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Conference Paper

Playing Mastermind with Constant-size Memory


Doerr,  Benjamin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Doerr,  Carola
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Doerr, B., & Doerr, C. (2012). Playing Mastermind with Constant-size Memory. In C. Dürr, & T. Wilke (Eds.), 29th International Symposium on Theoretical Aspects of Computer Science (pp. 441-452). Dagstuhl: Schloss Dagstuhl/ Leibniz-Zentrum für Informatik. doi:10.4230/LIPIcs.STACS.2012.441.

Cite as:
We analyze the classic board game of Mastermind with n holes and a constant number of colors. The classic result of Chvátal (Combinatorica 3 (1983), 325-329) states that the codebreaker can find the secret code with \Theta(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.