Complete Solutions for a Combinatorial Puzzle in Linear Time and Its Computer Implementation

Authors

Daxin Zhu, Faculty of Mathematics & Computer Science, Quanzhou Normal University, 362000 Quanzhou, ChinaFollow
Yingjie Wu, School of Mathematics and Computer Science, Fuzhou University, 350002 Fuzhou, ChinaFollow
Lei Wang, Microsoft AdCenter, Bellevue, WA 98004, USAFollow
Xiaodong Wang, Faculty of Mathematics & Computer Science, Quanzhou Normal University, 362000 Quanzhou, China\\ School of Mathematics and Computer Science, Fuzhou University, 350002 Fuzhou, ChinaFollow

Author Country (or Countries)

China

Abstract

In this paper we study a single player game consisting of n black checkers and m white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general n and m is nm+n+m. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of n black checkers and m white checkers, and finally, we present an explicit solution for the general game.

Recommended Citation

Zhu, Daxin; Wu, Yingjie; Wang, Lei; and Wang, Xiaodong (2015) "Complete Solutions for a Combinatorial Puzzle in Linear Time and Its Computer Implementation," Applied Mathematics & Information Sciences: Vol. 09: Iss. 2, Article 34.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss2/34