{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","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":"2026-05-26T00:00:00.000Z","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":2622,"title":"Packing oranges - one layer","description":"Help the seller to pack oranges efficiently. How many oranges can be put into a box in one layer without squeezing them?\r\n\r\nGiven dimension(s) return the maximum number. Assume that oranges are perfect spheres with unitary diameter.","description_html":"\u003cp\u003eHelp the seller to pack oranges efficiently. How many oranges can be put into a box in one layer without squeezing them?\u003c/p\u003e\u003cp\u003eGiven dimension(s) return the maximum number. Assume that oranges are perfect spheres with unitary diameter.\u003c/p\u003e","function_template":"function n = fit(x, varargin)\r\n  % nargcheck\r\n  if nargin \u003e 1\r\n    y = varargin{1};\r\n  else\r\n    y = x;\r\n  end\r\n\r\n  % main code\r\n  n = floor(x * y);\r\n  % ...\r\nend","test_suite":"%%\r\nx = 1;\r\ny = 1;\r\nn = 1;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 1;\r\nfor y = randi(100,1,10);\r\n n = y;\r\n assert(isequal(fit(x,y),n))\r\nend\r\n\r\n%%\r\nx = randi(20,1,10);\r\ny = randi(20,1,10);\r\nfor k=1:10\r\n  assert(isequal(fit(x(k),y(k)),fit(y(k),x(k))))\r\nend\r\n%%\r\nx = 1;\r\n%y = 1;\r\nn = 1;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 2;\r\nn = 4;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 1.7;\r\nn = 1;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 1.8;\r\nn = 2;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 1.98;\r\nn = 3;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 2;\r\ny = 1.8;\r\nn = 2;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 2;\r\ny = 1.9;\r\nn = 3;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 10;\r\ny = 1.44;\r\nn = 11;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 1+sin(acos(2/3));\r\nfor k = 1:10\r\n  y = 2 * k + 1.1;\r\n  n = 3 * k + 1;\r\n  assert(isequal(fit(x,y),n))\r\nend\r\n\r\n%%\r\nx = 8;\r\ny = 7.93;\r\nn = 68;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = Inf;\r\ny = 0.9;\r\nn = 0;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = Inf;\r\nn = Inf;\r\nassert(isequal(fit(2,x),n))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2014-10-13T10:21:51.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-10-08T14:42:50.000Z","updated_at":"2026-05-22T13:09:46.000Z","published_at":"2014-10-08T14:42:50.000Z","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\",\"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\u003eHelp the seller to pack oranges efficiently. How many oranges can be put into a box in one layer without squeezing them?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 dimension(s) return the maximum number. Assume that oranges are perfect spheres with unitary diameter.\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\"}]}"}],"problem_search":{"problems":[{"id":2622,"title":"Packing oranges - one layer","description":"Help the seller to pack oranges efficiently. How many oranges can be put into a box in one layer without squeezing them?\r\n\r\nGiven dimension(s) return the maximum number. Assume that oranges are perfect spheres with unitary diameter.","description_html":"\u003cp\u003eHelp the seller to pack oranges efficiently. How many oranges can be put into a box in one layer without squeezing them?\u003c/p\u003e\u003cp\u003eGiven dimension(s) return the maximum number. Assume that oranges are perfect spheres with unitary diameter.\u003c/p\u003e","function_template":"function n = fit(x, varargin)\r\n  % nargcheck\r\n  if nargin \u003e 1\r\n    y = varargin{1};\r\n  else\r\n    y = x;\r\n  end\r\n\r\n  % main code\r\n  n = floor(x * y);\r\n  % ...\r\nend","test_suite":"%%\r\nx = 1;\r\ny = 1;\r\nn = 1;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 1;\r\nfor y = randi(100,1,10);\r\n n = y;\r\n assert(isequal(fit(x,y),n))\r\nend\r\n\r\n%%\r\nx = randi(20,1,10);\r\ny = randi(20,1,10);\r\nfor k=1:10\r\n  assert(isequal(fit(x(k),y(k)),fit(y(k),x(k))))\r\nend\r\n%%\r\nx = 1;\r\n%y = 1;\r\nn = 1;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 2;\r\nn = 4;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 1.7;\r\nn = 1;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 1.8;\r\nn = 2;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 1.98;\r\nn = 3;\r\nassert(isequal(fit(x),n))\r\n\r\n%%\r\nx = 2;\r\ny = 1.8;\r\nn = 2;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 2;\r\ny = 1.9;\r\nn = 3;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 10;\r\ny = 1.44;\r\nn = 11;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = 1+sin(acos(2/3));\r\nfor k = 1:10\r\n  y = 2 * k + 1.1;\r\n  n = 3 * k + 1;\r\n  assert(isequal(fit(x,y),n))\r\nend\r\n\r\n%%\r\nx = 8;\r\ny = 7.93;\r\nn = 68;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = Inf;\r\ny = 0.9;\r\nn = 0;\r\nassert(isequal(fit(x,y),n))\r\n\r\n%%\r\nx = Inf;\r\nn = Inf;\r\nassert(isequal(fit(2,x),n))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2014-10-13T10:21:51.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-10-08T14:42:50.000Z","updated_at":"2026-05-22T13:09:46.000Z","published_at":"2014-10-08T14:42:50.000Z","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\",\"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\u003eHelp the seller to pack oranges efficiently. How many oranges can be put into a box in one layer without squeezing them?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 dimension(s) return the maximum number. Assume that oranges are perfect spheres with unitary diameter.\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\"}]}"}],"errors":[],"facets":[[{"value":"Computational Geometry III","count":1,"selected":false}],[{"value":"hard","count":1,"selected":false}]],"term":"tag:\"kepler conjecture\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}