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

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Author(s): Boris S. Verkhovsky

Journal: International Journal of Communications, Network and System Sciences
ISSN 1913-3715

Volume: 03;
Issue: 10;
Start page: 793;
Date: 2010;
Original page

Keywords: Nim-type Game | Two-person Strategy Game | Winning Strategies | Newton Algorithm | Fibonacci Numbers

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.

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