TITLE:
Winning Strategies and Complexity of Nim-Type Computer Game on Plane
AUTHORS:
Boris S. Verkhovsky
KEYWORDS:
Nim-type Game, Two-person Strategy Game, Winning Strategies, Newton Algorithm, Fibonacci Numbers
JOURNAL NAME:
International Journal of Communications, Network and System Sciences,
Vol.3 No.10,
October
27,
2010
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.