Novel Algorithms for Deductive Games

Abstract

This paper presents two novel algorithms for deductive games. First, a k-way-branching algorithm, taking advantage of a clustering technique, is able to efficiently obtain an optimal strategy in the worst case and a near-optimal strategy in the expected case for a typical deductive game “Bulls and Cows.” Second, a pigeonholeprinciple- based backtracking algorithm has been successfully applied to efficiently reduce the search space for the game. By using the algorithms, we not only obtain the lower bound on number of guesses required for the game in the worst case, but also derive the main theorem: 7 guesses are necessary and sufficient for the “Bulls and Cows” in the worst case. This is the first paper to prove the exact bound of this problem.