Problem 44237. Mastermind II: Solve in 8 or less

Created by Richard Zapor

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Mastermind_(board_game)\"><w:r><w:t>Mastermind</w:t></w:r></w:hyperlink><w:r><w:t> is a code breaking logic puzzle. A pattern of 6 colors(values 1:6) of four positions (1111;1112;....6666) for a possible 6^4(1296) cases is generated. The solver plays a length 4 vector with values 1:6. Accuracy of the play is returned by a count of values in the right position and a count of values(excluding those in the right positions) common to the solution.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Answer:1233 Guess:3231 Response: 2,2 as x23x are right value/position, 3xx1 are right values.]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>[guess]=solve_mastermind(mguess,mpegs,m,mpc,mc,mpc5c,v)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where guess is a 1x4 vector, mguess is the kx4 matrix of prior guesses and is empty on first try, mpegs is kx2 giving right [value/position, values] for mguess, m is a 1296x4 array [1 1 1 1;...6 6 6 6] of all solutions, mpc is a 1296x1296 array of 0:4 for value/position solutions, mc is a 1296x1296 array of 0:4 for value solutions, mpc5c is state array of a combined mpc and pc of values 0:20, 5*mpc+mc, and v is integer value of solutions 1111 thru 6666.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Challenge: All 1296 cases will be provided. The maximum number of guesses allowed is 8 with a time limit of 45 seconds. The user will see their prior guesses and the guess response.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Theory: Simple elimination of invalid cases is sufficient to reduce max guesses to 8. The optimal minimal guess solution requires only 5 guesses.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Future: Four Mastermind challenges will be created, [Solve no limit, Solve in 8 or less, Solve in 1 given a guess pattern, Solve in 5 or less]</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

<a href = "https://en.wikipedia.org/wiki/Mastermind_(board_game)">Mastermind</a> is a code breaking logic puzzle. A pattern of 6 colors(values 1:6) of four positions (1111;1112;....6666) for a possible 6^4(1296) cases is generated. The solver plays a length 4 vector with values 1:6. Accuracy of the play is returned by a count of values in the right position and a count of values(excluding those in the right positions) common to the solution.<pre class="language-matlab">Answer:1233 Guess:3231 Response: 2,2 as x23x are right value/position, 3xx1 are right values.
</pre>[guess]=solve_mastermind(mguess,mpegs,m,mpc,mc,mpc5c,v)where guess is a 1x4 vector, mguess is the kx4 matrix of prior guesses and is empty on first try, mpegs is kx2 giving right [value/position, values] for mguess, m is a 1296x4 array [1 1 1 1;...6 6 6 6] of all solutions, mpc is a 1296x1296 array of 0:4 for value/position solutions, mc is a 1296x1296 array of 0:4 for value solutions, mpc5c is state array of a combined mpc and pc of values 0:20, 5*mpc+mc, and v is integer value of solutions 1111 thru 6666.Challenge: All 1296 cases will be provided. The maximum number of guesses allowed is 8 with a time limit of 45 seconds. The user will see their prior guesses and the guess response.Theory: Simple elimination of invalid cases is sufficient to reduce max guesses to 8. The optimal minimal guess solution requires only 5 guesses.Future: Four Mastermind challenges will be created, [Solve no limit, Solve in 8 or less, Solve in 1 given a guess pattern, Solve in 5 or less]

<https://en.wikipedia.org/wiki/Mastermind_(board_game) Mastermind> is a code breaking logic puzzle. A pattern of 6 colors(values 1:6) of four positions (1111;1112;....6666) for a possible 6^4(1296) cases is generated. The solver plays a length 4 vector with values 1:6. Accuracy of the play is returned by a count of values in the right position and a count of values(excluding those in the right positions) common to the solution.

Answer:1233  Guess:3231 Response: 2,2  as x23x are right value/position, 3xx1 are right values.

[guess]=solve_mastermind(mguess,mpegs,m,mpc,mc,mpc5c,v)

where guess is a 1x4 vector, mguess is the kx4 matrix of prior guesses and is empty on first try, mpegs is kx2 giving right [value/position, values] for mguess, m is a 1296x4 array [1 1 1 1;...6 6 6 6] of all solutions, mpc is a 1296x1296 array of 0:4 for value/position solutions, mc is a 1296x1296 array of 0:4 for value solutions, mpc5c is state array of a combined mpc and pc of values 0:20, 5*mpc+mc, and v is integer value of solutions 1111 thru 6666.

Challenge: All 1296 cases will be provided. The maximum number of guesses allowed is 8 with a time limit of 45 seconds. The user will see their prior guesses and the guess response.

Theory: Simple elimination of invalid cases is sufficient to reduce max guesses to 8.  The optimal minimal guess solution requires only 5 guesses.

Future: Four Mastermind challenges will be created, [Solve no limit, Solve in 8 or less, Solve in 1 given a guess pattern, Solve in 5 or less]

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Last Solution submitted on May 25, 2023

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Problem 44237. Mastermind II: Solve in 8 or less

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Problem 44237. Mastermind II: Solve in 8 or less

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