{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","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":"2026-04-16T00:00:00.000Z","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":3061,"title":"Mirror, mirror on the wall, who is fairest of them all?","description":"The Elo rating system was featured in the movie *The Social Network* during the \u003chttps://www.youtube.com/watch?v=BzZRr4KV59I/ algorithm scene\u003e where Mark Zuckerberg released Facemash. \r\n\r\nIn the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. \r\nThe Elo system is employed to rank coeds by their attractiveness. \r\nThe equations driving the algorithm are shown briefly (Ea and Eb). \r\n\r\nYou should know these equations now (See problem \u003chttp://www.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/ 3056\u003e) :\r\n\r\n\r\n\u003c\u003chttp://upload.wikimedia.org/math/b/0/3/b0366725c224ee55eab6e2371dc6a0ef.png\u003e\u003e\r\n \r\n* \r\n\r\n\r\nEa is the expected probability that Girl A will win the match against Girl B.\r\n\r\nRa is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.\r\n\r\nNow imagine a single round-robin tournament where each girl plays (is compared with)  every other girl once.\r\nA judge (me for the problem) gives a note :\r\n\r\n* 1   if girl A is more attractive than girl B\r\n* 0   if girl B is more attractive than girl A\r\n* 0.5 if same attractiveness\r\n\r\nI give you the tournament results (2 on the main diagonal).\r\n\r\nFind the final rating of Snow White (she is unique).\r\n\r\nConsider that all girl begin the tournament with a rating of 1000.\r\n\r\nYou can observe that the total number of attractiveness (ELO) points remains constant.\r\n","description_html":"\u003cp\u003eThe Elo rating system was featured in the movie \u003cb\u003eThe Social Network\u003c/b\u003e during the \u003ca href = \"https://www.youtube.com/watch?v=BzZRr4KV59I/\"\u003ealgorithm scene\u003c/a\u003e where Mark Zuckerberg released Facemash.\u003c/p\u003e\u003cp\u003eIn the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. \r\nThe Elo system is employed to rank coeds by their attractiveness. \r\nThe equations driving the algorithm are shown briefly (Ea and Eb).\u003c/p\u003e\u003cp\u003eYou should know these equations now (See problem \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/\"\u003e3056\u003c/a\u003e) :\u003c/p\u003e\u003cimg src = \"http://upload.wikimedia.org/math/b/0/3/b0366725c224ee55eab6e2371dc6a0ef.png\"\u003e\u003cul\u003e\u003cli\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eEa is the expected probability that Girl A will win the match against Girl B.\u003c/p\u003e\u003cp\u003eRa is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.\u003c/p\u003e\u003cp\u003eNow imagine a single round-robin tournament where each girl plays (is compared with)  every other girl once.\r\nA judge (me for the problem) gives a note :\u003c/p\u003e\u003cul\u003e\u003cli\u003e1   if girl A is more attractive than girl B\u003c/li\u003e\u003cli\u003e0   if girl B is more attractive than girl A\u003c/li\u003e\u003cli\u003e0.5 if same attractiveness\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eI give you the tournament results (2 on the main diagonal).\u003c/p\u003e\u003cp\u003eFind the final rating of Snow White (she is unique).\u003c/p\u003e\u003cp\u003eConsider that all girl begin the tournament with a rating of 1000.\u003c/p\u003e\u003cp\u003eYou can observe that the total number of attractiveness (ELO) points remains constant.\u003c/p\u003e","function_template":"function y = fairest_girl(X)\r\n  y = X;\r\nend","test_suite":"%%\r\nA=[2 1 1 1 1;0 2 1 1 1;0 0 2 1 1;0 0 0 2 1;0 0 0 0 2];\r\nassert(isequal(fairest_girl(A),1064));\r\n%%\r\nA=[2 1;0 2];\r\nassert(isequal(fairest_girl(A),1016));\r\n%%\r\nassert(isequal(fairest_girl([2 1 0.5;0 2 0.5;0.5 0.5 2]),1016));\r\n%%\r\nA=[2 1 1 1 1 1;0 2 1 1 1 1;0 0 2 1 1 1;0 0 0 2 0.5 0.5;0 0 0 0.5 2 0.5;0 0 0 0.5 0.5 2];\r\nassert(isequal(fairest_girl(A),1080));\r\n%%\r\nA=[2 0.5 1;0.5 2 0.5;0 0.5 2];\r\nassert(isequal(fairest_girl(A),1016));\r\n%%\r\nA=[2 1 1 1 1 1 1;0 2 1 1 1 1 1;0 0 2 1 1 1 1;0 0 0 2 0.5 0.5 1;0 0 0 0.5 2 0.5 1;0 0 0 0.5 0.5 2 1;0 0 0 0 0 0 2];\r\nassert(isequal(fairest_girl(A),1096));\r\n%%\r\nA=[2 1 1 1 1 1 0.5;0 2 1 1 1 1 0.5;0 0 2 1 1 1 0.5;0 0 0 2 0.5 0.5 0.5;0 0 0 0.5 2 0.5 0.5;0 0 0 0.5 0.5 2 0.5;0.5 0.5 0.5 0.5 0.5 0.5 2];\r\nassert(isequal(fairest_girl(A),1080));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2015-03-03T18:22:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-03T18:06:46.000Z","updated_at":"2026-04-01T09:44:49.000Z","published_at":"2015-03-03T18:13:07.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"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 Elo rating system was featured in the movie\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\u003eThe Social Network\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e during 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=\\\"https://www.youtube.com/watch?v=BzZRr4KV59I/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ealgorithm scene\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e where Mark Zuckerberg released Facemash.\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\u003eIn the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. The Elo system is employed to rank coeds by their attractiveness. The equations driving the algorithm are shown briefly (Ea and Eb).\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\u003eYou should know these equations now (See 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/3056-chess-probability/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e3056\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\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=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\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\u003eEa is the expected probability that Girl A will win the match against Girl B.\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\u003eRa is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.\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\u003eNow imagine a single round-robin tournament where each girl plays (is compared with) every other girl once. A judge (me for the problem) gives a note :\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\u003e1 if girl A is more attractive than girl B\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\u003e0 if girl B is more attractive than girl A\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\u003e0.5 if same attractiveness\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\u003eI give you the tournament results (2 on the main diagonal).\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\u003eFind the final rating of Snow White (she is unique).\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\u003eConsider that all girl begin the tournament with a rating of 1000.\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\u003eYou can observe that the total number of attractiveness (ELO) points remains constant.\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\"},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":3061,"title":"Mirror, mirror on the wall, who is fairest of them all?","description":"The Elo rating system was featured in the movie *The Social Network* during the \u003chttps://www.youtube.com/watch?v=BzZRr4KV59I/ algorithm scene\u003e where Mark Zuckerberg released Facemash. \r\n\r\nIn the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. \r\nThe Elo system is employed to rank coeds by their attractiveness. \r\nThe equations driving the algorithm are shown briefly (Ea and Eb). \r\n\r\nYou should know these equations now (See problem \u003chttp://www.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/ 3056\u003e) :\r\n\r\n\r\n\u003c\u003chttp://upload.wikimedia.org/math/b/0/3/b0366725c224ee55eab6e2371dc6a0ef.png\u003e\u003e\r\n \r\n* \r\n\r\n\r\nEa is the expected probability that Girl A will win the match against Girl B.\r\n\r\nRa is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.\r\n\r\nNow imagine a single round-robin tournament where each girl plays (is compared with)  every other girl once.\r\nA judge (me for the problem) gives a note :\r\n\r\n* 1   if girl A is more attractive than girl B\r\n* 0   if girl B is more attractive than girl A\r\n* 0.5 if same attractiveness\r\n\r\nI give you the tournament results (2 on the main diagonal).\r\n\r\nFind the final rating of Snow White (she is unique).\r\n\r\nConsider that all girl begin the tournament with a rating of 1000.\r\n\r\nYou can observe that the total number of attractiveness (ELO) points remains constant.\r\n","description_html":"\u003cp\u003eThe Elo rating system was featured in the movie \u003cb\u003eThe Social Network\u003c/b\u003e during the \u003ca href = \"https://www.youtube.com/watch?v=BzZRr4KV59I/\"\u003ealgorithm scene\u003c/a\u003e where Mark Zuckerberg released Facemash.\u003c/p\u003e\u003cp\u003eIn the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. \r\nThe Elo system is employed to rank coeds by their attractiveness. \r\nThe equations driving the algorithm are shown briefly (Ea and Eb).\u003c/p\u003e\u003cp\u003eYou should know these equations now (See problem \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/\"\u003e3056\u003c/a\u003e) :\u003c/p\u003e\u003cimg src = \"http://upload.wikimedia.org/math/b/0/3/b0366725c224ee55eab6e2371dc6a0ef.png\"\u003e\u003cul\u003e\u003cli\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eEa is the expected probability that Girl A will win the match against Girl B.\u003c/p\u003e\u003cp\u003eRa is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.\u003c/p\u003e\u003cp\u003eNow imagine a single round-robin tournament where each girl plays (is compared with)  every other girl once.\r\nA judge (me for the problem) gives a note :\u003c/p\u003e\u003cul\u003e\u003cli\u003e1   if girl A is more attractive than girl B\u003c/li\u003e\u003cli\u003e0   if girl B is more attractive than girl A\u003c/li\u003e\u003cli\u003e0.5 if same attractiveness\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eI give you the tournament results (2 on the main diagonal).\u003c/p\u003e\u003cp\u003eFind the final rating of Snow White (she is unique).\u003c/p\u003e\u003cp\u003eConsider that all girl begin the tournament with a rating of 1000.\u003c/p\u003e\u003cp\u003eYou can observe that the total number of attractiveness (ELO) points remains constant.\u003c/p\u003e","function_template":"function y = fairest_girl(X)\r\n  y = X;\r\nend","test_suite":"%%\r\nA=[2 1 1 1 1;0 2 1 1 1;0 0 2 1 1;0 0 0 2 1;0 0 0 0 2];\r\nassert(isequal(fairest_girl(A),1064));\r\n%%\r\nA=[2 1;0 2];\r\nassert(isequal(fairest_girl(A),1016));\r\n%%\r\nassert(isequal(fairest_girl([2 1 0.5;0 2 0.5;0.5 0.5 2]),1016));\r\n%%\r\nA=[2 1 1 1 1 1;0 2 1 1 1 1;0 0 2 1 1 1;0 0 0 2 0.5 0.5;0 0 0 0.5 2 0.5;0 0 0 0.5 0.5 2];\r\nassert(isequal(fairest_girl(A),1080));\r\n%%\r\nA=[2 0.5 1;0.5 2 0.5;0 0.5 2];\r\nassert(isequal(fairest_girl(A),1016));\r\n%%\r\nA=[2 1 1 1 1 1 1;0 2 1 1 1 1 1;0 0 2 1 1 1 1;0 0 0 2 0.5 0.5 1;0 0 0 0.5 2 0.5 1;0 0 0 0.5 0.5 2 1;0 0 0 0 0 0 2];\r\nassert(isequal(fairest_girl(A),1096));\r\n%%\r\nA=[2 1 1 1 1 1 0.5;0 2 1 1 1 1 0.5;0 0 2 1 1 1 0.5;0 0 0 2 0.5 0.5 0.5;0 0 0 0.5 2 0.5 0.5;0 0 0 0.5 0.5 2 0.5;0.5 0.5 0.5 0.5 0.5 0.5 2];\r\nassert(isequal(fairest_girl(A),1080));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2015-03-03T18:22:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-03T18:06:46.000Z","updated_at":"2026-04-01T09:44:49.000Z","published_at":"2015-03-03T18:13:07.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"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 Elo rating system was featured in the movie\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\u003eThe Social Network\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e during 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=\\\"https://www.youtube.com/watch?v=BzZRr4KV59I/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ealgorithm scene\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e where Mark Zuckerberg released Facemash.\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\u003eIn the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. The Elo system is employed to rank coeds by their attractiveness. The equations driving the algorithm are shown briefly (Ea and Eb).\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\u003eYou should know these equations now (See 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/3056-chess-probability/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e3056\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\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=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\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\u003eEa is the expected probability that Girl A will win the match against Girl B.\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\u003eRa is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.\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\u003eNow imagine a single round-robin tournament where each girl plays (is compared with) every other girl once. A judge (me for the problem) gives a note :\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\u003e1 if girl A is more attractive than girl B\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\u003e0 if girl B is more attractive than girl A\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\u003e0.5 if same attractiveness\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\u003eI give you the tournament results (2 on the main diagonal).\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\u003eFind the final rating of Snow White (she is unique).\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\u003eConsider that all girl begin the tournament with a rating of 1000.\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\u003eYou can observe that the total number of attractiveness (ELO) points remains 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