In the past three decades, deductive games have become interesting from the
algorithmic point of view. Deductive games are two players zero sum games 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. A well known deductive game is the famous
Mastermind game. 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
colors where no repetition of colors is allowed. We present a strategy that
identifies the secret code in O(n log n) queries. Our algorithm improves the
previous result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2
for the case k = n. To our knowledge there is no previous work dealing with the
case k > n.
Keywords: Mastermind; combinatorial problems; permutations; algorithm
