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Mastermind. (English) Zbl 0717.05002

In the game “Mastermind” a player must determine a vector \((x_ 1,...,x_ n)\), \(1\leq x_ i\leq k\). He guesses a vector \((q_ 1,...,q_ n)\) and is told the number of i for which \(q_ i=x_ i\) and the maximum number, over all permutations \(\phi\) on \(\{\) 1,...,n\(\}\), of i with \(q_ i=x_{\phi_ i}\). For \(n=4\) and \(k=6\) this is a popular commercial game. The strategy of selecting vectors q at random is examined and shown to be close to optimal in some cases.

MSC:

05A05 Permutations, words, matrices
91A05 2-person games

Keywords:

game; Mastermind
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References:

[1] D. E. Knuth, The computer as a Master Mind,Journal of Recreational Mathematics 9 (1976–77), 1–6. · Zbl 0358.90075
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