{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":2582,"title":"Cut an orange","description":"Inspired by problem \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/2175 2175\u003e.\r\n\r\nA hungry matlab enthusiast has an orange. He decides to cut it into pieces using three dimensional grid.\r\n\r\nGiven grid density _N_ please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.\r\n\r\nExample: For _N=3_ matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!\r\n\r\nRelated problems:\r\n\r\n\u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/554 554\u003e, \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/1283 1283\u003e, \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/1387 1387\u003e\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eInspired by problem \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/2175\"\u003e2175\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eA hungry matlab enthusiast has an orange. He decides to cut it into pieces using three dimensional grid.\u003c/p\u003e\u003cp\u003eGiven grid density \u003ci\u003eN\u003c/i\u003e please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.\u003c/p\u003e\u003cp\u003eExample: For \u003ci\u003eN=3\u003c/i\u003e matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/554\"\u003e554\u003c/a\u003e, \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/1283\"\u003e1283\u003c/a\u003e, \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/1387\"\u003e1387\u003c/a\u003e\u003c/p\u003e","function_template":"function pieces=cut_orange(N)\r\n \r\n  cubes = ...\r\n  rest = ...\r\n  pieces=[cubes, rest];\r\n\r\nend\r\n","test_suite":"%% Grid with N=1 doesn't cut the orange, it represents the smallest cube that orange can fit in. There are no juicy cubes, one piece sorrounded by peel.\r\nN = 1;\r\ny_correct = [0 1];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 1;\r\ny_correct = [0 1];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 2;\r\ny_correct = [0 8];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 3;\r\ny_correct = [1 26];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 4;\r\ny_correct = [8 56];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 5;\r\ny_correct = [19 98]; % was [27 90] \r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 6;\r\ny_correct = [32 152]; % was [56 128];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 7;\r\ny_correct = [81 194];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 8;\r\ny_correct = [136 272]; % was [160 248];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 9;\r\ny_correct = [203 362]; % was [251 314];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 10;\r\ny_correct = [304 416]; % was [312 408];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\n% finally more cubes than peels!\r\nN = 13;\r\nassert(isequal(-diff(cut_orange(N)),5))\r\n\r\n%%\r\nN = 19;\r\ny_correct = [2769 1658];\r\nassert(isequal(cut_orange(N),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2014-10-08T09:45:10.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-09-12T10:39:45.000Z","updated_at":"2026-02-19T10:43:30.000Z","published_at":"2014-09-12T12:37:15.000Z","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\u003eInspired by 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.co.uk/matlabcentral/cody/problems/2175\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2175\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hungry matlab enthusiast has an orange. He decides to cut it into pieces using three dimensional grid.\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 grid density\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.\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: For\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!\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\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/554\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e554\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/1283\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1283\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/1387\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1387\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":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":"2026-02-19T10:48:58.000Z","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. 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He decides to cut it into pieces using three dimensional grid.\r\n\r\nGiven grid density _N_ please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.\r\n\r\nExample: For _N=3_ matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!\r\n\r\nRelated problems:\r\n\r\n\u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/554 554\u003e, \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/1283 1283\u003e, \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/1387 1387\u003e\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eInspired by problem \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/2175\"\u003e2175\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eA hungry matlab enthusiast has an orange. He decides to cut it into pieces using three dimensional grid.\u003c/p\u003e\u003cp\u003eGiven grid density \u003ci\u003eN\u003c/i\u003e please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.\u003c/p\u003e\u003cp\u003eExample: For \u003ci\u003eN=3\u003c/i\u003e matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/554\"\u003e554\u003c/a\u003e, \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/1283\"\u003e1283\u003c/a\u003e, \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/1387\"\u003e1387\u003c/a\u003e\u003c/p\u003e","function_template":"function pieces=cut_orange(N)\r\n \r\n  cubes = ...\r\n  rest = ...\r\n  pieces=[cubes, rest];\r\n\r\nend\r\n","test_suite":"%% Grid with N=1 doesn't cut the orange, it represents the smallest cube that orange can fit in. There are no juicy cubes, one piece sorrounded by peel.\r\nN = 1;\r\ny_correct = [0 1];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 1;\r\ny_correct = [0 1];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 2;\r\ny_correct = [0 8];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 3;\r\ny_correct = [1 26];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 4;\r\ny_correct = [8 56];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 5;\r\ny_correct = [19 98]; % was [27 90] \r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 6;\r\ny_correct = [32 152]; % was [56 128];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 7;\r\ny_correct = [81 194];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 8;\r\ny_correct = [136 272]; % was [160 248];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 9;\r\ny_correct = [203 362]; % was [251 314];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\nN = 10;\r\ny_correct = [304 416]; % was [312 408];\r\nassert(isequal(cut_orange(N),y_correct))\r\n\r\n%%\r\n% finally more cubes than peels!\r\nN = 13;\r\nassert(isequal(-diff(cut_orange(N)),5))\r\n\r\n%%\r\nN = 19;\r\ny_correct = [2769 1658];\r\nassert(isequal(cut_orange(N),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2014-10-08T09:45:10.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-09-12T10:39:45.000Z","updated_at":"2026-02-19T10:43:30.000Z","published_at":"2014-09-12T12:37:15.000Z","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\u003eInspired by 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.co.uk/matlabcentral/cody/problems/2175\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2175\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hungry matlab enthusiast has an orange. He decides to cut it into pieces using three dimensional grid.\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 grid density\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.\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: For\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!\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\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/554\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e554\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/1283\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1283\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/1387\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1387\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":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":"2026-02-19T10:48:58.000Z","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. 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