Open Access Open Access  Restricted Access Subscription or Fee Access

An Algorithmic Analysis of a Combinatorial Game

Daxin Zhu, Lei Wang, Jun Tian, Xiaodong Wang


In this paper, we study an interesting shifting checkers game consisting of n black checkers and 1 white checkers, called Moving Checkers Game, as a means to elucidate the process of analyzing a problem and synthesizing observations into an algorithm that, in turn, can be used to generate a programming solution. While not directly presented as such, the material discussed could be easily adapted to allow for small-group cooperative learning. Some properties of the optimal solutions of the problem are also interesting. We have proved that the minimum number of steps needed to play the game for general n is 2n+1.
We have also presented an optimal algorithm to generate all of the optimal solutions in linear time for very large size. The number of solutions for the game of size n is the (n+2)th Fibonacci number. We present also an explicit solution for the general game. This explicit solution will give the exact actions for each number of moves in constant time. The step by step process used to solve the problem is reflective of the process an expert goes through when solving the problem.


Computer games, optimal algorithms, explicit solutions.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.