{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":"2026-02-19T10:48:58.000Z","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. 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":{"errors":[],"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":"2026-02-19T10:48:58.000Z","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. 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\"}]}"}],"term":"tag:\"kepler conjecture\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"kepler conjecture\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"kepler conjecture\"","","\"","kepler conjecture","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fbf315d4920\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fbf315d4880\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fbf315d3de0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fbf315d4c40\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fbf315d4ba0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fbf315d4a60\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fbf315d49c0\u003e":"tag:\"kepler conjecture\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fbf315d49c0\u003e":"tag:\"kepler conjecture\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"kepler conjecture\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"kepler conjecture\"","","\"","kepler conjecture","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fbf315d4920\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fbf315d4880\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fbf315d3de0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fbf315d4c40\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fbf315d4ba0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fbf315d4a60\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fbf315d49c0\u003e":"tag:\"kepler conjecture\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fbf315d49c0\u003e":"tag:\"kepler conjecture\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":2622,"difficulty_rating":"hard"}]}}