International Journal of Game Theory

, Volume 47, Issue 2, pp 595–611

# Global Fibonacci nim

• Simon Rubinstein-Salzedo
Original Paper

## 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

## Notes

### Acknowledgements

Part of the work for this paper was completed at the Games at Dal workshop at Dalhousie University in Halifax, Nova Scotia, in August 2015. The first author was supported by the Killam Trusts. We would like to thank the referees for their helpful suggestions.

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