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Fibonacci Nim and
a full characterization of winning moves
Cody Allen and Vadim Ponomarenko
Vol. 7 (2014), No. 6, 807–822
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Abstract |
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In this paper we will fully characterize all types of winning moves in the “take-away” game of Fibonacci Nim. We prove the known winning algorithm as a corollary of the general winning algorithm and then show that no other winning algorithms exist. As a by-product of our investigation of the game, we will develop useful properties of Fibonacci numbers. We conclude with an exploration of the probability that unskilled player may beat a skilled player and show that as the number of tokens increase, this probability goes to zero exponentially. |
Keywords
Fibonacci Nim, take away games, dynamic Nim, combinatorial
games, Fibonacci
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Mathematical Subject Classification 2010
Primary: 91A46
Secondary: 11A63
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Milestones
Received: 23 December 2013
Revised: 8 January 2014
Accepted: 24 January 2014
Published: 20 October 2014
Communicated by Scott T. Chapman
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Authors |
| Cody Allen | |
| Department of Mathematics and
Statistics San Diego State University 5500 Campanile Drive San Diego, CA 92182-7720 United States |
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| Vadim Ponomarenko | |
| Department of Mathematics and
Statistics San Diego State University 5500 Campanile Drive San Diego, CA 92182-7720 United States |
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