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]

Solve

Solution Stats

25 Solutions
13 Solvers

Last Solution submitted on Aug 16, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers13

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44237. Mastermind II: Solve in 8 or less

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers13

Suggested Problems

More from this Author260

Problem Tags

Community Treasure Hunt

Problem 44237. Mastermind II: Solve in 8 or less

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers13

Suggested Problems

More from this Author260

Problem Tags

Community Treasure Hunt

Players