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

Authors:
Michael T. Goodrich
Affiliations:
Dept. of Computer Science and Secure Computing and Networking Center, University of California, Irvine, CA, USA
Venue:
Information Processing Letters
Year:
2009

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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.