Optimal Strategies for Static Black-Peg AB Game with Two and Three Pegs

The AB Game is a game similar to the popular Mastermind. We study version of this called Static Black-Peg Game. It played by two players, codemaker and codebreaker. creates so-called secret placing color from set [Formula: see text] colors on each pegs, subject condition that every used at most once. codebreaker tries determine asking questions, where all questions are given once question possible secret. As an answer reveals number correctly placed for questions. After that, only has one more try thus win game. For text], our goal find smallest needs win, regardless secret, corresponding list text]-strategy. present text]-strategy show optimality both strategies, i.e., we prove no smaller exists.