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arXiv · 0904.4911

On the Algorithmic Complexity of the Mastermind Game with Black-Peg Results

Michael T. Goodrich
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Abstract

In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-color Mastermind results have a satisfying vector. We also show how to devise efficient algorithms for discovering a hidden vector through single-color queries. Indeed, our algorithm improves a previous method of Chvatal by almost a factor of 2.

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Michael T. Goodrich. 2009-04-30. On the Algorithmic Complexity of the Mastermind Game with Black-Peg Results. https://doi.org/10.1016/j.ipl.2009.02.021

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