Winning Strategies and Complexity of Nim-Type Computer Game on Plane

• 作者: Boris S. Verkhovsky
• 来源期刊: 通讯、网络与系统学国际期刊(英文)
• 学科: 数学
• 关键词: Nim-type GAME Two-person Strategy GAME Winning Strategies NEWTON Algorithm FIBONACCI NUMBERS
• 年，卷（期）: 2010,（10）
• 页码范围: 793-800
• 页数: 8页
• 分类号: O1

摘要

A Nim-type computer game of strategy on plane is described in this paper. It is demonstrated that winning strategies of this two-person game are determined by a system of equations with two unknown integer sequences. Properties of winning points/states are discussed and an O(loglogn) algorithm for the winning states is provided. Two varieties of the Game are also introduced and their winning strategies are analyzed.