  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 colors
where no repetition of colors is allowed. We present upper and lower bounds on
the number of guesses necessary to break the secret code. We first come back to
the upper bound results introduced by El Ouali and Sauerland (2013). For the
case k=n the secret code can be algorithmically identified within less than
(n-3)*ld(n)+5n/2 queries. That result improves the result of Ker-I Ko and
Shia-Chung Teng (1985) by almost a factor of 2. For the case 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.
