群在某对策论中的应用

Application of Groups in Some Countemeasure Theory

对于两人玩取棋子游戏 ,文章给出了一种能够取胜的方法 .文中先给出了“必胜集’的定义 ,再利用模 2的剩余类加群 {0 ,1 }的加法定义了一个“二进制群” :N ={0 ,1 ,2 ,… }给出了该二进制群的一些性质 (即文中命题 2 ) .接着利用此二进制群及其性质证明了必胜集G ={(a ,b,c) |a b c=0 }的存在性 .那么 ,只要想办法让对方面对必胜集中的一组数 ,无论对方怎么取 ,我们都有最后赢的把握 .最后 ,文中又提供了一个编写让人和计算机玩取棋游戏程序思路 .该程序中由于计算机知道取胜对策 .人输入任意一组数 ,一般都是计算机赢 .除非输入的数字太过简单 .

This paper proposes a method to win the taking chess game, which carried out between two people. Firstly the paper define a 'win set'. Then the paper define a binary group on the basis of the residue class add group of model 2: N={0,1,2,...}. The paper also give some properties of it (such as proposition 2). Then proof the existence of 'win set': G={a,b,c)|abc=0} , which based on the binary and its properties. According to the set, we can win the game if we make our rival run into the situation he has to take one of number in the set. Finally, this paper proposes a idea on how to write a computer programe.