×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. E. Knuth, The computer as a Master Mind,Journal of Recreational Mathematics 9 (1976–77), 1–6. · Zbl 0358.90075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.