Article

Theory of Computing Systems

, Volume 55, Issue 4, pp 658-684

First online:

Playing Mastermind with Constant-Size Memory

  • Benjamin DoerrAffiliated withD1: Algorithms and Complexity, Max Planck Institute for Informatics
  • , Carola WinzenAffiliated withD1: Algorithms and Complexity, Max Planck Institute for Informatics

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Abstract

We analyze the classic board game of Mastermind with n holes and a constant number of colors. The classic result of Chvátal (Combinatorica 3:325–329, 1983) states that the codebreaker can find the secret code with Θ(n/logn) questions. We show that this bound remains valid if the codebreaker may only store a constant number of guesses and answers. In addition to an intrinsic interest in this question, our result also disproves a conjecture of Droste, Jansen, and Wegener (Theory Comput. Syst. 39:525–544, 2006) on the memory-restricted black-box complexity of the OneMax function class.

Keywords

Mastermind Query complexity Memory-restricted algorithms