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

Boris S. Verkhovsky

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DOI: 10.4236/ijcns.2010.310106                

Abstract

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.

Keywords

Nim-type Game, Two-person Strategy Game, Winning Strategies, Newton Algorithm, Fibonacci Numbers

Conflicts of Interest

The authors declare no conflicts of interest.

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