On the algorithmic complexity of the Mastermind game with black-peg results

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 Chvátal by almost a factor of 2.

DOI: 10.1016/j.ipl.2009.02.021

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Cite this paper

@article{Goodrich2009OnTA, title={On the algorithmic complexity of the Mastermind game with black-peg results}, author={Michael T. Goodrich}, journal={Inf. Process. Lett.}, year={2009}, volume={109}, pages={675-678} }