Problem 44237. Mastermind II: Solve in 8 or less
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.
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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