Playing Mastermind With Constant-Size Memory

2011/10/17 by Doerr, Benjamin, Winzen, Carola
#Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #Neural and Evolutionary Computing (cs.NE)

paper · doi:10.48550/arxiv.1110.3619

Abstract

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 / log 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.

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