Improved Approximation Algorithm for the Number of Queries Necessary to Identify a Permutation

Abstract

In the past three decades, deductive games have become interesting from the algorithmic point of view. A well known deductive game is the famous Mastermind game. In this paper, we consider the so called Black-Peg variant of Mastermind. 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 $\mathcal{O}(n\log_2{n})$ queries. Our algorithm improves the previous result of Ker-I Ko and Shia-Chung Teng (1986) 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.