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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
game; Mastermind
Full Text:
##### 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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