Mastermind game is a two players zero sum game of imperfect information. The first player, called codemaker, chooses a secret code and the second player, called codebreaker, tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k n we prove an upper bound for the problem of (n-1)*ld(n)+k+1. Furthermore we prove a new lower bound for (a generalization of) the case k=n that improves the recent result of Berger et al. (2016) from n-log(log(n)) to n. We also give a lower bound of k queries for the case k>n.
['Mourad El Ouali', 'Christian Glazik', 'Volkmar Sauerland', 'Anand Srivastav']
On the Query Complexity of Black-Peg AB-Mastermind