关键词:Hex博弈; 步数; 最优策略
New approach on optimal play in Hex game
PENG Yuan1, XU Xiao-dong1, LUO Hai-peng1, CUI Xiu-feng2
(1.Guangxi Academy of Sciences, Nanning 530007, China; 2. Network Information Center, Qiqihar University, Qiqihar Heilongjiang 161006, China)
Abstract:Hex game Hex(n) is a two person game played on an n×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.
Key words:Hex game; moves; optimal play ......