Playing Mastermind With Constant-Size Memory

10/17/2011

∙

by   Benjamin Doerr, et al.

∙

0

∙

share

We analyze the classic board game of Mastermind with n holes and a constant number of colors. A result of Chvátal (Combinatorica 3 (1983), 325-329) states that the codebreaker can find the secret code with Θ(n / n) 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 of Computing Systems 39 (2006), 525-544) on the memory-restricted black-box complexity of the OneMax function class.