Playing Mastermind With Constant-Size Memory

Benjamin Doerr & Carola Winzen
We analyze the classic board game of Mastermind with n holes and a constant number of colors. The classic result of Chvatal (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...