{"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":2063,"title":"A matrix of extroverts","description":"Now that the introverts have had their script, the extroverts spoke up (naturally!) and demanded one as well.  You will be given a matrix.  Write a MATLAB script to output a new matrix consisting of the average of all four terms that are next to each other.\r\n\r\nIf your input is magic(3)\r\n\r\n     8     1     6\r\n     3     5     7\r\n     4     9     2\r\n\r\nYour output will be:\r\n\r\n  4.2500    4.7500\r\n  5.2500    5.7500\r\n\r\nThe top left term (4.25) is the average of [8 1 ; 3 5].  The bottom left term is the average of [3 5 ; 4 9], and so on.  You can assume that the size of each of these matrices will be at least 2x2.  Good luck!","description_html":"\u003cp\u003eNow that the introverts have had their script, the extroverts spoke up (naturally!) and demanded one as well.  You will be given a matrix.  Write a MATLAB script to output a new matrix consisting of the average of all four terms that are next to each other.\u003c/p\u003e\u003cp\u003eIf your input is magic(3)\u003c/p\u003e\u003cpre\u003e     8     1     6\r\n     3     5     7\r\n     4     9     2\u003c/pre\u003e\u003cp\u003eYour output will be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e4.2500    4.7500\r\n5.2500    5.7500\r\n\u003c/pre\u003e\u003cp\u003eThe top left term (4.25) is the average of [8 1 ; 3 5].  The bottom left term is the average of [3 5 ; 4 9], and so on.  You can assume that the size of each of these matrices will be at least 2x2.  Good luck!\u003c/p\u003e","function_template":"function y = extroverts(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = magic(3);\r\ny = extroverts(x);\r\ny_c = [4.2500    4.7500 ; 5.2500    5.7500];\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);\r\n%%\r\nx = [1 2 3 ; 4 5 6];\r\ny = extroverts(x);\r\ny_c = [3 4];\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);\r\n%%\r\nx=[magic(4) -magic(4)];\r\ny = extroverts(x);\r\ny_c=[8.5  6.5 8.5 0   -8.5  -6.5 -8.5\r\n     8    8.5 9   1.5 -8    -8.5 -9\r\n     8.5 10.5 8.5 0   -8.5 -10.5 -8.5];\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);\r\n%%\r\nx = ones(20);\r\ny = extroverts(x);\r\ny_c = ones(19);\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":266,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":23,"created_at":"2013-12-18T19:37:17.000Z","updated_at":"2026-02-21T21:48:09.000Z","published_at":"2013-12-18T19:37:17.000Z","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\u003eNow that the introverts have had their script, the extroverts spoke up (naturally!) and demanded one as well. You will be given a matrix. Write a MATLAB script to output a new matrix consisting of the average of all four terms that are next to each other.\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 your input is magic(3)\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[     8     1     6\\n     3     5     7\\n     4     9     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\u003eYour output will 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[4.2500    4.7500\\n5.2500    5.7500]]\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\u003eThe top left term (4.25) is the average of [8 1 ; 3 5]. The bottom left term is the average of [3 5 ; 4 9], and so on. You can assume that the size of each of these matrices will be at least 2x2. Good luck!\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":2063,"title":"A matrix of extroverts","description":"Now that the introverts have had their script, the extroverts spoke up (naturally!) and demanded one as well.  You will be given a matrix.  Write a MATLAB script to output a new matrix consisting of the average of all four terms that are next to each other.\r\n\r\nIf your input is magic(3)\r\n\r\n     8     1     6\r\n     3     5     7\r\n     4     9     2\r\n\r\nYour output will be:\r\n\r\n  4.2500    4.7500\r\n  5.2500    5.7500\r\n\r\nThe top left term (4.25) is the average of [8 1 ; 3 5].  The bottom left term is the average of [3 5 ; 4 9], and so on.  You can assume that the size of each of these matrices will be at least 2x2.  Good luck!","description_html":"\u003cp\u003eNow that the introverts have had their script, the extroverts spoke up (naturally!) and demanded one as well.  You will be given a matrix.  Write a MATLAB script to output a new matrix consisting of the average of all four terms that are next to each other.\u003c/p\u003e\u003cp\u003eIf your input is magic(3)\u003c/p\u003e\u003cpre\u003e     8     1     6\r\n     3     5     7\r\n     4     9     2\u003c/pre\u003e\u003cp\u003eYour output will be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e4.2500    4.7500\r\n5.2500    5.7500\r\n\u003c/pre\u003e\u003cp\u003eThe top left term (4.25) is the average of [8 1 ; 3 5].  The bottom left term is the average of [3 5 ; 4 9], and so on.  You can assume that the size of each of these matrices will be at least 2x2.  Good luck!\u003c/p\u003e","function_template":"function y = extroverts(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = magic(3);\r\ny = extroverts(x);\r\ny_c = [4.2500    4.7500 ; 5.2500    5.7500];\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);\r\n%%\r\nx = [1 2 3 ; 4 5 6];\r\ny = extroverts(x);\r\ny_c = [3 4];\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);\r\n%%\r\nx=[magic(4) -magic(4)];\r\ny = extroverts(x);\r\ny_c=[8.5  6.5 8.5 0   -8.5  -6.5 -8.5\r\n     8    8.5 9   1.5 -8    -8.5 -9\r\n     8.5 10.5 8.5 0   -8.5 -10.5 -8.5];\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);\r\n%%\r\nx = ones(20);\r\ny = extroverts(x);\r\ny_c = ones(19);\r\nassert(max(max(abs(y-y_c)))\u003c1e-9);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":266,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":23,"created_at":"2013-12-18T19:37:17.000Z","updated_at":"2026-02-21T21:48:09.000Z","published_at":"2013-12-18T19:37:17.000Z","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\u003eNow that the introverts have had their script, the extroverts spoke up (naturally!) and demanded one as well. You will be given a matrix. Write a MATLAB script to output a new matrix consisting of the average of all four terms that are next to each other.\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 your input is magic(3)\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[     8     1     6\\n     3     5     7\\n     4     9     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\u003eYour output will 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[4.2500    4.7500\\n5.2500    5.7500]]\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\u003eThe top left term (4.25) is the average of [8 1 ; 3 5]. The bottom left term is the average of [3 5 ; 4 9], and so on. You can assume that the size of each of these matrices will be at least 2x2. Good luck!\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 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