Global Fibonacci nim

Urban Larsson () and Simon Rubinstein-Salzedo ()
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Urban Larsson: Technion–Israel Institute of Technology
Simon Rubinstein-Salzedo: Euler Circle

International Journal of Game Theory, 2018, vol. 47, issue 2, No 11, 595-611

Abstract: Abstract Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones: two players alternate in removing no more than twice the previous player’s removal. The game is appealing due to its surprising connections with the Fibonacci numbers and the Zeckendorf representation. In this article, we investigate some properties of a variant played with multiple piles of stones, and solve the 2-pile case. A player chooses one of the piles and plays as in Fibonacci nim, but here the move-size restriction is a global parameter, valid for any pile.

Keywords: Combinatorial game; Complementary value; Complementary equation; Fibonacci sequence; Fibonacci word; Impartial game; Power-of-two nim; Sturmian word; Zeckendorf representation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00182-017-0574-x

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