{"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":44883,"title":"Bridge and Torch Problem - Minimum time","description":"\u003chttps://en.wikipedia.org/wiki/Bridge_and_torch_problem Details of the problem ...\u003e \r\n\r\nInput is crossing time list. (for example x= [1 2 5 8])\r\n\r\nOutput is the minimum time. (for original problem y_correct= 15)\r\n\r\n\r\n*Assumption 1:* for this problem only four people will cross the bridge\r\n\r\n*Assumption 2:* crossing times are integer","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\"\u003eDetails of the problem ...\u003c/a\u003e\u003c/p\u003e\u003cp\u003eInput is crossing time list. (for example x= [1 2 5 8])\u003c/p\u003e\u003cp\u003eOutput is the minimum time. (for original problem y_correct= 15)\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 1:\u003c/b\u003e for this problem only four people will cross the bridge\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 2:\u003c/b\u003e crossing times are integer\u003c/p\u003e","function_template":"function y = bridgeRiddle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('bridgeRiddle.m');\r\nassert(isempty(strfind(filetext, 'assert')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\n\r\n\r\n%%\r\nx = [1 1 1 1];\r\ny_correct = 5;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 1 1 10];\r\ny_correct = 14;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 2 5 8];\r\ny_correct = 15;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 2 5 10];\r\ny_correct = 17;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 2 5 11];\r\ny_correct = 18;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [2 5 9 11];\r\ny_correct = 28;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3 8 13 16];\r\ny_correct = 43;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [7 13 15 16];\r\ny_correct = 58;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3 34 43 47];\r\ny_correct = 130;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [21 35 38 39];\r\ny_correct = 154;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [5 10 34 36];\r\ny_correct = 71;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [ 55 97 154 193];\r\ny_correct = 539;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [107 116 165 170];\r\ny_correct = 625;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [329 592 611 641];\r\ny_correct = 2502;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3259 4164 5259 6544];\r\ny_correct = 22295;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [5947 6267 8477 9254];\r\ny_correct = 34002;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n\r\n%%\r\nx = [12 24 24 30];\r\ny_correct = 102;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [6 6 10 12];\r\ny_correct = 36;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3 4 9 9];\r\ny_correct = 24;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2019-04-23T18:37:57.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2019-04-21T06:48:30.000Z","updated_at":"2024-11-12T04:56:45.000Z","published_at":"2019-04-21T06:48:30.000Z","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:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDetails of the problem ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eInput is crossing time list. (for example x= [1 2 5 8])\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\u003eOutput is the minimum time. (for original problem y_correct= 15)\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for this problem only four people will cross the bridge\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crossing times are integer\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\"}]}"},{"id":44884,"title":"Bridge and Torch Problem - Length of Unique Time List","description":"\u003chttps://en.wikipedia.org/wiki/Bridge_and_torch_problem Details of the problem ...\u003e \r\n\r\nInput is crossing time list. (for example x= [1 2 5 8])\r\n\r\nOutput is the length of all possible crossing time records. (for original problem y_correct= 14. In other words it is possible to cross the bridge in [15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 34, 40] minutes.\r\n\r\n*Assumption 1:* for this problem only four people will cross the bridge\r\n\r\n*Assumption 2:* crossing times are integer\r\n\r\n\r\n*Crossing Model:* 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\"\u003eDetails of the problem ...\u003c/a\u003e\u003c/p\u003e\u003cp\u003eInput is crossing time list. (for example x= [1 2 5 8])\u003c/p\u003e\u003cp\u003eOutput is the length of all possible crossing time records. (for original problem y_correct= 14. In other words it is possible to cross the bridge in [15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 34, 40] minutes.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 1:\u003c/b\u003e for this problem only four people will cross the bridge\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 2:\u003c/b\u003e crossing times are integer\u003c/p\u003e\u003cp\u003e\u003cb\u003eCrossing Model:\u003c/b\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\u003c/p\u003e","function_template":"function y = howManyWays(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('howManyWays.m');\r\nassert(isempty(strfind(filetext, 'assert')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\n\r\n\r\n%%\r\nx = [1 1 1 1];\r\ny_correct = 1;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 1 1 10];\r\ny_correct = 3; %[14,32,50]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [12 24 24 30];\r\ny_correct = 5; %[102,114,126,138,150]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [22 34 34 43];\r\ny_correct = 6; %[155 167 179 185 197 215]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [6 6 10 12];\r\ny_correct = 7; %[36 40 44 48 52 56 60]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [6 6 7 8];\r\ny_correct = 8; %[32 33 34 35 36 37 38 40]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3 4 9 9];\r\ny_correct = 9; \r\nassert(isequal(howManyWays(x),y_correct))\r\n\r\n%%\r\nx = [4 6 8 11];\r\ny_correct = 10; \r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 5 6 7];\r\ny_correct = 13; \r\nassert(isequal(howManyWays(x),y_correct))\r\n\r\n\r\n%%\r\nx = [1 2 5 8];\r\ny_correct = 14;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 2 5 10];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 2 5 11];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [2 5 9 11];\r\ny_correct = 12;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3 8 13 16];\r\ny_correct = 11;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [7 13 15 16];\r\ny_correct = 11;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3 34 43 47];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [21 35 38 39];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [5 10 34 36];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [ 55 97 154 193];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [107 116 165 170];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [329 592 611 641];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3259 4164 5259 6544];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [5947 6267 8477 9254];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n\r\n%%\r\nx = [726 871 871 964];\r\ny_correct = 6; %[4158 4303 4448 4489 4634 4820]\r\nassert(isequal(howManyWays(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2019-04-22T11:56:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-21T07:08:50.000Z","updated_at":"2019-04-22T11:56:31.000Z","published_at":"2019-04-21T07:08:50.000Z","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\",\"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:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDetails of the problem ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eInput is crossing time list. (for example x= [1 2 5 8])\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\u003eOutput is the length of all possible crossing time records. (for original problem y_correct= 14. In other words it is possible to cross the bridge in [15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 34, 40] minutes.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for this problem only four people will cross the bridge\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crossing times are integer\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCrossing Model:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\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\"}]}"},{"id":44885,"title":"Bridge and Torch Problem - Probability","description":"\u003chttps://en.wikipedia.org/wiki/Bridge_and_torch_problem Details of the problem ...\u003e \r\n\r\nThere are four people who wants to cross the bridge. But we don't know exactly who will cross the bridge in which time. However, we know that a person can cross the bridge in n1 minutes (n1 is randomly selected from the range 1:n, n is the first input). All crossing times are integers. They use *Crossing Model* to cross the bridge. In each turn, they randomly select the person(s) who will cross the bridge. What is the probability that they will cross the bridge less than or equal to t minutes (t is the second input).\r\n\r\nLet's assume first input n = 3. That means people will cross the bridge in 1, 2 or 3 minutes. all of them can cross the bridge in 1 minute or maybe all of them can cross the bridge in 3 minutes. Possibilities are listed below.\r\n\r\n  crossingTimeList = [\r\n1\t1\t1\t1\r\n1\t1\t1\t2\r\n1\t1\t1\t3\r\n1\t1\t2\t2\r\n1\t1\t2\t3\r\n1\t1\t3\t3\r\n1\t2\t2\t2\r\n1\t2\t2\t3\r\n1\t2\t3\t3\r\n1\t3\t3\t3\r\n2\t2\t2\t2\r\n2\t2\t2\t3\r\n2\t2\t3\t3\r\n2\t3\t3\t3\r\n3\t3\t3\t3]\r\n\r\nIf first line is the case, all of the people will cross the bridge in 1 minute. There will be 108 cases  ( |108 = 4C2 X 2C1 X 3C2 X 3C1| ) taking 5 minutes. All of them will be less than or equal to 10 minutes (which is input 2). \r\n\r\nIf ninth line is the case, one person will cross the bridge in one minute, one person will cross the bridge in two minutes, and others will cross the bridge in 3 minutes. 8 out of 108 ways will take less than or equal to 10 minutes. \r\n\r\nIf last one is the case, all of them will cross the bridge in three minutes indicates that all of the journeys will take 15 minutes (longer than input2 or 10 minutes).\r\n\r\nResult of the crossingTimeList are as follow\r\n\r\n  result = [\r\n108\t108\r\n108\t108\r\n060\t108\r\n108\t108\r\n054\t108\r\n026\t108\r\n108\t108\r\n304\t108\r\n008\t108\r\n000\t108\r\n108\t108\r\n000\t108\r\n000\t108\r\n000\t108\r\n000\t108]\r\n\r\nAs a result 722 out of 1620 ways will take \u003c= 10 minutes (722/1620=0.4457).\r\n\r\n\r\n*Assumption 1:* for this problem only four people will cross the bridge\r\n\r\n*Assumption 2:* crossing times are integer\r\n\r\n*Crossing Model:* 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.  ","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\"\u003eDetails of the problem ...\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThere are four people who wants to cross the bridge. But we don't know exactly who will cross the bridge in which time. However, we know that a person can cross the bridge in n1 minutes (n1 is randomly selected from the range 1:n, n is the first input). All crossing times are integers. They use \u003cb\u003eCrossing Model\u003c/b\u003e to cross the bridge. In each turn, they randomly select the person(s) who will cross the bridge. What is the probability that they will cross the bridge less than or equal to t minutes (t is the second input).\u003c/p\u003e\u003cp\u003eLet's assume first input n = 3. That means people will cross the bridge in 1, 2 or 3 minutes. all of them can cross the bridge in 1 minute or maybe all of them can cross the bridge in 3 minutes. Possibilities are listed below.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ecrossingTimeList = [\r\n1\t1\t1\t1\r\n1\t1\t1\t2\r\n1\t1\t1\t3\r\n1\t1\t2\t2\r\n1\t1\t2\t3\r\n1\t1\t3\t3\r\n1\t2\t2\t2\r\n1\t2\t2\t3\r\n1\t2\t3\t3\r\n1\t3\t3\t3\r\n2\t2\t2\t2\r\n2\t2\t2\t3\r\n2\t2\t3\t3\r\n2\t3\t3\t3\r\n3\t3\t3\t3]\r\n\u003c/pre\u003e\u003cp\u003eIf first line is the case, all of the people will cross the bridge in 1 minute. There will be 108 cases  ( \u003ctt\u003e108 = 4C2 X 2C1 X 3C2 X 3C1\u003c/tt\u003e ) taking 5 minutes. All of them will be less than or equal to 10 minutes (which is input 2).\u003c/p\u003e\u003cp\u003eIf ninth line is the case, one person will cross the bridge in one minute, one person will cross the bridge in two minutes, and others will cross the bridge in 3 minutes. 8 out of 108 ways will take less than or equal to 10 minutes.\u003c/p\u003e\u003cp\u003eIf last one is the case, all of them will cross the bridge in three minutes indicates that all of the journeys will take 15 minutes (longer than input2 or 10 minutes).\u003c/p\u003e\u003cp\u003eResult of the crossingTimeList are as follow\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eresult = [\r\n108\t108\r\n108\t108\r\n060\t108\r\n108\t108\r\n054\t108\r\n026\t108\r\n108\t108\r\n304\t108\r\n008\t108\r\n000\t108\r\n108\t108\r\n000\t108\r\n000\t108\r\n000\t108\r\n000\t108]\r\n\u003c/pre\u003e\u003cp\u003eAs a result 722 out of 1620 ways will take \u0026lt;= 10 minutes (722/1620=0.4457).\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 1:\u003c/b\u003e for this problem only four people will cross the bridge\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 2:\u003c/b\u003e crossing times are integer\u003c/p\u003e\u003cp\u003e\u003cb\u003eCrossing Model:\u003c/b\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\u003c/p\u003e","function_template":"function y = bridgeProb(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('bridgeProb.m');\r\nassert(isempty(strfind(filetext, 'assert')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\n%%\r\nx = [3 10];\r\nassert(and( ge(bridgeProb(x), 0.43) , le(bridgeProb(x), 0.45)))\r\n%%\r\nx = [8 5];\r\nassert(and( ge(bridgeProb(x), 0.00) , le(bridgeProb(x), 0.01)))\r\n%%\r\nx = [10 5];\r\nassert(and( ge(bridgeProb(x), 0.00) , le(bridgeProb(x), 0.01)))\r\n%%\r\nx = [8 15];\r\nassert(and( ge(bridgeProb(x), 0.10) , le(bridgeProb(x), 0.12)))\r\n%%\r\nx = [8 17];\r\nassert(and( ge(bridgeProb(x), 0.15) , le(bridgeProb(x), 0.17)))\r\n%%\r\nx = [10 35];\r\nassert(and( ge(bridgeProb(x), 0.60) , le(bridgeProb(x), 0.62)))\r\n%%\r\nx = [10 35];\r\nassert(and( ge(bridgeProb(x), 0.60) , le(bridgeProb(x), 0.62)))\r\n%%\r\nx = [10 40];\r\nassert(and( ge(bridgeProb(x), 0.78) , le(bridgeProb(x), 0.80)))\r\n%%\r\nx = [7 20];\r\nassert(and( ge(bridgeProb(x), 0.35) , le(bridgeProb(x), 0.37)))\r\n%%\r\nx = [8 25];\r\nassert(and( ge(bridgeProb(x), 0.45) , le(bridgeProb(x), 0.47)))\r\n%%\r\nx = [8 10];\r\nassert(and( ge(bridgeProb(x), 0.01) , le(bridgeProb(x), 0.03)))\r\n%%\r\nx = [9 15];\r\nassert(and( ge(bridgeProb(x), 0.06) , le(bridgeProb(x), 0.08)))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2019-04-23T07:16:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-21T08:29:03.000Z","updated_at":"2025-05-02T02:43:56.000Z","published_at":"2019-04-22T12:28:10.000Z","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:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDetails of the problem ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eThere are four people who wants to cross the bridge. But we don't know exactly who will cross the bridge in which time. However, we know that a person can cross the bridge in n1 minutes (n1 is randomly selected from the range 1:n, n is the first input). All crossing times are integers. They use\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\u003eCrossing Model\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to cross the bridge. In each turn, they randomly select the person(s) who will cross the bridge. What is the probability that they will cross the bridge less than or equal to t minutes (t is the second input).\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\u003eLet's assume first input n = 3. That means people will cross the bridge in 1, 2 or 3 minutes. all of them can cross the bridge in 1 minute or maybe all of them can cross the bridge in 3 minutes. Possibilities are listed below.\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[crossingTimeList = [\\n1  1  1  1\\n1  1  1  2\\n1  1  1  3\\n1  1  2  2\\n1  1  2  3\\n1  1  3  3\\n1  2  2  2\\n1  2  2  3\\n1  2  3  3\\n1  3  3  3\\n2  2  2  2\\n2  2  2  3\\n2  2  3  3\\n2  3  3  3\\n3  3  3  3]]]\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\u003eIf first line is the case, all of the people will cross the bridge in 1 minute. There will be 108 cases (\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e108 = 4C2 X 2C1 X 3C2 X 3C1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ) taking 5 minutes. All of them will be less than or equal to 10 minutes (which is input 2).\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 ninth line is the case, one person will cross the bridge in one minute, one person will cross the bridge in two minutes, and others will cross the bridge in 3 minutes. 8 out of 108 ways will take less than or equal to 10 minutes.\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 last one is the case, all of them will cross the bridge in three minutes indicates that all of the journeys will take 15 minutes (longer than input2 or 10 minutes).\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\u003eResult of the crossingTimeList are as follow\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[result = [\\n108  108\\n108  108\\n060  108\\n108  108\\n054  108\\n026  108\\n108  108\\n304  108\\n008  108\\n000  108\\n108  108\\n000  108\\n000  108\\n000  108\\n000  108]]]\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\u003eAs a result 722 out of 1620 ways will take \u0026lt;= 10 minutes (722/1620=0.4457).\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for this problem only four people will cross the bridge\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crossing times are integer\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCrossing Model:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\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":44883,"title":"Bridge and Torch Problem - Minimum time","description":"\u003chttps://en.wikipedia.org/wiki/Bridge_and_torch_problem Details of the problem ...\u003e \r\n\r\nInput is crossing time list. (for example x= [1 2 5 8])\r\n\r\nOutput is the minimum time. (for original problem y_correct= 15)\r\n\r\n\r\n*Assumption 1:* for this problem only four people will cross the bridge\r\n\r\n*Assumption 2:* crossing times are integer","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\"\u003eDetails of the problem ...\u003c/a\u003e\u003c/p\u003e\u003cp\u003eInput is crossing time list. (for example x= [1 2 5 8])\u003c/p\u003e\u003cp\u003eOutput is the minimum time. (for original problem y_correct= 15)\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 1:\u003c/b\u003e for this problem only four people will cross the bridge\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 2:\u003c/b\u003e crossing times are integer\u003c/p\u003e","function_template":"function y = bridgeRiddle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('bridgeRiddle.m');\r\nassert(isempty(strfind(filetext, 'assert')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\n\r\n\r\n%%\r\nx = [1 1 1 1];\r\ny_correct = 5;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 1 1 10];\r\ny_correct = 14;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 2 5 8];\r\ny_correct = 15;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 2 5 10];\r\ny_correct = 17;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [1 2 5 11];\r\ny_correct = 18;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [2 5 9 11];\r\ny_correct = 28;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3 8 13 16];\r\ny_correct = 43;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [7 13 15 16];\r\ny_correct = 58;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3 34 43 47];\r\ny_correct = 130;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [21 35 38 39];\r\ny_correct = 154;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [5 10 34 36];\r\ny_correct = 71;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [ 55 97 154 193];\r\ny_correct = 539;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [107 116 165 170];\r\ny_correct = 625;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [329 592 611 641];\r\ny_correct = 2502;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3259 4164 5259 6544];\r\ny_correct = 22295;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [5947 6267 8477 9254];\r\ny_correct = 34002;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n\r\n%%\r\nx = [12 24 24 30];\r\ny_correct = 102;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [6 6 10 12];\r\ny_correct = 36;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n%%\r\nx = [3 4 9 9];\r\ny_correct = 24;\r\nassert(isequal(bridgeRiddle(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2019-04-23T18:37:57.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2019-04-21T06:48:30.000Z","updated_at":"2024-11-12T04:56:45.000Z","published_at":"2019-04-21T06:48:30.000Z","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:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDetails of the problem ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eInput is crossing time list. (for example x= [1 2 5 8])\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\u003eOutput is the minimum time. (for original problem y_correct= 15)\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for this problem only four people will cross the bridge\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crossing times are integer\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\"}]}"},{"id":44884,"title":"Bridge and Torch Problem - Length of Unique Time List","description":"\u003chttps://en.wikipedia.org/wiki/Bridge_and_torch_problem Details of the problem ...\u003e \r\n\r\nInput is crossing time list. (for example x= [1 2 5 8])\r\n\r\nOutput is the length of all possible crossing time records. (for original problem y_correct= 14. In other words it is possible to cross the bridge in [15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 34, 40] minutes.\r\n\r\n*Assumption 1:* for this problem only four people will cross the bridge\r\n\r\n*Assumption 2:* crossing times are integer\r\n\r\n\r\n*Crossing Model:* 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\"\u003eDetails of the problem ...\u003c/a\u003e\u003c/p\u003e\u003cp\u003eInput is crossing time list. (for example x= [1 2 5 8])\u003c/p\u003e\u003cp\u003eOutput is the length of all possible crossing time records. (for original problem y_correct= 14. In other words it is possible to cross the bridge in [15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 34, 40] minutes.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 1:\u003c/b\u003e for this problem only four people will cross the bridge\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 2:\u003c/b\u003e crossing times are integer\u003c/p\u003e\u003cp\u003e\u003cb\u003eCrossing Model:\u003c/b\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\u003c/p\u003e","function_template":"function y = howManyWays(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('howManyWays.m');\r\nassert(isempty(strfind(filetext, 'assert')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\n\r\n\r\n%%\r\nx = [1 1 1 1];\r\ny_correct = 1;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 1 1 10];\r\ny_correct = 3; %[14,32,50]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [12 24 24 30];\r\ny_correct = 5; %[102,114,126,138,150]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [22 34 34 43];\r\ny_correct = 6; %[155 167 179 185 197 215]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [6 6 10 12];\r\ny_correct = 7; %[36 40 44 48 52 56 60]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [6 6 7 8];\r\ny_correct = 8; %[32 33 34 35 36 37 38 40]\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3 4 9 9];\r\ny_correct = 9; \r\nassert(isequal(howManyWays(x),y_correct))\r\n\r\n%%\r\nx = [4 6 8 11];\r\ny_correct = 10; \r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 5 6 7];\r\ny_correct = 13; \r\nassert(isequal(howManyWays(x),y_correct))\r\n\r\n\r\n%%\r\nx = [1 2 5 8];\r\ny_correct = 14;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 2 5 10];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [1 2 5 11];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [2 5 9 11];\r\ny_correct = 12;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3 8 13 16];\r\ny_correct = 11;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [7 13 15 16];\r\ny_correct = 11;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3 34 43 47];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [21 35 38 39];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [5 10 34 36];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [ 55 97 154 193];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [107 116 165 170];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [329 592 611 641];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [3259 4164 5259 6544];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n%%\r\nx = [5947 6267 8477 9254];\r\ny_correct = 15;\r\nassert(isequal(howManyWays(x),y_correct))\r\n\r\n%%\r\nx = [726 871 871 964];\r\ny_correct = 6; %[4158 4303 4448 4489 4634 4820]\r\nassert(isequal(howManyWays(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2019-04-22T11:56:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-21T07:08:50.000Z","updated_at":"2019-04-22T11:56:31.000Z","published_at":"2019-04-21T07:08:50.000Z","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\",\"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:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDetails of the problem ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eInput is crossing time list. (for example x= [1 2 5 8])\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\u003eOutput is the length of all possible crossing time records. (for original problem y_correct= 14. In other words it is possible to cross the bridge in [15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 34, 40] minutes.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for this problem only four people will cross the bridge\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crossing times are integer\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCrossing Model:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\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\"}]}"},{"id":44885,"title":"Bridge and Torch Problem - Probability","description":"\u003chttps://en.wikipedia.org/wiki/Bridge_and_torch_problem Details of the problem ...\u003e \r\n\r\nThere are four people who wants to cross the bridge. But we don't know exactly who will cross the bridge in which time. However, we know that a person can cross the bridge in n1 minutes (n1 is randomly selected from the range 1:n, n is the first input). All crossing times are integers. They use *Crossing Model* to cross the bridge. In each turn, they randomly select the person(s) who will cross the bridge. What is the probability that they will cross the bridge less than or equal to t minutes (t is the second input).\r\n\r\nLet's assume first input n = 3. That means people will cross the bridge in 1, 2 or 3 minutes. all of them can cross the bridge in 1 minute or maybe all of them can cross the bridge in 3 minutes. Possibilities are listed below.\r\n\r\n  crossingTimeList = [\r\n1\t1\t1\t1\r\n1\t1\t1\t2\r\n1\t1\t1\t3\r\n1\t1\t2\t2\r\n1\t1\t2\t3\r\n1\t1\t3\t3\r\n1\t2\t2\t2\r\n1\t2\t2\t3\r\n1\t2\t3\t3\r\n1\t3\t3\t3\r\n2\t2\t2\t2\r\n2\t2\t2\t3\r\n2\t2\t3\t3\r\n2\t3\t3\t3\r\n3\t3\t3\t3]\r\n\r\nIf first line is the case, all of the people will cross the bridge in 1 minute. There will be 108 cases  ( |108 = 4C2 X 2C1 X 3C2 X 3C1| ) taking 5 minutes. All of them will be less than or equal to 10 minutes (which is input 2). \r\n\r\nIf ninth line is the case, one person will cross the bridge in one minute, one person will cross the bridge in two minutes, and others will cross the bridge in 3 minutes. 8 out of 108 ways will take less than or equal to 10 minutes. \r\n\r\nIf last one is the case, all of them will cross the bridge in three minutes indicates that all of the journeys will take 15 minutes (longer than input2 or 10 minutes).\r\n\r\nResult of the crossingTimeList are as follow\r\n\r\n  result = [\r\n108\t108\r\n108\t108\r\n060\t108\r\n108\t108\r\n054\t108\r\n026\t108\r\n108\t108\r\n304\t108\r\n008\t108\r\n000\t108\r\n108\t108\r\n000\t108\r\n000\t108\r\n000\t108\r\n000\t108]\r\n\r\nAs a result 722 out of 1620 ways will take \u003c= 10 minutes (722/1620=0.4457).\r\n\r\n\r\n*Assumption 1:* for this problem only four people will cross the bridge\r\n\r\n*Assumption 2:* crossing times are integer\r\n\r\n*Crossing Model:* 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.  ","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\"\u003eDetails of the problem ...\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThere are four people who wants to cross the bridge. But we don't know exactly who will cross the bridge in which time. However, we know that a person can cross the bridge in n1 minutes (n1 is randomly selected from the range 1:n, n is the first input). All crossing times are integers. They use \u003cb\u003eCrossing Model\u003c/b\u003e to cross the bridge. In each turn, they randomly select the person(s) who will cross the bridge. What is the probability that they will cross the bridge less than or equal to t minutes (t is the second input).\u003c/p\u003e\u003cp\u003eLet's assume first input n = 3. That means people will cross the bridge in 1, 2 or 3 minutes. all of them can cross the bridge in 1 minute or maybe all of them can cross the bridge in 3 minutes. Possibilities are listed below.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ecrossingTimeList = [\r\n1\t1\t1\t1\r\n1\t1\t1\t2\r\n1\t1\t1\t3\r\n1\t1\t2\t2\r\n1\t1\t2\t3\r\n1\t1\t3\t3\r\n1\t2\t2\t2\r\n1\t2\t2\t3\r\n1\t2\t3\t3\r\n1\t3\t3\t3\r\n2\t2\t2\t2\r\n2\t2\t2\t3\r\n2\t2\t3\t3\r\n2\t3\t3\t3\r\n3\t3\t3\t3]\r\n\u003c/pre\u003e\u003cp\u003eIf first line is the case, all of the people will cross the bridge in 1 minute. There will be 108 cases  ( \u003ctt\u003e108 = 4C2 X 2C1 X 3C2 X 3C1\u003c/tt\u003e ) taking 5 minutes. All of them will be less than or equal to 10 minutes (which is input 2).\u003c/p\u003e\u003cp\u003eIf ninth line is the case, one person will cross the bridge in one minute, one person will cross the bridge in two minutes, and others will cross the bridge in 3 minutes. 8 out of 108 ways will take less than or equal to 10 minutes.\u003c/p\u003e\u003cp\u003eIf last one is the case, all of them will cross the bridge in three minutes indicates that all of the journeys will take 15 minutes (longer than input2 or 10 minutes).\u003c/p\u003e\u003cp\u003eResult of the crossingTimeList are as follow\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eresult = [\r\n108\t108\r\n108\t108\r\n060\t108\r\n108\t108\r\n054\t108\r\n026\t108\r\n108\t108\r\n304\t108\r\n008\t108\r\n000\t108\r\n108\t108\r\n000\t108\r\n000\t108\r\n000\t108\r\n000\t108]\r\n\u003c/pre\u003e\u003cp\u003eAs a result 722 out of 1620 ways will take \u0026lt;= 10 minutes (722/1620=0.4457).\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 1:\u003c/b\u003e for this problem only four people will cross the bridge\u003c/p\u003e\u003cp\u003e\u003cb\u003eAssumption 2:\u003c/b\u003e crossing times are integer\u003c/p\u003e\u003cp\u003e\u003cb\u003eCrossing Model:\u003c/b\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. Remaining two people will cross the bridge.\u003c/p\u003e","function_template":"function y = bridgeProb(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('bridgeProb.m');\r\nassert(isempty(strfind(filetext, 'assert')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\n%%\r\nx = [3 10];\r\nassert(and( ge(bridgeProb(x), 0.43) , le(bridgeProb(x), 0.45)))\r\n%%\r\nx = [8 5];\r\nassert(and( ge(bridgeProb(x), 0.00) , le(bridgeProb(x), 0.01)))\r\n%%\r\nx = [10 5];\r\nassert(and( ge(bridgeProb(x), 0.00) , le(bridgeProb(x), 0.01)))\r\n%%\r\nx = [8 15];\r\nassert(and( ge(bridgeProb(x), 0.10) , le(bridgeProb(x), 0.12)))\r\n%%\r\nx = [8 17];\r\nassert(and( ge(bridgeProb(x), 0.15) , le(bridgeProb(x), 0.17)))\r\n%%\r\nx = [10 35];\r\nassert(and( ge(bridgeProb(x), 0.60) , le(bridgeProb(x), 0.62)))\r\n%%\r\nx = [10 35];\r\nassert(and( ge(bridgeProb(x), 0.60) , le(bridgeProb(x), 0.62)))\r\n%%\r\nx = [10 40];\r\nassert(and( ge(bridgeProb(x), 0.78) , le(bridgeProb(x), 0.80)))\r\n%%\r\nx = [7 20];\r\nassert(and( ge(bridgeProb(x), 0.35) , le(bridgeProb(x), 0.37)))\r\n%%\r\nx = [8 25];\r\nassert(and( ge(bridgeProb(x), 0.45) , le(bridgeProb(x), 0.47)))\r\n%%\r\nx = [8 10];\r\nassert(and( ge(bridgeProb(x), 0.01) , le(bridgeProb(x), 0.03)))\r\n%%\r\nx = [9 15];\r\nassert(and( ge(bridgeProb(x), 0.06) , le(bridgeProb(x), 0.08)))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2019-04-23T07:16:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-21T08:29:03.000Z","updated_at":"2025-05-02T02:43:56.000Z","published_at":"2019-04-22T12:28:10.000Z","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:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bridge_and_torch_problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDetails of the problem ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eThere are four people who wants to cross the bridge. But we don't know exactly who will cross the bridge in which time. However, we know that a person can cross the bridge in n1 minutes (n1 is randomly selected from the range 1:n, n is the first input). All crossing times are integers. They use\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\u003eCrossing Model\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to cross the bridge. In each turn, they randomly select the person(s) who will cross the bridge. What is the probability that they will cross the bridge less than or equal to t minutes (t is the second input).\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\u003eLet's assume first input n = 3. That means people will cross the bridge in 1, 2 or 3 minutes. all of them can cross the bridge in 1 minute or maybe all of them can cross the bridge in 3 minutes. Possibilities are listed below.\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[crossingTimeList = [\\n1  1  1  1\\n1  1  1  2\\n1  1  1  3\\n1  1  2  2\\n1  1  2  3\\n1  1  3  3\\n1  2  2  2\\n1  2  2  3\\n1  2  3  3\\n1  3  3  3\\n2  2  2  2\\n2  2  2  3\\n2  2  3  3\\n2  3  3  3\\n3  3  3  3]]]\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\u003eIf first line is the case, all of the people will cross the bridge in 1 minute. There will be 108 cases (\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e108 = 4C2 X 2C1 X 3C2 X 3C1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ) taking 5 minutes. All of them will be less than or equal to 10 minutes (which is input 2).\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 ninth line is the case, one person will cross the bridge in one minute, one person will cross the bridge in two minutes, and others will cross the bridge in 3 minutes. 8 out of 108 ways will take less than or equal to 10 minutes.\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 last one is the case, all of them will cross the bridge in three minutes indicates that all of the journeys will take 15 minutes (longer than input2 or 10 minutes).\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\u003eResult of the crossingTimeList are as follow\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[result = [\\n108  108\\n108  108\\n060  108\\n108  108\\n054  108\\n026  108\\n108  108\\n304  108\\n008  108\\n000  108\\n108  108\\n000  108\\n000  108\\n000  108\\n000  108]]]\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\u003eAs a result 722 out of 1620 ways will take \u0026lt;= 10 minutes (722/1620=0.4457).\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for this problem only four people will cross the bridge\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAssumption 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crossing times are integer\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCrossing Model:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2 out of 4 people will cross the bridge, one of them will return. two out of 3 people will cross the bridge, one out of three people will return. 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