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

Extracted Key Phrases

Showing 1-6 of 6 references

V. Chvátal. Mastermind. Combinatorica

  • 1983
Highly Influential
4 Excerpts

The computer as a master mind

  • D Knuth
  • 1977
1 Excerpt
Showing 1-10 of 17 extracted citations