摘要
Hex博奕Hex(n)是一种在六边形拼接的n×n棋盘上进行的二人博奕,博奕中二人轮流下红色和蓝色棋子,先构造出一条从一边连到对边的单色路者为胜者。Hex博奕中先手有必胜策略。设δ(n)为Hex(n)中先手能保证获胜所需的最少步数,Garikai Campbell通过研究其他对象间接地证明了δ(n)>n对任意n≥4成立。利用新的方法来分析对称性,给出了δ(n)>n一个直接而简单的证明,并在此基础上利用计算证明了δ(5)=7。
Hex game Hex(n) is a two person game played on an n x n board of hexagonal tiles, in which the players take turns trying to construct paths from one side of the board to the other. There exists a winning strategy for the first player. Let δ(n) be the minimum number of moves that player one must make to guarantee a win in Hex (n), Garikai Campbell proved δ (n) 〉 n for any n≥4 by studying another question. In this note, gave a directed and much simpler proof based on a new approach, based on what proved δ(5 ) = 7 by computing.
出处
《计算机应用研究》
CSCD
北大核心
2010年第2期498-499,502,共3页
Application Research of Computers
基金
广西自然科学基金资助项目(0991074)
广西科学院基本科研业务费资助项目(09YJ17XX01)