brake Mean Effective Pressure (BMEP)","description":"BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\r\nA higher BMEP indicates a more efficient use of displacement.\r\n\r\nGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: 599.719px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 299.859px; transform-origin: 468.5px 299.859px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 488.719px; 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 244.359px; text-align: left; transform-origin: 444.5px 244.359px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\" data-image-state=\"image-loaded\"\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bmep = calcBMEP(T, Vd, k)\r\nbmep = 0;\r\nend","test_suite":"%%\r\nT = 200; Vd = 0.002; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 350; Vd = 0.003; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 80; Vd = 0.0005; k = 2;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-26T03:50:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:38:18.000Z","updated_at":"2026-08-31T18:03:05.000Z","published_at":"2026-05-21T09:38:18.000Z","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\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\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 higher BMEP indicates a more efficient use of displacement.\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"802\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1477\\\"/\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\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58897,"title":"Neural Net: Calculate Bias Single Perceptron (AND/NAND/OR/NOR/XOR)","description":"This challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\r\nSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\r\n \r\nThe function template includes the code to create this figure using Matlab Latex","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: 664.65px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.325px; transform-origin: 407px 332.325px; 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: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\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: 243.5px 8px; transform-origin: 243.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 553.65px; 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 276.825px; text-align: left; transform-origin: 384px 276.825px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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: 250px 8px; transform-origin: 250px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function template includes the code to create this figure using Matlab Latex\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P=Calc_Single_Bias_Perceptron(X,WH,WP)\r\n%The P value in this case is a single value for each case\r\n%X will be four rows and three columns\r\n%No ReLU,Softmax, or Sigmoid applied to the output P\r\n  P=[0 0 0 0]';\r\nend\r\n\r\n%The figure was generated using Matlab and Latex\r\n%{\r\nfunction perceptron_bias\r\nfigure(1);clf;\r\nplot([0;140;140;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\nr = 10;\r\nphi = 0:0.01:2*pi;\r\ncxA = r*cos(phi);\r\ncyA = r*sin(phi);\r\n\r\nrxA=[0 2*r 2*r   0 0]';\r\nryA=[0   0 2*r 2*r 0]';\r\n\r\ntext(1,95,'Single Bias Perceptron','Fontsize',20);\r\n\r\npatch(cxA+10,cyA+80,'y');text(10-2,80,'X_{1}','Fontsize',20);\r\npatch(cxA+10,cyA+20,'y');text(10-2,20,'X_{2}','Fontsize',20);\r\n\r\npatch(cxA+80,cyA+80,'y');text(80-6,94,'H_{1}','Fontsize',20);text(80-8,80,'\\Sigma','Fontsize',30);\r\npatch(cxA+80,cyA+20,'y');text(80-6,34,'H_{2}','Fontsize',20);text(80-8,20,'\\Sigma','Fontsize',30);\r\n\r\npatch(cxA+130,cyA+50,'y');text(130-2,50,'P','Fontsize',20);\r\n\r\npatch(rxA+80,ryA+70,'y');text(85,80,'ReLU','Fontsize',20);text(100,92,'Y_{1}','Fontsize',20);\r\npatch(rxA+80,ryA+10,'y');text(85,20,'ReLU','Fontsize',20);text(100,32,'Y_{2}','Fontsize',20);\r\n\r\nquiver(20,20,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,20,58.5,58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,58.5,-58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\nquiver(100,20,25,25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(100,80,25,-25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n%quiver(100,80,25,-25,'k','LineWidth',3.5,'Color','r'); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(53,93,20,-10,'k','LineWidth',3.5,'MaxHeadSize',.6); text(53-8,92,'bH_{31}','Fontsize',20);\r\nquiver(60,5,13,10,'k','LineWidth',3.5,'MaxHeadSize',.7); text(60-6,4,'bH_{32}','Fontsize',20);\r\nquiver(130,26,0,15,'k','LineWidth',3.5,'MaxHeadSize',.8); text(130-6,25,'bP_{31}','Fontsize',20);\r\n\r\n\r\ntext(30,85,'WH_{11}','Fontsize',20);\r\ntext(20,65,'WH_{12}','Fontsize',20);\r\ntext(40,25,'WH_{22}','Fontsize',20);\r\ntext(20,38,'WH_{21}','Fontsize',20);\r\n\r\ntext(110,73,'WP_{11}','Fontsize',20);\r\ntext(107,23,'WP_{21}','Fontsize',20);\r\n\r\nstr='$$ X=\\left[\\matrix{ X_{1} \u0026 X_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(1,50,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; %valid\r\ntext(1,3,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ H=\\left[\\matrix{ H_{1} \u0026 H_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,65,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ ReLU(H)=Y  $$'; %valid\r\ntext(75,58,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y=\\left[\\matrix{ Y_{1} \u0026 Y_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,51,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ X*WH=H  $$'; %valid\r\ntext(80,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y*WP=P  $$'; %valid\r\ntext(80,0,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11}\\cr WP_{21} \\cr bP_{31} } \\right]  $$'; %valid\r\ntext(110,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nend %perceptron_bias\r\n\r\n%}","test_suite":"%%\r\n%XOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;0 -1 1];\r\nWP=[1;-2;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 0]')\r\nassert(valid)\r\n%%\r\n%AND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[.5;.5;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 0 0 1]')\r\nassert(valid)\r\n%%\r\n%NAND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[-.5;-.5;1];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 1 1 0]')\r\nassert(valid)\r\n%%\r\n%OR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 -.5 0;-.5 1 0;0 0 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 1]')\r\nassert(valid)\r\n%%\r\n%NOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[-1 -1 0;-1 -1 0;0.5 .5 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 0 0 0]')\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-21T05:50:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-21T04:23:55.000Z","updated_at":"2026-09-03T10:14:08.000Z","published_at":"2023-08-21T05:50:47.000Z","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 challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\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\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"930\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1303\\\"/\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\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 function template includes the code to create this figure using Matlab 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.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average (variable kernel length)","description":"Find the moving average in a vector. The kernel length is a variable.\r\nFor example \r\n\r\n x = 1:10\r\n kernel_length = 2 \r\n\r\nwould result in\r\n\r\n [ 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 ]\r\n\r\nand\r\n\r\n x = 1:10\r\n kernel_length = 3 \r\n\r\nwould result in\r\n\r\n [ 2 3 4 5 6 7 8 9 ]\r\n","description_html":"\u003cp\u003eFind the moving average in a vector. The kernel length is a variable.\r\nFor example\u003c/p\u003e\u003cpre\u003e x = 1:10\r\n kernel_length = 2 \u003c/pre\u003e\u003cp\u003ewould result in\u003c/p\u003e\u003cpre\u003e [ 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 ]\u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e x = 1:10\r\n kernel_length = 3 \u003c/pre\u003e\u003cp\u003ewould result in\u003c/p\u003e\u003cpre\u003e [ 2 3 4 5 6 7 8 9 ]\u003c/pre\u003e","function_template":"function y = moving_avg(x,kernel_length)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1:10;\r\nkernel_length=4\r\ny_correct = [  2.5000    3.5000    4.5000    5.5000    6.5000    7.5000    8.5000];\r\nassert(isequal(moving_avg(x,kernel_length),y_correct))\r\n\r\n%%\r\n\r\nx = 10:20;\r\nkernel_length=5\r\ny_correct = [  12.0000   13.0000   14.0000   15.0000   16.0000   17.0000   18.0000];\r\nassert(isequal(moving_avg(x,kernel_length),y_correct))\r\n\r\n%%\r\nx = ones(1,10);\r\nkernel_length=5\r\ny_correct = ones(1,6);\r\nassert(isequal(moving_avg(x,kernel_length),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1023,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":139,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-15T03:02:53.000Z","updated_at":"2026-09-10T12:09:17.000Z","published_at":"2013-03-15T03:02:52.000Z","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\u003eFind the moving average in a vector. The kernel length is a variable. 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 = 1:10\\n kernel_length = 2]]\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\u003ewould result in\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[ [ 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 ]]]\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\u003eand\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 = 1:10\\n kernel_length = 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\u003ewould result in\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[ [ 2 3 4 5 6 7 8 9 ]]]\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":61413,"title":"Title","description":"Make a plot for x and add title \"My Plot\".\r\nNOTICE: YOU CAN NOT USE ans INSTEAD OF [y ax]!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; 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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a plot for \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ex \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand add title \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eMy Plot\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; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eNOTICE: YOU CAN NOT USE ans INSTEAD OF [y ax]!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y ax] = makeTitle(x)\r\n  \r\nend","test_suite":"%%\r\nx = [1:50];\r\ny = makeTitle(x)\r\nassert(isequal(y.YData,x))\r\nax = y.Parent;\r\nassert(strcmp(ax.Title.String, 'My Plot'));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-17T19:12:43.000Z","updated_at":"2026-09-14T04:56:20.000Z","published_at":"2026-06-17T19:12:43.000Z","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:rPr/\u003e\u003cw:t\u003eMake a plot for \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\u003ex \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand add title \\\"\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\u003eMy Plot\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\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\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTICE: YOU CAN NOT USE ans INSTEAD OF [y ax]!\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":57595,"title":"MATLAB 101: Find alternating sum","description":"Given an array, find alternating sum i.e. – y = x (1) – x (2) + x (3) – x (4) + x (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: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 10.4972px; transform-origin: 406.996px 10.5043px; 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: 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 an array, find alternating sum i.e. – y = x (1) – x (2) + x (3) – x (4) + x (5) - …\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 = [2,5,4,6,1];\r\ny_correct = -4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = repmat([1,0],1,20);\r\ny_correct = 20;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1:100;\r\ny_correct = -50;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1000:23:1000000;\r\ny_correct = 500491;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":2294940,"edited_at":"2026-06-13T16:23:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-20T10:52:03.000Z","updated_at":"2026-09-18T03:45:44.000Z","published_at":"2023-01-20T10:52:03.000Z","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 an array, find alternating sum i.e. – y = x (1) – x (2) + x (3) – x (4) + x (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":42438,"title":"row removal ","description":"Consider a matrix and remove the first row of the matrix.\r\n","description_html":"\u003cp\u003eConsider a matrix and remove the first row of the matrix.\u003c/p\u003e","function_template":"function y = remove_row(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx  = [ 1, 2, 3; 3, 5, 9; 1, 8, 0 ]\r\ny_correct  = [3, 5, 9; 1, 8, 0]\r\nassert(isequal(remove_row(x),y_correct))\r\n\r\n%%\r\nx  = [ 3, 5; 1, 0 ]\r\ny_correct  = [1, 0]\r\nassert(isequal(remove_row(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":43484,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":414,"test_suite_updated_at":"2015-07-14T21:03:19.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-06-29T06:48:13.000Z","updated_at":"2026-09-05T18:23:56.000Z","published_at":"2015-06-29T06:48:13.000Z","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\u003eConsider a matrix and remove the first row of the matrix.\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":49082,"title":"Energy Conversion 1","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; 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 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: 239px 8px; transform-origin: 239px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an energy in the unit of BTU (British Thermal Unit), convert it to Joule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = convert_stuff(x)\r\n  y = x+273.15;\r\nend","test_suite":"%%\r\nx = 123;\r\ny_correct = 129772.38;\r\nassert(abs(convert_stuff(x)-y_correct)\u003c1e-4)\r\n\r\n%%\r\nx = 0.015;\r\ny_correct = 15.8259;\r\nassert(abs(convert_stuff(x)-y_correct)\u003c1e-4)\r\n\r\n%%\r\nx = 66.3;\r\ny_correct = 69950.478;\r\nassert(abs(convert_stuff(x)-y_correct)\u003c1e-4)","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1079,"test_suite_updated_at":"2021-03-22T11:36:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T22:07:55.000Z","updated_at":"2026-08-25T15:48:09.000Z","published_at":"2020-12-22T22:07:55.000Z","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 an energy in the unit of BTU (British Thermal Unit), convert it to Joule.\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":120,"title":"radius of a spherical planet","description":"You just measured its surface area, that is the input.","description_html":"\u003cp\u003eYou just measured its surface area, that is the input.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 4*pi;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 400*pi;\r\ny_correct = 10;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 40000*pi;\r\ny_correct = 100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = -4*pi;\r\ny_correct = 1i;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":19,"comments_count":9,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4603,"test_suite_updated_at":"2012-02-15T16:29:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-27T21:02:01.000Z","updated_at":"2026-09-21T14:31:03.000Z","published_at":"2012-02-15T16:45:42.000Z","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\u003eYou just measured its surface area, that is the 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":45803,"title":"SatCom #7: Thermal Noise in a Receiver ","description":"Satellite and Space Engineering - Problem #7\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\r\nYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\r\nYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\r\nHint: See https://en.wikipedia.org/wiki/Noise_figure#General - but don't forget to convert to dB!\r\nExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","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: 294px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 147px; transform-origin: 407px 147px; 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: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #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: 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: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\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: 359.5px 8px; transform-origin: 359.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\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: 334.5px 8px; transform-origin: 334.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\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: 209px 8px; transform-origin: 209px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\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: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: See\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=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Noise_figure#General\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Noise_figure#General\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: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - but don't forget to convert to dB!\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: 354px 8px; transform-origin: 354px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function power = thermal_noise_power(Bandwidth, Noise_Temp)\r\n  power = Bandwidth+Noise_Temp;\r\nend","test_suite":"%%\r\nBandwidth = 2e6;\r\nNoise_Temp = 200;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -142.5786;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\nBandwidth = 20e6;\r\nNoise_Temp = 120;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -134.7971;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\nBandwidth = 1;\r\nNoise_Temp = 290;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -203.9752;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\ns=fileread('thermal_noise_power.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":3,"created_by":437780,"edited_by":223089,"edited_at":"2023-03-01T17:32:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":"2023-03-01T17:32:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-09T20:05:50.000Z","updated_at":"2026-08-25T14:54:37.000Z","published_at":"2020-09-25T16:48:19.000Z","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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\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\u003eDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\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\u003eYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\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\u003eYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\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\u003eHint: See\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/Noise_figure#General\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Noise_figure#General\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e - but don't forget to convert to dB!\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: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\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":640,"title":"Getting logical indexes","description":"This is a basic MATLAB operation.  It is for instructional purposes.\r\n\r\n---\r\n\r\nLogical indexing works like this.\r\n\r\n  thresh = 4;\r\n  vec    = [1 2 3 4 5 6 7 8];\r\n  \r\n  vi     = (vec \u003e thresh)\r\n  \r\n  vi =\r\n  \r\n       0     0     0     0     1     1     1     1\r\n\r\nOnce you have this TRUE FALSE vector (I call it vi: Valid Indices)\r\n\r\nIt can be used to get the values out:\r\n\r\n  big = vec(vi)\r\n  \r\n  big =\r\n  \r\n       5     6     7     8\r\n\r\nGiven a vector, vec, and a value, v, return a binary vector that represents the indices where vector, vec, is equal to scalar, v.\r\n\r\nNote, this works just as well with scalars and matrices.\r\n\r\n----\r\n\r\nTo get the indices where this comparison is true, see this \u003chttp://www.mathworks.com/matlabcentral/cody/problems/645-getting-the-indices-from-a-vector Cody problem\u003e.","description_html":"\u003cp\u003eThis is a basic MATLAB operation.  It is for instructional purposes.\u003c/p\u003e\u003cp\u003e---\u003c/p\u003e\u003cp\u003eLogical indexing works like this.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ethresh = 4;\r\nvec    = [1 2 3 4 5 6 7 8];\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003evi     = (vec \u003e thresh)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003evi =\r\n\u003c/pre\u003e\u003cpre\u003e       0     0     0     0     1     1     1     1\u003c/pre\u003e\u003cp\u003eOnce you have this TRUE FALSE vector (I call it vi: Valid Indices)\u003c/p\u003e\u003cp\u003eIt can be used to get the values out:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ebig = vec(vi)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ebig =\r\n\u003c/pre\u003e\u003cpre\u003e       5     6     7     8\u003c/pre\u003e\u003cp\u003eGiven a vector, vec, and a value, v, return a binary vector that represents the indices where vector, vec, is equal to scalar, v.\u003c/p\u003e\u003cp\u003eNote, this works just as well with scalars and matrices.\u003c/p\u003e\u003cp\u003e----\u003c/p\u003e\u003cp\u003eTo get the indices where this comparison is true, see this \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/645-getting-the-indices-from-a-vector\"\u003eCody problem\u003c/a\u003e.\u003c/p\u003e","function_template":"function vi = binaryEqualsVector(vec, v)\r\n  vi = true;\r\nend","test_suite":"%%\r\nvec = [1 2 3 3 2 1];\r\nv = 2;\r\ny_correct = [false true false false true false];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n\r\n%%\r\nvec = [1 2 3 4 5 6];\r\nv = 0;\r\ny_correct = [false false false false false false];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n\r\n%%\r\nvec = [1 1 1 1 1];\r\nv = 1;\r\ny_correct = [true true true true true];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n\r\n%%\r\nvec = 'abcdef';\r\nv = 'a';\r\ny_correct = [true false false false false false];\r\nassert(isequal(binaryEqualsVector(vec,v),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":0,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1197,"test_suite_updated_at":"2012-04-30T18:48:13.000Z","rescore_all_solutions":false,"group_id":12,"created_at":"2012-04-30T18:46:03.000Z","updated_at":"2026-09-15T12:13:09.000Z","published_at":"2012-04-30T18:48:13.000Z","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 a basic MATLAB operation. It is for instructional purposes.\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\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\u003eLogical indexing works like this.\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[thresh = 4;\\nvec    = [1 2 3 4 5 6 7 8];\\n\\nvi     = (vec \u003e thresh)\\n\\nvi =\\n\\n       0     0     0     0     1     1     1     1]]\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\u003eOnce you have this TRUE FALSE vector (I call it vi: Valid Indices)\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\u003eIt can be used to get the values out:\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[big = vec(vi)\\n\\nbig =\\n\\n       5     6     7     8]]\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, vec, and a value, v, return a binary vector that represents the indices where vector, vec, is equal to scalar, 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\u003eNote, this works just as well with scalars and matrices.\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\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\u003eTo get the indices where this comparison is true, see this\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/645-getting-the-indices-from-a-vector\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody problem\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\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":2779,"title":"Rule of mixtures (composites) - weighted bound","description":"The \u003chttp://en.wikipedia.org/wiki/Rule_of_mixtures rule of mixtures\u003e is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:\r\n\r\n* Ef: elastic modulus of the fiber material\r\n* Em: elastic modulus of the matrix material\r\n* ff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)\r\n\r\nBased on these values, the lower-bound estimate of elastic modulus is calculated by:\r\n\r\nEc = 1 / (ff / Ef + (1 – ff) / Em).\r\n\r\nOn the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:\r\n\r\nEc = ff * Ef + (1 – ff) * Em.\r\n\r\nWrite a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)\r\n","description_html":"\u003cp\u003eThe \u003ca href = \"http://en.wikipedia.org/wiki/Rule_of_mixtures\"\u003erule of mixtures\u003c/a\u003e is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:\u003c/p\u003e\u003cul\u003e\u003cli\u003eEf: elastic modulus of the fiber material\u003c/li\u003e\u003cli\u003eEm: elastic modulus of the matrix material\u003c/li\u003e\u003cli\u003eff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eBased on these values, the lower-bound estimate of elastic modulus is calculated by:\u003c/p\u003e\u003cp\u003eEc = 1 / (ff / Ef + (1 – ff) / Em).\u003c/p\u003e\u003cp\u003eOn the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:\u003c/p\u003e\u003cp\u003eEc = ff * Ef + (1 – ff) * Em.\u003c/p\u003e\u003cp\u003eWrite a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)\u003c/p\u003e","function_template":"function [Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt)\r\n Ec = 1;\r\nend","test_suite":"%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 19.5240) \u003c 1e-4)\r\n\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 25.3493) \u003c 1e-4)\r\n\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 31.1747) \u003c 1e-4)\r\n\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 14.5455) \u003c 1e-4)\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 17.5303) \u003c 1e-4)\r\n\r\n%%\r\nEf = 100;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 20.5152) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 87.4186) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 160.6124) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.30;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 233.8062) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.25;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 48.4330) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.50;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 85.1220) \u003c 1e-4)\r\n\r\n%%\r\nEf = 1000;\r\nEm = 10;\r\nff = 0.15;\r\nwt = 0.75;\r\n[Ec] = rule_of_mixtures_wt_bound(Ef,Em,ff,wt);\r\nassert(abs(Ec - 121.8110) \u003c 1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":99,"test_suite_updated_at":"2014-12-16T23:05:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-16T04:22:51.000Z","updated_at":"2026-06-22T03:08:37.000Z","published_at":"2014-12-16T04:22:51.000Z","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\",\"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://en.wikipedia.org/wiki/Rule_of_mixtures\\\"\u003e\u003cw:r\u003e\u003cw:t\u003erule of mixtures\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:\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\u003eEf: elastic modulus of the fiber material\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\u003eEm: elastic modulus of the matrix material\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\u003eff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)\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\u003eBased on these values, the lower-bound estimate of elastic modulus is calculated 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:t\u003eEc = 1 / (ff / Ef + (1 – ff) / Em).\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 other hand, the upper-bound (linear) estimate of elastic modulus is calculated 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:t\u003eEc = ff * Ef + (1 – ff) * Em.\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\u003eWrite a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)\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":45446,"title":"Create logarithmically spaced values (★)","description":"Given three numbers a,b,n with b\u003ea, create a vector y with n logarithmic spaced values between 10^a and 10^b.\r\nThus, if a = -2, b = 3 and n = 6, then \r\n\r\n  y = [10^-2 10^-1 10^0 10^1 10^2 10^3] = [0.01 0.1 1.0 10.0 100.0 1000.0]  ","description_html":"\u003cp\u003eGiven three numbers a,b,n with b\u0026gt;a, create a vector y with n logarithmic spaced values between 10^a and 10^b.\r\nThus, if a = -2, b = 3 and n = 6, then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey = [10^-2 10^-1 10^0 10^1 10^2 10^3] = [0.01 0.1 1.0 10.0 100.0 1000.0]  \r\n\u003c/pre\u003e","function_template":"function y = logarithmic_spacing(a,b,n)\r\n  y = 1;\r\nend","test_suite":"%%\r\na = -2; b = 3; n = 6;\r\ny_correct = [0.01 0.1 1.0 10.0 100.0 1000.0];\r\nassert(isequal(y_correct,logarithmic_spacing(a,b,n)))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":118,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-12T21:20:54.000Z","updated_at":"2026-05-30T05:51:27.000Z","published_at":"2020-04-12T21:20:54.000Z","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 three numbers a,b,n with b\u0026gt;a, create a vector y with n logarithmic spaced values between 10^a and 10^b. Thus, if a = -2, b = 3 and n = 6, 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[y = [10^-2 10^-1 10^0 10^1 10^2 10^3] = [0.01 0.1 1.0 10.0 100.0 1000.0]]]\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":51755,"title":"Make the first letter of a sentence Capital.","description":"In this problem you will be given a string of 2 or 3 lines. Your work is to make the first letters of every line Capital. You will not be given a string with any names. You have to keep all the spaces, symbols as they are given, except the first letter of the sentence.\r\nHappy coding!!!","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: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem you will be given a string of 2 or 3 lines. Your work is to make the first letters of every line Capital. You will not be given a string with any names. You have to keep all the spaces, symbols as they are given, except the first letter of the sentence.\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: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHappy coding!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = making_capital(x)\r\n\r\nend","test_suite":"%%\r\nx = 'hello everyone. how are you? its a nice day for walk';\r\ny_correct = 'Hello everyone. How are you? Its a nice day for walk';\r\nassert(isequal(making_capital(x),y_correct))\r\n\r\n%%\r\nx = 'long long day ago there was a king. he was very kind to his people. people loved him very much';\r\ny_correct = 'Long long day ago there was a king. He was very kind to his people. People loved him very much';\r\nassert(isequal(making_capital(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1022097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2021-07-16T06:51:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-12T16:33:03.000Z","updated_at":"2026-07-24T15:16:07.000Z","published_at":"2021-05-17T06:20:52.000Z","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\u003eIn this problem you will be given a string of 2 or 3 lines. Your work is to make the first letters of every line Capital. You will not be given a string with any names. You have to keep all the spaces, symbols as they are given, except the first letter of the sentence.\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\u003eHappy coding!!!\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":43608,"title":"Namespace","description":"Create a set of n variable names 'a_1',...,'a_n'\r\n\r\nThe result should be a column oriented cell array of strings.\r\n\r\nExample input:\r\n\r\n  n=5\r\n\r\nExample output: \r\n\r\n  {'a_1';'a_2';'a_3';'a_4';'a_5'}","description_html":"\u003cp\u003eCreate a set of n variable names 'a_1',...,'a_n'\u003c/p\u003e\u003cp\u003eThe result should be a column oriented cell array of strings.\u003c/p\u003e\u003cp\u003eExample input:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003en=5\r\n\u003c/pre\u003e\u003cp\u003eExample output:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e{'a_1';'a_2';'a_3';'a_4';'a_5'}\r\n\u003c/pre\u003e","function_template":"function varnames = your_fcn_name(n)\r\n  varnames = {};\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = {'a_1';'a_2';'a_3';'a_4';'a_5';'a_6';'a_7';'a_8';'a_9';'a_10'};\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = {'a_1';'a_2';'a_3';'a_4';'a_5';'a_6'};\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":29461,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2016-12-05T18:26:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T15:52:10.000Z","updated_at":"2026-07-26T02:06:35.000Z","published_at":"2016-10-24T15:52:10.000Z","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\u003eCreate a set of n variable names 'a_1',...,'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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe result should be a column oriented cell array of strings.\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 input:\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]]\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\u003eExample output:\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[{'a_1';'a_2';'a_3';'a_4';'a_5'}]]\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":2012,"title":"Tony's trick for duplicating an mx1 vector n times","description":"Without using repmat, or for loop, or concatenation, create a function to duplicate a vector, v, a specified number of times, n. v can be numeric or character. n may be 0.\r\n\r\nExamples\r\n\r\nIf\r\n\r\n v = 5;\r\n n = 3;\r\n\r\nthen return v1:\r\n\r\n v1 = [5 5 5] \r\n\r\nIf a 2d matrix is supplied then the vector v will be the first column.\r\n\r\n V = magic(4);\r\n n = 4;\r\n\r\nthen v and v1 are returned as shown below.\r\n\r\n v = [16 5 9 4]'\r\n v1 = [16 16 16 16; 5 5 5 5; 9 9 9 9; 4 4 4 4] \r\n\r\nHint: use indexing\r\n","description_html":"\u003cp\u003eWithout using repmat, or for loop, or concatenation, create a function to duplicate a vector, v, a specified number of times, n. v can be numeric or character. n may be 0.\u003c/p\u003e\u003cp\u003eExamples\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre\u003e v = 5;\r\n n = 3;\u003c/pre\u003e\u003cp\u003ethen return v1:\u003c/p\u003e\u003cpre\u003e v1 = [5 5 5] \u003c/pre\u003e\u003cp\u003eIf a 2d matrix is supplied then the vector v will be the first column.\u003c/p\u003e\u003cpre\u003e V = magic(4);\r\n n = 4;\u003c/pre\u003e\u003cp\u003ethen v and v1 are returned as shown below.\u003c/p\u003e\u003cpre\u003e v = [16 5 9 4]'\r\n v1 = [16 16 16 16; 5 5 5 5; 9 9 9 9; 4 4 4 4] \u003c/pre\u003e\u003cp\u003eHint: use indexing\u003c/p\u003e","function_template":"function v1 = reproduce_nv(v,n)\r\n  v1 = v;\r\nend","test_suite":"%%\r\nx=magic(3);\r\nn=3;\r\ny_correct=[8 8 8; 3 3 3; 4 4 4];\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n%%\r\nx=magic(10);\r\nn=19;\r\ny_correct=repmat(x(:,1),1,19);\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n%% \r\nx=1;\r\nn=0;\r\ny_correct=linspace(x,x,n); %arbitrary way to get the soln\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n%%\r\nx='1';\r\nn=7;\r\ny_correct=['1' '1' '1' '1' '1' '1' '1'];\r\nassert(isequal(reproduce_nv(x,n),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":17471,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-23T08:42:47.000Z","updated_at":"2026-09-03T20:43:41.000Z","published_at":"2013-11-23T08:48:28.000Z","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\u003eWithout using repmat, or for loop, or concatenation, create a function to duplicate a vector, v, a specified number of times, n. v can be numeric or character. n may be 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\u003eExamples\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\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[ v = 5;\\n n = 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\u003ethen return v1:\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[ v1 = [5 5 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\u003eIf a 2d matrix is supplied then the vector v will be the first column.\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[ V = magic(4);\\n n = 4;]]\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\u003ethen v and v1 are returned as shown below.\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[ v = [16 5 9 4]'\\n v1 = [16 16 16 16; 5 5 5 5; 9 9 9 9; 4 4 4 4]]]\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\u003eHint: use indexing\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":61020,"title":"The Case of the Missing Prototype - Count the Fingerprints Found at the Lab Door to Begin Your Investigation","description":"You arrive at the Innovation Lab where the secret prototype was stolen. The door has been dusted for fingerprints, and a technician provides you with a binary vector prints.\r\nHere, 1 represents a fingerprint found and 0 means a clean spot.\r\nYour first task as Detective Alex Verma is to count the total number of fingerprints discovered at the scene. Every fingerprint brings you one step closer to the truth.\r\nReturn a single number — the count of 1s in prints.","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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 153px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 76.5px; transform-origin: 408px 76.5px; 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: 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=\"\"\u003eYou arrive at 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eInnovation Lab\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003esecret prototype\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e was stolen. The door has been dusted for fingerprints, and a technician provides you with a binary vector \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eprints\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; 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: 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=\"\"\u003eHere, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e represents 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e fingerprint found\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e0\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e means 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eclean spot\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; unicode-bidi: normal; \"\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; 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=\"\"\u003eYour first task as Detective Alex Verma is to \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecount the total 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of fingerprints discovered at the scene. Every fingerprint brings you one step closer to the truth.\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=\"\"\u003eReturn a single number — 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecount 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003es\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eprints\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; 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 count = countFingerprints(prints)\r\n  y = x;\r\nend","test_suite":"%%\r\nprints = [1 0 1 1 0 0 1];\r\nprints_correct = 4;\r\nassert(isequal(countFingerprints(prints),prints_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4953963,"edited_by":4953963,"edited_at":"2025-10-20T15:41:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-20T15:39:33.000Z","updated_at":"2026-09-12T23:32:44.000Z","published_at":"2025-10-20T15:41:28.000Z","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\u003eYou arrive at the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInnovation Lab\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esecret prototype\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e was stolen. The door has been dusted for fingerprints, and a technician provides you with a binary vector \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\u003eprints\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\u003eHere, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e represents a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e fingerprint found\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:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eclean spot\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\u003eYour first task as Detective Alex Verma is to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecount the total number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of fingerprints discovered at the scene. Every fingerprint brings you one step closer to the truth.\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\u003eReturn a single number — the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecount of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in \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\u003eprints\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":50048,"title":"Number Puzzles - 016","description":null,"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: 413px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.5px; transform-origin: 407px 206.5px; 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=\"\"\u003eA smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 332px; 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 166px; text-align: left; transform-origin: 384px 166px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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2XdiM4f7zbRgjK/OuWHzbRbydvKzpt0vmQvK2Wi/dsu7EZw/3m2jBGV+dcsPm226Kvlff8v8AIjmXb8/8yot5O3lZ026XzIXlbLRfu2XdiM4f7zbRgjK/OuWHzbey+G+qXcPgq1jj0HUJ1ebUJmljktwsbi7uD5R3Sg7yQBkArlhlgMkcxXc/C/8A5EKH/r+v/wD0smrz8amorU7sG029DWXWr9vKz4Y1VfMheVsy2v7tl3YjOJ/vNtGCMr865YfNtF1q/bys+GNVXzIXlbMtr+7Zd2Izif7zbRgjK/OuWHzbdiivNPRMddav28rPhjVV8yF5WzLa/u2XdiM4n+820YIyvzrlh820XWr9vKz4Y1VfMheVsy2v7tl3YjOJ/vNtGCMr865YfNt2KKAOT8OaneQ6ZsXwzdKJbi+uG+yXNtIkb/aZ28tybgnzWIG4LlFd8ZUAhdRdav28rPhjVV8yF5WzLa/u2XdiM4n+820YIyvzrlh8208Lrs0iceTbw/8AExvjtt5fMU5upTuJ3Nhj1Zc/KxYYXG0bFJbDe5jrrV+3lZ8MaqvmQvK2ZbX92y7sRnE/3m2jBGV+dcsPm2i61ft5WfDGqr5kLytmW1/dsu7EZxP95towRlfnXLD5tuxRTEY661ft5WfDGqr5kLytmW1/dsu7EZxP95towRlfnXLD5tuX4c1O8h0zYvhm6US3F9cN9kubaRI3+0zt5bk3BPmsQNwXKK74yoBC9ZWP4XXZpE48m3h/4mN8dtvL5inN1KdxO5sMerLn5WLDC42hdR9AXWr9vKz4Y1VfMheVsy2v7tl3YjOJ/vNtGCMr865YfNtF1q/bys+GNVXzIXlbMtr+7Zd2Izif7zbRgjK/OuWHzbdiimIx11q/bys+GNVXzIXlbMtr+7Zd2Izif7zbRgjK/OuWHzbRdav28rPhjVV8yF5WzLa/u2XdiM4n+820YIyvzrlh823YooA5D9nz/khPh7/t5/8ASmWvSa82/Z8/5IT4e/7ef/SmWvSa5jpCiiigAoorPv8AX9H0qdYNT1axs5WXeI7i5SNiuSM4JHGQefamk3sF7D7qws7vVLK4uQrz2u94FY9CQAWA9QDj/gX0q7Xl/wARPGFnFcaHe+HNWsru5tLl5ClvcLJ8u3BDBSeCMj8a9A0PWbXX9Ft9Ssj+7mXJU9Ubup9weK2nSnGnGb2ZnGcXJxRoUUUVgaBRRRQAUUUUAFFFFABRRRQB8q/Db/knum/9tf8A0a9dTXLfDb/knum/9tf/AEa9dTX1FD+FH0X5HzVb+LL1YUUUVsZBVTTV2WrjybeH/SJjtt5fMU5lY7idzYY9WXPysWGFxtFuqmmrstXHk28P+kTHbby+YpzKx3E7mwx6suflYsMLjaIfxr5/oUvhf9dy3RRRVkhRRRQBU01dlq48m3h/0iY7beXzFOZWO4nc2GPVlz8rFhhcbRbqppq7LVx5NvD/AKRMdtvL5inMrHcTubDHqy5+ViwwuNot1FP4EVP4mFFFFWSFdz8L/wDkQof+v6//APSyauGrufhf/wAiFD/1/X//AKWTV52O+GJ34LdnXUUUV5Z6QUUUUAY/hddmkTjybeH/AImN8dtvL5inN1KdxO5sMerLn5WLDC42jYrH8Lrs0iceTbw/8TG+O23l8xTm6lO4nc2GPVlz8rFhhcbRsULYHuFFFFABWP4XXZpE48m3h/4mN8dtvL5inN1KdxO5sMerLn5WLDC42jYrH8Lrs0iceTbw/wDExvjtt5fMU5upTuJ3Nhj1Zc/KxYYXG0HUOhsUUUUAFFFFAHIfs+f8kJ8Pf9vP/pTLXpNebfs+f8kJ8Pf9vP8A6Uy16TXMdIUUUUAFeJ/F/wD5HqH/ALBsX/o2WvbK8s+JXhHX9c8Vw3mj6a13biyjiLrNGmGDyEjDMD0YV3YCcYV05OyObExcqdkeWV2nwz8TS6L4iTTpA8llqLhCiKWKS9FcAdux9sHtXPax4b1rw+kL61p72iTMVjYyxvkgZP3WNekfCnwl9mt/+Ei1CPE06lbNT/BGer/Vu3t/vV7WMrUXh227329TgoQmqq6HpdFFFfLnsBVLVhqjWO3Qms47pnUeZeKzRxrn5m2KQXOOi7lz6irtYfjDX7nw34bnv9P0q71a7yI4La1geUlmOAzBFZgg6kgHgcZJApPYaKPhjxBq1z4k13w/ry2c13pSwTJdWMbRJNHKrEAxs7FGBRv4iCCDxVPwx4s8Qap4+1bRde0q10yG2sobu2hSXzZlV3df3rg7M/JnC5Azjc1L8PBZ21rdh21S51i8f7Zqd7eaTdWizSEAYTzY1G1QAqoOQB06msrSNZjl+M2paiNO1tLO90y1tIJ5dEvI0MqySFgS0Q2gBl+ZsDnrVfaS/rZ/qS/hbX9ar9D0qiiikMKKKKAPlX4bf8k903/tr/6NeuprM+FXgwat8MtKvTruqWnm+d+5gFvsXEzjjfEzds8k9a6//hXa/wDQza1/3zaf/GK96lioxpxVnsv63PDq4aUqkndbsw6K3P8AhXa/9DNrX/fNp/8AGKP+Fdr/ANDNrX/fNp/8YrT63Ds/w/zM/qs+6/H/ACMOqmmrstXHk28P+kTHbby+YpzKx3E7mwx6suflYsMLjaOn/wCFdr/0M2tf982n/wAYrM8P/DwnTZfM8R6mh+3XeBbvaSKR9okwSRE3zEYLDPDEjC42ifrUOZOz/D/Mr6tLlauv6+RWorc/4V2v/Qza1/3zaf8Axij/AIV2v/Qza1/3zaf/ABiq+tw7P8P8yfqs+6/H/Iw6K3P+Fdr/ANDNrX/fNp/8Yo/4V2v/AEM2tf8AfNp/8Yo+tw7P8P8AMPqs+6/H/I5jTV2WrjybeH/SJjtt5fMU5lY7idzYY9WXPysWGFxtFurPh/4eE6bL5niPU0P267wLd7SRSPtEmCSIm+YjBYZ4YkYXG0af/Cu1/wChm1r/AL5tP/jFTDFQUUrP8P8AMqWGk5N3X9fIw6K3P+Fdr/0M2tf982n/AMYo/wCFdr/0M2tf982n/wAYqvrcOz/D/Mn6rPuvx/yMOu5+F/8AyIUP/X9f/wDpZNWF/wAK7X/oZta/75tP/jFZ3hSy1e10Wa3s/FWq28MOo30axpDaEcXcoJy0BOSRk84yTgAYA5sRU9tZRR00Kbo3cmeuUV575Ov/APQ5av8A+A9l/wDI9Hk6/wD9Dlq//gPZf/I9cvsZnT7WJ6FRXnvk6/8A9Dlq/wD4D2X/AMj0eTr/AP0OWr/+A9l/8j0exmHtYnVeF12aROPJt4f+JjfHbby+YpzdSncTubDHqy5+ViwwuNo2K8p8PWevW+mTIPFuoRZvrx9sCWMindcyNknyWwxzllz8rErhcbRqeTr/AP0OWr/+A9l/8j0lRnYbqRuehUV575Ov/wDQ5av/AOA9l/8AI9Hk6/8A9Dlq/wD4D2X/AMj0/YzF7WJ6FWP4XXZpE48m3h/4mN8dtvL5inN1KdxO5sMerLn5WLDC42jlfJ1//octX/8AAey/+R6y/D1nr1vpkyDxbqEWb68fbAljIp3XMjZJ8lsMc5Zc/KxK4XG0L2M7j9pGx6tRXnvk6/8A9Dlq/wD4D2X/AMj0eTr/AP0OWr/+A9l/8j0/YzF7WJ6FRXnvk6//ANDlq/8A4D2X/wAj0eTr/wD0OWr/APgPZf8AyPR7GYe1iaf7Pn/JCfD3/bz/AOlMtek15t+z5/yQnw9/28/+lMtek1wHcFFFFABRRRQBzPizwqPFN9pEdycWVrM81wM/fGAAn4nr7Z9q6VVVFCoAqqMAAYAFRSXcEN1DbSyqks4bylJxv2jJA98c49M+lTVblJxSeyJSSbYUUUVBQUUUUAFFFFABRRRQAUUUUAeIfBP/AJI9on/bf/0okrvK4P4J/wDJHtE/7b/+lEld5XoQ+FHBP4mFFFFUSFZXh1dmlzDybeH/AE+8O23l8xTm5kO4nc2GPVlz8rFhhcbRq1leHV2aXMPJt4f9PvDtt5fMU5uZDuJ3Nhj1Zc/KxYYXG0LqPoatFFFMQUUUUAZXh1dmlzDybeH/AE+8O23l8xTm5kO4nc2GPVlz8rFhhcbRq1leHV2aXMPJt4f9PvDtt5fMU5uZDuJ3Nhj1Zc/KxYYXG0atJbDe4UUUUxBXGeGv+Qdd/wDYV1D/ANLJq7OuM8Nf8g67/wCwrqH/AKWTVdP4iZ/Ca9FFFdBiFFFFAGdoS7NPlHk28P8Apl0dtvL5inNxIdxO5sMerLn5WLDC42jRrO0JdmnyjybeH/TLo7beXzFObiQ7idzYY9WXPysWGFxtGjUx+FDluwoooqhBWdoS7NPlHk28P+mXR228vmKc3Eh3E7mwx6suflYsMLjaNGs7Ql2afKPJt4f9Mujtt5fMU5uJDuJ3Nhj1Zc/KxYYXG0T9ofQ0aKKKoQUUUUATfs+f8kJ8Pf8Abz/6Uy16TXm37Pn/ACQnw9/28/8ApTLXpNeEeyFFFFABWFrfjTQfDt8tnrF60Fw8YlCLbySfKSQDlVI6qfyrdrxP4v8A/I9Q/wDYNi/9Gy11YSjGvVUJGNao6cOZFz4g+ONN1VtHn8M38j3dlcNNu+zyR7Pl4+8oBB6EelekeFvEVv4n0GHUIMLJ9yeIHPlSDqv9R7EV8411vw31q90vxfBbWkUlxDfnyp4Ex0HIk5/u8k+2favVxOBjGh7m8Tio4lup73U95ooorwD0wooqlq2j2Gu2P2LV7Zbq1Lq7QOTskKnIDrnDLn+Fsg9xQBdorz74dWtonibxXN4ZiW18NNPFDaRwDbAbhFIneFcbQudikrwWRqq+EdFi0L41+IoI7q8vZJtItJprm9mMkkrmWUEk8ADAACqAoA4AoWrS7/5XB6J+X+dj0uiiigAooooA8Q+Cf/JHtE/7b/8ApRJXeV5j8H/Eeiaf8INLW/1nT7U27yRzCa6RPKZ5pWRWyeCyqxAPUAkdK7mfxT4ftftP2nXdNh+yTC3uPMvI18mU7sRvk/K3yPweflb0Nd8GuVHDJPmZq0VlT+KfD9r9p+067psP2SYW9x5l5GvkyndiN8n5W+R+Dz8rehon8U+H7X7T9p13TYfskwt7jzLyNfJlO7Eb5Pyt8j8Hn5W9DVXRNmatZXh1dmlzDybeH/T7w7beXzFObmQ7idzYY9WXPysWGFxtBP4p8P2v2n7Trumw/ZJhb3HmXka+TKd2I3yflb5H4PPyt6Gs7Stf0XStPvo9R1LSNOe21K5jnjF+hETyTzOm8lztd1VnKkjB3gKu3aFdXHZ2OmorKn8U+H7X7T9p13TYfskwt7jzLyNfJlO7Eb5Pyt8j8Hn5W9DRP4p8P2v2n7Trumw/ZJhb3HmXka+TKd2I3yflb5H4PPyt6GndCszVorKn8U+H7X7T9p13TYfskwt7jzLyNfJlO7Eb5Pyt8j8Hn5W9DRP4p8P2v2n7Trumw/ZJhb3HmXka+TKd2I3yflb5H4PPyt6Gi6CzDw6uzS5h5NvD/p94dtvL5inNzIdxO5sMerLn5WLDC42jVrmdK1/RdK0++j1HUtI057bUrmOeMX6ERPJPM6byXO13VWcqSMHeAq7do0Z/FPh+1+0/add02H7JMLe48y8jXyZTuxG+T8rfI/B5+VvQ0k1YbTuatFZU/inw/a/aftOu6bD9kmFvceZeRr5Mp3YjfJ+Vvkfg8/K3oaJ/FPh+1+0/add02H7JMLe48y8jXyZTuxG+T8rfI/B5+VvQ07oVmatcZ4a/5B13/wBhXUP/AEsmren8U+H7X7T9p13TYfskwt7jzLyNfJlO7Eb5Pyt8j8Hn5W9DXJ6Nrmk6fYamt/qllatbazfRTie4RDE73c7IrZPykhWIB6hSR0q4SXNuTJPlOlorOn8RaJa/aftOsWEP2SYW9x5l0i+TKd2I3yflb5H4PPyt6GifxFolr9p+06xYQ/ZJhb3HmXSL5Mp3YjfJ+Vvkfg8/K3oa35o9zHll2NGis6fxFolr9p+06xYQ/ZJhb3HmXSL5Mp3YjfJ+Vvkfg8/K3oaJ/EWiWv2n7TrFhD9kmFvceZdIvkyndiN8n5W+R+Dz8reho5o9w5Zdg0JdmnyjybeH/TLo7beXzFObiQ7idzYY9WXPysWGFxtGjWBp+s6Vpdjex6he6Xp7W2oTxzxi9QiJ3mlZQ5LnbI4VmKEgg7xtXbtF6fxFolr9p+06xYQ/ZJhb3HmXSL5Mp3YjfJ+Vvkfg8/K3oamMo8q1KlF3eho0VnT+ItEtftP2nWLCH7JMLe48y6RfJlO7Eb5Pyt8j8Hn5W9DRP4i0S1+0/adYsIfskwt7jzLpF8mU7sRvk/K3yPweflb0NVzR7k8suxo1naEuzT5R5NvD/pl0dtvL5inNxIdxO5sMerLn5WLDC42gn8RaJa/aftOsWEP2SYW9x5l0i+TKd2I3yflb5H4PPyt6GqOn6zpWl2N7HqF7pentbahPHPGL1CIneaVlDkudsjhWYoSCDvG1du0TzR5tyuV22N+is6fxFolr9p+06xYQ/ZJhb3HmXSL5Mp3YjfJ+Vvkfg8/K3oaJ/EWiWv2n7TrFhD9kmFvceZdIvkyndiN8n5W+R+Dz8rehquaPcnll2NGis6fxFolr9p+06xYQ/ZJhb3HmXSL5Mp3YjfJ+Vvkfg8/K3oaJ/EWiWv2n7TrFhD9kmFvceZdIvkyndiN8n5W+R+Dz8reho5o9w5ZdjX/Z8/5IT4e/7ef/AEplr0mvNv2fP+SE+Hv+3n/0plr0mvEPYCiiigArznx94A1jxP4ki1DTJrFIltEgK3Erq24O7Z4RuMOK9GorWlVlRlzw3InBTjyyPnfxN4N1XwnDby6rJZOlwzKv2eV2IIGedyLXpfww8I/2Ppn9r6hHi/vUGxWHMMR5C+xPBP4DtXQ6/wCGoPEOo6VJfYa2sJWnaI/8tGwAoPtnk/THetyuutjZ1aSg9+phTw8YTckFFFFeedQVh+MNE1HxF4bn0vSdY/seWcgSXIgMhMefmQYdCNw4yDkDOOeRuUUmk9GNO2xg+GtH1fRLOOxurzSXsLeERW1vYaZJbeVjpktPJkY7YB96ydP8I+JLXxzP4kufEGlTPdW8VrcQR6PIgMUbMw2k3J2sd55IYdOK7Siqu783UmytYKKKKQwooooA8Q+Cf/JHtE/7b/8ApRJXeVwfwT/5I9on/bf/ANKJK7yvQh8KOCfxMKKKKokKyvDq7NLmHk28P+n3h228vmKc3Mh3E7mwx6suflYsMLjaNWsrw6uzS5h5NvD/AKfeHbby+YpzcyHcTubDHqy5+ViwwuNoXUfQ1aKKKYgooooAyvDq7NLmHk28P+n3h228vmKc3Mh3E7mwx6suflYsMLjaNWsrw6uzS5h5NvD/AKfeHbby+YpzcyHcTubDHqy5+ViwwuNo1aS2G9wooopiCuM8Nf8AIOu/+wrqH/pZNXZ1xnhr/kHXf/YV1D/0smq6fxEz+E16KKK6DEKKKKAM7Ql2afKPJt4f9Mujtt5fMU5uJDuJ3Nhj1Zc/KxYYXG0aNZ2hLs0+UeTbw/6ZdHbby+YpzcSHcTubDHqy5+ViwwuNo0amPwoct2FFFFUIKztCXZp8o8m3h/0y6O23l8xTm4kO4nc2GPVlz8rFhhcbRo1naEuzT5R5NvD/AKZdHbby+YpzcSHcTubDHqy5+ViwwuNon7Q+ho0UUVQgooooAm/Z8/5IT4e/7ef/AEplr0mvNv2fP+SE+Hv+3n/0plr0mvCPZCiiigAooryz4leLtf0PxXDZ6PqTWlubKOUosMb5YvICcspPRRW1GjKtPkjuZ1Kipx5mdb4t8U/8Itf6PJcY+xXUzw3JxygwCHH0PX2z3xXSqyuoZCGVhkEHIIr5t1jxJrXiBIU1rUHu0hYtGpijTBIwfuqK9I+FPi37Tbjw7qEmZoFLWbH+OMdU+q9vb6V218DOlRU+q3OeniYzqcp6XRRRXmHYFFFUtW1I6XY+eljeahIzrGlvZxhpHYnHViFUdyzMAO5oAu0VhaB4rtddutRsms7zTNQ01kF1Z3yoHRXGUcFGZGUgHkMehziqvhz4gaN4q8QX+laMt1IbKFJvtTwFIZ0ZmUNEx5cZVhuA2nHBNHWwdLnT0UUUAFFFFAHiHwT/AOSPaJ/23/8ASiSu8rg/gn/yR7RP+2//AKUSV3lehD4UcE/iYUUUVRIVleHV2aXMPJt4f9PvDtt5fMU5uZDuJ3Nhj1Zc/KxYYXG0atZXh1dmlzDybeH/AE+8O23l8xTm5kO4nc2GPVlz8rFhhcbQuo+hq0UUUxBRRRQBleHV2aXMPJt4f9PvDtt5fMU5uZDuJ3Nhj1Zc/KxYYXG0atZXh1dmlzDybeH/AE+8O23l8xTm5kO4nc2GPVlz8rFhhcbRq0lsN7hRRRTEFcZ4a/5B13/2FdQ/9LJq7OuM8Nf8g67/AOwrqH/pZNV0/iJn8Jr0UUV0GIUUUUAZ2hLs0+UeTbw/6ZdHbby+YpzcSHcTubDHqy5+ViwwuNo0aztCXZp8o8m3h/0y6O23l8xTm4kO4nc2GPVlz8rFhhcbRo1MfhQ5bsKKKKoQVnaEuzT5R5NvD/pl0dtvL5inNxIdxO5sMerLn5WLDC42jRrO0JdmnyjybeH/AEy6O23l8xTm4kO4nc2GPVlz8rFhhcbRP2h9DRoooqhBRRRQBN+z5/yQnw9/28/+lMtek15t+z5/yQnw9/28/wDpTLXpNeEeyFFFFABXifxf/wCR6h/7BsX/AKNlr2ys+/0DR9VnWfU9JsbyVV2CS4tkkYLknGSDxknj3rpwtZUKnO1cxrU3UhynzTXafDPwzLrXiJNRcvHZac4cujFS8vVUBH5n2wO9dH8RPB1pLcaJZeG9Is7S5url0Z7e3WPC7eSxUdB1rv8AQtGtfD+i2+m2Q/dwrgsesjd2PuTzXqYjHqVD3dG/yOOlhWqmuyNCiiivCPSCs/XNcsPDmjz6nq03lW0IGSAWZ2Jwqqo5ZiSAAOSTWhVPVNH0zXLP7JrWnWmo224P5N3Asqbh0O1gRnnrSd+g0c94J0nUftWp+J9fh+zalrZjIs85+x28YIiib1f5mZj6sR2qlpn/ACXjX/8AsB2f/o2auk0rwp4e0KaSXRNB0zTpJU2SPZ2ccRdeuCVAyPaq1t4D8IWV5Fd2fhXRLe5hcPHNFp0KujDkEMFyD71WnMn2/wAmidWmu/8Amn+ljfooopDCiiigD5X+Gvj7UdE+Hum6fbaJa3UcPm7ZpNQaJmzK7fdETY646npXU/8AC09W/wChbsv/AAav/wDGK8z8Ff8AIn2X/bT/ANGNW7X0VHC05Uot9keBVxM41JJd2df/AMLT1b/oW7L/AMGr/wDxij/haerf9C3Zf+DV/wD4xXIUVr9Up+Zl9aqHX/8AC09W/wChbsv/AAav/wDGKp6Z8RtUsLR4Y/DWmANcTzHyNYZlzJKznJ8t/myx3DIw2RtTGxecqK2XZEw8m3h/eOdtvL5inLE7idzYY9WXPysWGFxtEvC0+ZL+uhf1mfK2dp/wtPVv+hbsv/Bq/wD8Yo/4Wnq3/Qt2X/g1f/4xXIUVX1Sn5kfWqh1//C09W/6Fuy/8Gr//ABij/haerf8AQt2X/g1f/wCMVyFFH1Sn5h9aqHR6Z8RtUsLR4Y/DWmANcTzHyNYZlzJKznJ8t/myx3DIw2RtTGxbn/C09W/6Fuy/8Gr/APxiuLtl2RMPJt4f3jnbby+YpyxO4nc2GPVlz8rFhhcbRLUwwtNxTLniZqTR1/8AwtPVv+hbsv8Awav/APGKP+Fp6t/0Ldl/4NX/APjFchRVfVKfmR9aqHX/APC09W/6Fuy/8Gr/APxiuV0r4m31jb3MI0G3kzfXcpP9oMMF7iRyP9UehbGe+M4HSoq5SD71x/19T/8Ao1qxqUIwa5TanXlNO533/C2b/wD6F22/8GTf/GaP+Fs3/wD0Ltt/4Mm/+M1w1FRyeZfP5Hc/8LZv/wDoXbb/AMGTf/GaP+Fs3/8A0Ltt/wCDJv8A4zXDUUcnmHP5HY2XxLvdPt2hTw5p6hppJsQaqzLmR2kOTsf5st8wyMNkbUxsWx/wtm//AOhdtv8AwZN/8ZrhQuwY8m3h5ztt5fMU553E7mwx6suflYsMLjaFqYx91ajlP3nodz/wtm//AOhdtv8AwZN/8Zo/4Wzf/wDQu23/AIMm/wDjNcNRVcnmLn8juf8AhbN//wBC7bf+DJv/AIzVey+Jd7p9u0KeHNPUNNJNiDVWZcyO0hydj/NlvmGRhsjamNi8dSBdgx5NvDznbby+YpzzuJ3Nhj1Zc/KxYYXG0Ty+8tR8/u7Hdf8AC2b/AP6F22/8GTf/ABmj/hbN/wD9C7bf+DJv/jNcNRVcnmLn8juf+Fs3/wD0Ltt/4Mm/+M0f8LZv/wDoXbb/AMGTf/Ga4aijk8w5/I+i/wBnz/khPh7/ALef/SmWvSa82/Z8/wCSE+Hv+3n/ANKZa9JrwT2wooooAKKKwtb8aaD4dvls9YvWguHjEoRbeST5SSAcqpHVT+VVGMpO0VcTaSuzVlntYr63imZFuJlcQhurAYLAfkDj29qsV4/8QfHGm6q2jz+Gb+R7uyuGm3fZ5I9ny8feUAg9CPSvSPC3iK38T6DDqEGFk+5PEDnypB1X+o9iK2qYecKam1uZxqxlJxRsUUUVzmoUUUUAFFFFABRRRQAUUUUAfGngr/kT7L/tp/6Mat2sLwV/yJ9l/wBtP/RjVu19Zh/4MPRfkfL1/wCLL1f5hRRRWxiFRWy7ImHk28P7xztt5fMU5YncTubDHqy5+ViwwuNolqK2XZEw8m3h/eOdtvL5inLE7idzYY9WXPysWGFxtEP416P9C18D+X6ktFFFWQFFFFAEVsuyJh5NvD+8c7beXzFOWJ3E7mwx6suflYsMLjaJaitl2RMPJt4f3jnbby+YpyxO4nc2GPVlz8rFhhcbRLUU/gXoXU+NhRRRVkBXKQfeuP8Ar6n/APRrV1dcpB964/6+p/8A0a1c1fdHTR2ZLRRRXObBRRRQAgXYMeTbw85228vmKc87idzYY9WXPysWGFxtC0gXYMeTbw85228vmKc87idzYY9WXPysWGFxtC1MPhRUviYUUUVRIUgXYMeTbw85228vmKc87idzYY9WXPysWGFxtC0gXYMeTbw85228vmKc87idzYY9WXPysWGFxtE/aRX2RaKKKokKKKKAPov9nz/khPh7/t5/9KZa9Jrzb9nz/khPh7/t5/8ASmWvSa+ePfCiiigArxP4v/8AI9Q/9g2L/wBGy17ZXnPj7wBrHifxJFqGmTWKRLaJAVuJXVtwd2zwjcYcV24GpGnWUpuyOfERlOnaJ4/XW/DfWr3S/F8FtaRSXEN+fKngTHQciTn+7yT7Z9qoeJvBuq+E4beXVZLJ0uGZV+zyuxBAzzuRa9L+GHhH+x9M/tfUI8X96g2Kw5hiPIX2J4J/Adq9nF4ik8O2tb7HBQpTVW21jvaKKK+ZPXCqWrWl7e2PkabqTabKzruuEhWR1TPIQPlQx6ZYMB6GrtYfjC816y8Nzv4S0z+0dUciOJC8aiME8yHeyhto525GTgcDJCew0ZPhLU9W/wCEt8S6BqGotrEOl/Z3t72WJI5AZUYtE5jVUJXaDkKDhxmqnhXV/FMnxN1rSPE97ZyxR6fb3cFrZQ4jti7yLtDsN8hwgyxwCeiir/gOzk0fTHsH8P6tZSEtcXN/qMtq73s7H5nYxTOdx9wAAAAeAKytK/t7/ha9/rlx4R1W3sL6wtrJZJLizJiZJJGZ2Czk7cOPu5PB4qvtL+uj/X5kv4X/AF1X6f5HodFFFIYUUUUAfGngr/kT7L/tp/6Mat2sDwcgl8K6dKxYNHDNAArFVKs8mSQOC3znDn5hhcEbVxtLbInlYaX91C8C5lY5V92Scn5m+c4c5ZcLgjauPqaDn7KOnRdfL0Pmqyj7WWvV/wBbktFRLbInlYaX91C8C5lY5V92Scn5m+c4c5ZcLgjauBbZE8rDS/uoXgXMrHKvuyTk/M3znDnLLhcEbVxtefZff/wDG0O/4f8ABJaitl2RMPJt4f3jnbby+YpyxO4nc2GPVlz8rFhhcbQLbInlYaX91C8C5lY5V92Scn5m+c4c5ZcLgjauI7a2VY4/3UUJijlgVba5aRGVmfLsd7ZlO8sWJ3I3A2bFVYbnzrTv19PItKPK9e3T18yzRUS2yJ5WGl/dQvAuZWOVfdknJ+ZvnOHOWXC4I2rgW2RPKw0v7qF4FzKxyr7sk5PzN85w5yy4XBG1cXefZff/AMAi0O/4f8EloqJbZE8rDS/uoXgXMrHKvuyTk/M3znDnLLhcEbVwLbInlYaX91C8C5lY5V92Scn5m+c4c5ZcLgjauC8+y+//AIAWh3/D/ghbLsiYeTbw/vHO23l8xTlidxO5sMerLn5WLDC42iWq1tbKscf7qKExRywKttctIjKzPl2O9syneWLE7kbgbNiqsi2yJ5WGl/dQvAuZWOVfdknJ+ZvnOHOWXC4I2riKbnyLT8f+AXNR5nr+H/BJaKiW2RPKw0v7qF4FzKxyr7sk5PzN85w5yy4XBG1cC2yJ5WGl/dQvAuZWOVfdknJ+ZvnOHOWXC4I2ri7z7L7/APgEWh3/AA/4JLXKQfeuP+vqf/0a1dMtsieVhpf3ULwLmVjlX3ZJyfmb5zhzllwuCNq45i3+Vmx/yxe5t1zzlWllBLf3n+c4dssMLgjauOau5XWn9fcdFHls9f6+8mopFGzysZ/dQvAuTnKvuyTn7zfOcOcsuFwRtXAo2eVjP7qF4Fyc5V92Sc/eb5zhzllwuCNq4w97sbe73FopFGzysZ/dQvAuTnKvuyTn7zfOcOcsuFwRtXAo2eVjP7qF4Fyc5V92Sc/eb5zhzllwuCNq4Pe7B7vcAuwY8m3h5ztt5fMU553E7mwx6suflYsMLjaFpFXZ5X7m3h8qB4FW3l8xWV92XY7mzKd5JJO5G4GzYqqKNnlYz+6heBcnOVfdknP3m+c4c5ZcLgjauJjzcq0Kly8zFopFGzysZ/dQvAuTnKvuyTn7zfOcOcsuFwRtXAo2eVjP7qF4Fyc5V92Sc/eb5zhzllwuCNq4r3uxPu9xaQLsGPJt4ec7beXzFOedxO5sMerLn5WLDC42gUbPKxn91C8C5Ocq+7JOfvN85w5yy4XBG1cCrs8r9zbw+VA8Crby+YrK+7LsdzZlO8kkncjcDZsVVn3uZaFe7yi0UijZ5WM/uoXgXJzlX3ZJz95vnOHOWXC4I2rgUbPKxn91C8C5Ocq+7JOfvN85w5yy4XBG1cV73Yn3e4tFIo2eVjP7qF4Fyc5V92Sc/eb5zhzllwuCNq4FGzysZ/dQvAuTnKvuyTn7zfOcOcsuFwRtXB73YPd7n0Z+z5/yQnw9/wBvP/pTLXpNebfs+f8AJCfD3/bz/wClMtek14B7oUUUUAFFFFAGHr/hqDxDqOlSX2GtrCVp2iP/AC0bACg+2eT9Md63KzNT1210nU9NtLz5BqMjQxyZ4DgAgH69Prj1rTq5OVlfYlWu7BRRRUFBRRRQAUUUUAFFFFABRRRQB8aeCv8AkT7L/tp/6Mat2sLwV/yJ9l/20/8ARjVu19Zh/wCDD0X5Hy9f+LL1f5hRRRWxiFRWy7ImHk28P7xztt5fMU5YncTubDHqy5+ViwwuNolqK2XZEw8m3h/eOdtvL5inLE7idzYY9WXPysWGFxtEP416P9C18D+X6ktFFFWQFFFFAEVsuyJh5NvD+8c7beXzFOWJ3E7mwx6suflYsMLjaJaitl2RMPJt4f3jnbby+YpyxO4nc2GPVlz8rFhhcbRLUU/gXoXU+NhRRRVkBXKQfeuP+vqf/wBGtXV1ykH3rj/r6n/9GtXNX3R00dmS0UUVzmwUUUUAIF2DHk28POdtvL5inPO4nc2GPVlz8rFhhcbQtIF2DHk28POdtvL5inPO4nc2GPVlz8rFhhcbQtTD4UVL4mFFFFUSFIF2DHk28POdtvL5inPO4nc2GPVlz8rFhhcbQtIF2DHk28POdtvL5inPO4nc2GPVlz8rFhhcbRP2kV9kWiiiqJCiiigD6L/Z8/5IT4e/7ef/AEplr0mvNv2fP+SE+Hv+3n/0plr0mvnj3wooooAK4fxn8Rn8J67Hp0ekreb7ZZzI115WNzOuMbG/udc967ivE/i//wAj1D/2DYv/AEbLXZgqUKtZRmtDDETlCnzRM7xl45l8YQWcT6YtiLWRn3rdGQkkY/uLj616d8PPFv8AwkuieTePnUbMBJ89ZR2k/Hv7g+1eEV1Pw4ttSn8cWr6S3l+SC1zIykr5PdT65OMe/PavYxWEpLD2jpbU4KNebq663PfaKKK+bPWCq99f2el2Ul5qV3BZ2sQzJPcSCNEGcZLHgc1YqC7gtJo1e/ihkS3cTq0ygiNl5DjPQj17UmBFpesaZrdn9r0XUbTUbbcU860nWVNw6jcpIzz0p8WpWM+oz6fDe28l7bqrzWySqZIlb7pZc5APbPWuN8BoNX8TeJvFdlCYNK1h4IrM42m6EKsrXOPRi2AepCA9xVHwnoem+HvjTr9no9qttCdGtJXwSzSO00xZ3ZiWdj3ZiSfWn9pLv/lcHom+3+aR6TRRRQAUUUUAfGngr/kT7L/tp/6Mat2sXw9pnifSdBt7K58D+Kmki3bjHpEpU5YnuB61p7fEP/Qi+Lf/AAUSV9JRxVGNKKcuiPn62GrSqSaj1ZPRUG3xD/0Ivi3/AMFElG3xD/0Ivi3/AMFEla/W6H8yMvqtb+UnqK2XZEw8m3h/eOdtvL5inLE7idzYY9WXPysWGFxtDdviH/oRfFv/AIKJKit4vEMcZX/hX3ieHLu22HSZipyxO75iTuOcntknAAwBDxVDmT5v60K+rVuVrl/rUuUVBt8Q/wDQi+Lf/BRJRt8Q/wDQi+Lf/BRJV/W6H8yJ+q1v5SeioNviH/oRfFv/AIKJKNviH/oRfFv/AIKJKPrdD+ZB9Vr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data-image-state=\"image-loaded\"\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=\"\"\u003eThe Sudoko board in this problem has \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-weight: 700; \"\u003ethree\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 numbers not in the right position. Please help fixing it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_016(x)\r\n  y = ones(6);\r\nend","test_suite":"%%\r\nx = [4\t1\t6\t5\t3\t4\r\n2\t3\t5\t6\t1\t4\r\n5\t3\t2\t1\t4\t3\r\n3\t4\t1\t2\t6\t5\r\n1\t2\t3\t4\t5\t6\r\n6\t5\t4\t6\t2\t1];\r\ny=puzzle_016(x);\r\nassert(unique(sum(y,1))==21)\r\nassert(unique(sum(y,2))==21)\r\nassert(length(unique(y-x))==4)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"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":"2021-01-29T16:07:44.000Z","updated_at":"2026-09-20T18:41:20.000Z","published_at":"2021-01-29T16:07:44.000Z","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 smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"326\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"377\\\"/\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\u003eThe Sudoko board in this problem has \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 numbers not in the right position. Please help fixing 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Puzzles - 015","description":null,"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: 413px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.5px; transform-origin: 407px 206.5px; 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=\"\"\u003eA smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 332px; 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 166px; text-align: left; transform-origin: 384px 166px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\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=\"\"\u003eThe Sudoko board in this problem has two numbers not in the right position. Please help fixing it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_015(x)\r\n  y = min(floor(rand(6).*6)+1,6);\r\nend","test_suite":"%%\r\nx = [1\t2\t3\t4\t5\t6\r\n6\t5\t1\t3\t2\t1\r\n5\t6\t2\t1\t4\t3\r\n3\t4\t1\t2\t6\t5\r\n4\t1\t6\t5\t3\t2\r\n2\t4\t5\t6\t1\t4];\r\ny=puzzle_015(x);\r\nassert(unique(sum(y,1))==21)\r\nassert(unique(sum(y,2))==21)\r\nassert(length(unique(y-x))==3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"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":"2021-01-29T16:01:59.000Z","updated_at":"2026-09-20T18:37:44.000Z","published_at":"2021-01-29T16:01:59.000Z","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 smaller Sudoku problem is of interest. The numbers involved are from 1 through 6. The sum of each row as well as each column is 21. In addition, the sum of the numbers in each colored block shown in the diagram below is also 21.\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"326\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"377\\\"/\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\u003eThe Sudoko board in this problem has two numbers not in the right position. Please help fixing 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roots of unity","description":"First, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\r\n\r\n\u003chttps://en.wikipedia.org/wiki/Root_of_unity\u003e\r\n\r\nSecond, raise each root to the power pi (.^pi).\r\n\r\nThird, sum the resulting numbers and use that as the output. \r\n","description_html":"\u003cp\u003eFirst, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Root_of_unity\"\u003ehttps://en.wikipedia.org/wiki/Root_of_unity\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSecond, raise each root to the power pi (.^pi).\u003c/p\u003e\u003cp\u003eThird, sum the resulting numbers and use that as the output.\u003c/p\u003e","function_template":"function y = your_fcn_name(n)\r\n  y = 0;\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct =  -0.467800202134647;\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 50;\r\ny_correct = -2.151544927902936 - 0.430301217000093i\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 7;\r\ny_correct =   -0.435928596902380\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n\r\n%%\r\nn = 70;\r\ny_correct =   -3.031653804728051 - 0.430301217000095i\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":65480,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-08-01T00:25:42.000Z","updated_at":"2026-02-24T14:03:00.000Z","published_at":"2016-08-01T00:25:42.000Z","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\u003eFirst, find the n nth roots of unity. eg if n = 6, find the n distinct (complex) numbers such that n^6 = 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\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Root_of_unity\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Root_of_unity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\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\u003eSecond, raise each root to the power pi (.^pi).\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\u003eThird, sum the resulting numbers and use that as the output.\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":45448,"title":"Vector raised to a power, element-wise (★)","description":"Given a vector A and a number x, raise each element of the vector to the power of x. Thus, if A = [2 5 7 1] and x = 0.5, then \r\n\r\n  y = [2^0.5 5^0.5 7^0.5 1^0.5] = [1.4142 2.2361 2.6458 1.0000]","description_html":"\u003cp\u003eGiven a vector A and a number x, raise each element of the vector to the power of x. Thus, if A = [2 5 7 1] and x = 0.5, then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey = [2^0.5 5^0.5 7^0.5 1^0.5] = [1.4142 2.2361 2.6458 1.0000]\r\n\u003c/pre\u003e","function_template":"function y = raise_vector(A,x)\r\n  y = 1;\r\nend","test_suite":"%%\r\nA = [1 2 3 4]; x = 2;\r\ny_correct = [1 4 9 16];\r\nassert(isequal(raise_vector(A,x),y_correct))\r\n%%\r\nA = [81 16 1296]; x = 0.25;\r\ny_correct = [3 2 6];\r\nassert(isequal(raise_vector(A,x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":134,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-12T21:41:15.000Z","updated_at":"2026-05-30T05:51:33.000Z","published_at":"2020-04-12T21:41:15.000Z","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 A and a number x, raise each element of the vector to the power of x. Thus, if A = [2 5 7 1] and x = 0.5, 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[y = [2^0.5 5^0.5 7^0.5 1^0.5] = [1.4142 2.2361 2.6458 1.0000]]]\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":2120,"title":"Rounding off numbers to n decimals","description":"Inspired by a mistake in one of the problems I created, I created this problem where you have to round off a floating point number to n decimals. There are 2 inputs to the function: x: floating point number and n: number of decimals which need to match with the given solutions.","description_html":"\u003cp\u003eInspired by a mistake in one of the problems I created, I created this problem where you have to round off a floating point number to n decimals. There are 2 inputs to the function: x: floating point number and n: number of decimals which need to match with the given solutions.\u003c/p\u003e","function_template":"function y = myround(x,n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\nn=1;\r\ny_correct = 1;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = pi;\r\nn=5;\r\ny_correct = 3.14159;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = 0.5*sqrt(2);\r\nn=6;\r\ny_correct = 0.707107;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = exp(1);\r\nn=9;\r\ny_correct = 2.718281828;\r\nassert(isequal(myround(x,n),y_correct))\r\n%%\r\nx = 0.00123456;\r\nn=6;\r\ny_correct = 0.001235;\r\nassert(isequal(myround(x,n),y_correct))\r\n","published":true,"deleted":false,"likes_count":24,"comments_count":3,"created_by":20079,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5810,"test_suite_updated_at":"2014-01-15T04:17:27.000Z","rescore_all_solutions":false,"group_id":38,"created_at":"2014-01-15T04:03:48.000Z","updated_at":"2026-09-19T05:06:03.000Z","published_at":"2014-01-15T04:14:20.000Z","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\u003eInspired by a mistake in one of the problems I created, I created this problem where you have to round off a floating point number to n decimals. There are 2 inputs to the function: x: floating point number and n: number of decimals which need to match with the given solutions.\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":61381,"title":"Switch-Case-Otherwise","description":"You should make random numbers to 10, by 3 rows and 3 columns.\r\nCases from 1 to 3, b = true.\r\nOtherwise, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 40.5px; transform-origin: 401px 40.5px; 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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCases from 1 to 3, b = true.\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: 377px 10.5px; text-align: left; transform-origin: 377px 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eOtherwise, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = CASE(a)\r\n  \r\nend","test_suite":"%%\r\na = 6;\r\nb = false;\r\nassert(isequal(CASE(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":124,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:39:29.000Z","updated_at":"2026-08-30T15:03:24.000Z","published_at":"2026-05-31T07:39:29.000Z","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:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\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\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCases from 1 to 3, b = true.\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\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOtherwise, b = false.\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":195,"title":"Program an exclusive OR operation with logical operators","description":"Program an exclusive or operation *without* using the MATLAB function xor.\r\n\r\nUse logical operators like |, \u0026, ~, ... instead.\r\n\r\nExamples:\r\n  \r\n  myXOR(1,1)\r\n    \r\n  ans = 0\r\n         \r\n    \r\n  myXOR(1,0)\r\n    \r\n  ans = 1\r\n    \r\n    \r\n  myXOR(0,1)\r\n    \r\n  ans = 1\r\n    \r\n         \r\n  myXOR(0,0)\r\n    \r\n  ans = 0","description_html":"\u003cp\u003eProgram an exclusive or operation \u003cb\u003ewithout\u003c/b\u003e using the MATLAB function xor.\u003c/p\u003e\u003cp\u003eUse logical operators like |, \u0026, ~, ... instead.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(1,1)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 0\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(1,0)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 1\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(0,1)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 1\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emyXOR(0,0)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 0\r\n\u003c/pre\u003e","function_template":"function y = myXOR(a,b)\r\n  y=0;\r\nend","test_suite":"%%\r\na=0;b=0;\r\nres=0;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=1;b=1;\r\nres=0;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=1;b=0;\r\nres=1;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=0;b=1;\r\nres=1;\r\nassert(isequal(myXOR(a,b),res))\r\n\r\n%%\r\na=[0 0 1 1];b=[1 0 1 0];\r\nres=[1 0 0 1];\r\nassert(isequal(myXOR(a,b),res))","published":true,"deleted":false,"likes_count":9,"comments_count":0,"created_by":564,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":803,"test_suite_updated_at":"2012-01-31T07:59:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T07:59:29.000Z","updated_at":"2026-08-14T04:17:49.000Z","published_at":"2012-01-31T08:03:50.000Z","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\u003eProgram an exclusive or operation\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\u003ewithout\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e using the MATLAB function xor.\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 logical operators like\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, \u0026amp;, ~, ... instead.\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[myXOR(1,1)\\n\\nans = 0\\n\\nmyXOR(1,0)\\n\\nans = 1\\n\\nmyXOR(0,1)\\n\\nans = 1\\n\\nmyXOR(0,0)\\n\\nans = 0]]\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":51820,"title":"Count unique orderings of vertices of a polygon","description":"Cody Problem 2671 asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\r\nHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \r\nWrite a function to determine the unique orderings of vertices of a polygon with  sides. \r\n","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: 356.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 178.458px; transform-origin: 407px 178.458px; 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2671\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 2671\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: 294.433px 7.91667px; transform-origin: 294.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\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: 383.133px 7.91667px; transform-origin: 383.133px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \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: 245.317px 7.91667px; transform-origin: 245.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the unique orderings of vertices of a polygon with \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: 22.1667px 7.91667px; transform-origin: 22.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 182.917px; 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 91.4583px; text-align: left; transform-origin: 384px 91.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 262px;height: 177px\" 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data-image-state=\"image-loaded\" width=\"262\" height=\"177\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polyVert(n)\r\n  y = nchoosek(2*n,n);\r\nend","test_suite":"%% Rectangle\r\nassert(isequal(polyVert(4),3))\r\n\r\n%% Triangle\r\nassert(isequal(polyVert(3),1))\r\n\r\n%% Heptagon\r\nassert(isequal(polyVert(7),360))\r\n\r\n%% Dodecagon\r\nassert(isequal(polyVert(12),19958400))\r\n\r\n%% Heptadecagon\r\nassert(isequal(polyVert(17),10461394944000))\r\n\r\n%% \r\nd = num2str(polyVert(19))-'0';\r\np = polyval(d(1:3:end),4);\r\np_correct = 3760;\r\nassert(isequal(p,p_correct))\r\n\r\n%% \r\nd = num2str(polyVert(15));\r\ns = polyVert(str2num(d(4)))+polyVert(str2num(d(6:7)));\r\ns_correct = 3113512920;\r\nassert(isequal(s,s_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":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-27T04:52:02.000Z","updated_at":"2026-05-25T05:51:39.000Z","published_at":"2021-05-27T04:56:25.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2671\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2671\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\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\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \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 unique orderings of vertices of a polygon with \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\u003e sides. \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 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hydraulic geometry relations","description":"Hydraulic geometry relations express the velocity , width , and depth  of a river as a function of the discharge (or flow) , which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\r\n\r\nwhere the coefficients have the appropriate dimensions. \r\nWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., ) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. ","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: 200px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100px; transform-origin: 407px 100px; 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-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=\"\"\u003eHydraulic geometry relations express the velocity \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, width \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);\"\u003eB\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and depth \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);\"\u003eH\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a river as a function of the discharge (or flow) \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);\"\u003eQ\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; 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 13px; text-align: left; transform-origin: 384px 13px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203.5\" height=\"26\" alt=\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\" style=\"width: 203.5px; height: 26px;\"\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-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=\"\"\u003ewhere the coefficients have the appropriate dimensions. \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-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 two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" alt=\"Q = VBH\" style=\"width: 63px; 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [anew,enew] = hydraulicGeometry(a,e)\r\n  anew = 1.1*a;\r\n  enew = 1.1*e;\r\nend","test_suite":"%\r\na = [NaN 7.2 0.27];\r\ne = [NaN 0.5 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5144 7.2 0.27];\r\nenew_correct = [0.2 0.5 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.5 NaN 0.3];\r\ne = [0.25 NaN 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5 6.6667 0.3];\r\nenew_correct = [0.25 0.45 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.45 7 NaN];\r\ne = [0.23 0.48 NaN];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.45 7 0.3175];\r\nenew_correct = [0.23 0.48 0.29];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.8 5 NaN];\r\ne = [NaN 0.3 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.8 5 0.25];\r\nenew_correct = [0.3 0.3 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.6 4 NaN];\r\ne = [0.1 NaN 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.6 4 0.4167];\r\nenew_correct = [0.1 0.5 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [NaN 4.6 0.8];\r\ne = [0.15 NaN 0.37];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.2717 4.6 0.8];\r\nenew_correct = [0.15 0.48 0.37];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-14T15:47:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-12-14T15:46:55.000Z","updated_at":"2026-06-06T01:59:06.000Z","published_at":"2024-12-14T15:47:02.000Z","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\u003eHydraulic geometry relations express the velocity \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=\\\"V\\\"/\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:t\u003e, width \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=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and depth \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=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a river as a function of the discharge (or flow) \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=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = a_1 Q^{e_1}, B = a_2 Q^{e_2}, H = a_3 Q^{e_3}\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\u003ewhere the coefficients have the appropriate dimensions. \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 two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \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=\\\"Q = VBH\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = VBH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \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":57615,"title":"About jokes (and compression)","description":"An argument can be made about jokes. The shorter they are, the funnier. Further explained here: https://en.wikipedia.org/wiki/Humour#Formula.Thus, jokes are data compression made art.\r\nYou will be given a single text for the whole problem. Your goal is to make it shorter so it would take less space. \r\nWrite a function that takes no argument. It always returns the same character array. You will find that exact array in the Test Suite. However, the content of your MATLAB file must be shorter than the source material. The number of characters you type counts and you must save at least 25%.\r\n\r\nFind patterns and/or useful documentation on your own. There are multiple ways to go about it. I know you will come up with a great one-liner. Have fun!","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: 225px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.5px; transform-origin: 407px 112.5px; 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=\"\"\u003eAn argument can be made about jokes. The shorter they are, the funnier. Further explained here: \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/dQw4w9WgXcQ\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Humour#Formula\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.Thus, jokes are \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Data_compression\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edata compression\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 made art.\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=\"\"\u003eYou will be given a single text for the whole problem. Your goal is to make it shorter so it would take less space. \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efunction\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 that takes \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; \"\u003eno argument.\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 It always \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; \"\u003ereturns the same character array.\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 You will find that exact array in the Test Suite. However, the content of your MATLAB file must be shorter than the source material. \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=\"text-decoration: underline; text-decoration-line: underline; \"\u003eThe number of characters you type counts and you must save at least 25%.\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: 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=\"\"\u003eFind patterns and/or useful documentation on your own. There are multiple ways to go about it. I know you will come up with a great one-liner. Have fun!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function never_gonna_give_you_up = roll()\r\n    % Did I mention Cody does not like running jokes?\r\n    never_gonna_give_you_up = ['We''re no strangers to love' ,char(10),...\r\n    'You know the rules and so do I (do I)' ,char(10),...\r\n    'A full commitment''s what I''m thinking of' ,char(10),...\r\n    'You wouldn''t get this from any other guy' ,char(10),...\r\n    'I just wanna tell you how I''m feeling' ,char(10),...\r\n    'Gotta make you understand' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'We''ve known each other for so long' ,char(10),...\r\n    'Your heart''s been aching, but you''re too shy to say it (say it)' ,char(10),...\r\n    'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n    'We know the game and we''re gonna play it' ,char(10),...\r\n    'And if you ask me how I''m feeling' ,char(10),...\r\n    'Don''t tell me you''re too blind to see' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'We''ve known each other for so long' ,char(10),...\r\n    'Your heart''s been aching, but you''re too shy to say it (to say it)' ,char(10),...\r\n    'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n    'We know the game and we''re gonna play it' ,char(10),...\r\n    'I just wanna tell you how I''m feeling' ,char(10),...\r\n    'Gotta make you understand' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you' ,char(10),...\r\n    'Never gonna give you up' ,char(10),...\r\n    'Never gonna let you down' ,char(10),...\r\n    'Never gonna run around and desert you' ,char(10),...\r\n    'Never gonna make you cry' ,char(10),...\r\n    'Never gonna say goodbye' ,char(10),...\r\n    'Never gonna tell a lie and hurt you']\r\nend","test_suite":"RICK = ['We''re no strangers to love' ,char(10),...\r\n'You know the rules and so do I (do I)' ,char(10),...\r\n'A full commitment''s what I''m thinking of' ,char(10),...\r\n'You wouldn''t get this from any other guy' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'And if you ask me how I''m feeling' ,char(10),...\r\n'Don''t tell me you''re too blind to see' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (to say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you'];\r\n\r\n%% Hint :)\r\nRICK = ['We''re no strangers to love' ,char(10),...\r\n'You know the rules and so do I (do I)' ,char(10),...\r\n'A full commitment''s what I''m thinking of' ,char(10),...\r\n'You wouldn''t get this from any other guy' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'And if you ask me how I''m feeling' ,char(10),...\r\n'Don''t tell me you''re too blind to see' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'We''ve known each other for so long' ,char(10),...\r\n'Your heart''s been aching, but you''re too shy to say it (to say it)' ,char(10),...\r\n'Inside, we both know what''s been going on (going on)' ,char(10),...\r\n'We know the game and we''re gonna play it' ,char(10),...\r\n'I just wanna tell you how I''m feeling' ,char(10),...\r\n'Gotta make you understand' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you' ,char(10),...\r\n'Never gonna give you up' ,char(10),...\r\n'Never gonna let you down' ,char(10),...\r\n'Never gonna run around and desert you' ,char(10),...\r\n'Never gonna make you cry' ,char(10),...\r\n'Never gonna say goodbye' ,char(10),...\r\n'Never gonna tell a lie and hurt you'];\r\ndisplay(RICK);\r\nroll();\r\n\r\n%% Content\r\nroll_ = roll();\r\ndisplay(roll_)\r\nassert(ischar(roll_), 'Output is not a char array.');\r\nassert(isequal(RICK, roll_), 'Text output does not match.');\r\n\r\n%% Compression\r\nfiletext = fileread('roll.m');\r\ndisplay(filetext);\r\nl0 = length(RICK);\r\nl1 = length(filetext);\r\nfprintf('\\nOriginal size:%d, Your file:%d\\n', [l0 l1]);\r\nassert(l0 \u003e l1, 'Your file should contain less characters than the original text.');\r\nspaceSaving = ceil(100*(1-l1/l0));\r\nfprintf('\\nYou saved %d/100!\\n', spaceSaving);\r\nif spaceSaving \u003e 85\r\n    display(\"but at what cost...\");\r\nelse\r\n    assert(spaceSaving \u003e 25, 'Try to reach 25/100.');\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3019900,"edited_by":3019900,"edited_at":"2023-01-26T01:47:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-01-26T01:47:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-25T23:33:10.000Z","updated_at":"2026-06-03T23:08:56.000Z","published_at":"2023-01-26T01:43:23.000Z","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\u003eAn argument can be made about jokes. The shorter they are, the funnier. Further explained here: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/dQw4w9WgXcQ\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Humour#Formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.Thus, jokes are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Data_compression\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata compression\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e made art.\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\u003eYou will be given a single text for the whole problem. Your goal is to make it shorter so it would take less space. \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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eno argument.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e It always \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ereturns the same character array.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e You will find that exact array in the Test Suite. However, the content of your MATLAB file must be shorter than the source material. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe number of characters you type counts and you must save at least 25%.\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\u003eFind patterns and/or useful documentation on your own. There are multiple ways to go about it. I know you will come up with a great one-liner. Have fun!\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":53950,"title":"Time reverse indices","description":"Time reverse the index values as follows\r\nIndexIn = [7 1 0]    \r\nIndexOut = [7 6 0]\r\nNote that the indices are zero based and sorted from largest to smallest.\r\nYou can think of this as a time reversal of a vector:\r\n[7 1 0] --\u003e [1     1     0     0     0     0     0     1 ] \r\n[7 6 0] --\u003e [1     0     0     0     0     0     1     1 ]\r\n\r\nHere is a second example\r\n[8 4 3 2 0]  --\u003e [ 1     0     1     1     1     0     0     0     1 ]\r\n[8 6 5 4 0]  --\u003e [ 1     0     0     0     1     1     1     0     1 ]\r\n\r\nBackground of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.","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: 465px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 331.5px 232.5px; transform-origin: 331.5px 232.5px; 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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTime reverse the index values as follows\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIndexIn = [7 1 0]    \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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIndexOut = [7 6 0]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eNote that the indices are zero based and sorted from largest to smallest.\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou can think of this as a time reversal of a vector:\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[7 1 0] --\u0026gt; [1     1     0     0     0     0     0     1 ] \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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[7 6 0] --\u0026gt; [1     0     0     0     0     0     1     1 ]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHere is a second example\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[8 4 3 2 0]  --\u0026gt; [ 1     0     1     1     1     0     0     0     1 ]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e[8 6 5 4 0]  --\u0026gt; [ 1     0     0     0     1     1     1     0     1 ]\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: 308.5px 10.5px; text-align: left; transform-origin: 308.5px 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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: 308.5px 52.5px; text-align: left; transform-origin: 308.5px 52.5px; 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=\"\"\u003eBackground of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function IndexOut = reverseIndices(IndexIn)\r\n  IndexOut = IndexIn;\r\nend","test_suite":"%%\r\nx = [7  1  0];\r\ny_correct = [7  6  0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [8  4  3  2  0];\r\ny_correct = [8  6  5  4  0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [9  4  0];\r\ny_correct = [9  5  0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [10   3   0];\r\ny_correct = [10   7   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [11   2   0];\r\ny_correct = [11   9   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [45   4   3   1   0];\r\ny_correct = [45  44  42  41   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [46   8   5   3   2   1   0];\r\ny_correct = [46  45  44  43  41  38   0];\r\nassert(isequal(reverseIndices(x),y_correct))\r\n%%\r\nx = [47   5   0];\r\ny_correct = [47  42   0];\r\nassert(isequal(reverseIndices(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":280816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-20T21:14:20.000Z","updated_at":"2026-06-11T02:46:39.000Z","published_at":"2022-01-20T21:14:20.000Z","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\u003eTime reverse the index values as follows\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\u003eIndexIn = [7 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIndexOut = [7 6 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\u003eNote that the indices are zero based and sorted from largest to smallest.\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\u003eYou can think of this as a time reversal of 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[7 1 0] --\u0026gt; [1     1     0     0     0     0     0     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\u003e[7 6 0] --\u0026gt; [1     0     0     0     0     0     1     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\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\u003eHere is a second example\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[8 4 3 2 0]  --\u0026gt; [ 1     0     1     1     1     0     0     0     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\u003e[8 6 5 4 0]  --\u0026gt; [ 1     0     0     0     1     1     1     0     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\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\u003eBackground of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.\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\"}]}"}],"errors":[],"facets":[[{"value":"Cody Challenge","count":75,"selected":false},{"value":"High School Challenge","count":40,"selected":false},{"value":"Number theory","count":37,"selected":false},{"value":"Cody5:Easy","count":30,"selected":false},{"value":"Strings I","count":29,"selected":false},{"value":"Algorithm I","count":25,"selected":false},{"value":"Indexing I","count":24,"selected":false},{"value":"Operations","count":23,"selected":false},{"value":"Polynomials","count":23,"selected":false},{"value":"Advent of Code","count":22,"selected":false},{"value":"Divisible by x","count":20,"selected":false},{"value":"Indexing II","count":20,"selected":false},{"value":"Computational Geometry I","count":19,"selected":false},{"value":"Introduction to MATLAB","count":19,"selected":false},{"value":"Prime Numbers I","count":19,"selected":false},{"value":"Prime Numbers II","count":19,"selected":false},{"value":"Probability \u0026 Stats","count":19,"selected":false},{"value":"Strings II","count":19,"selected":false},{"value":"Combinatorics III","count":18,"selected":false},{"value":"Groundwater","count":18,"selected":false},{"value":"Indexing III","count":18,"selected":false},{"value":"MATLAB 101","count":18,"selected":false},{"value":"Basics - 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