Winning Strategies and Complexity of Nim-Type Computer Game on Plane - International Journal of Communications, Network and System Sciences

IJCNS > Vol.3 No.10, October 2010

International Journal of Communications, Network and System Sciences

Volume 3, Issue 10 (October 2010)

ISSN Print: 1913-3715 ISSN Online: 1913-3723

Google-based Impact Factor: 0.66 Citations h5-index & Ranking

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

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DOI: 10.4236/ijcns.2010.310106 5,745 Downloads 10,129 Views Citations

Author(s)

Boris S. Verkhovsky

Affiliation(s)

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

Share and Cite:

B. Verkhovsky, "Winning Strategies and Complexity of Nim-Type Computer Game on Plane," International Journal of Communications, Network and System Sciences, Vol. 3 No. 10, 2010, pp. 793-800. doi: 10.4236/ijcns.2010.310106.

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