Fibonacci Nim is a variant of the traditional game of Nim, which introduces a unique twist using Fibonacci numbers. In Fibonacci Nim, players take turns removing objects (or stones) from a heap, with the number of objects that can be removed on any turn determined by Fibonacci numbers.
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A heap game in which, after the first move, a player may remove at most twice the number removed on the preceding move. Under the usual first-move restriction of fewer than all counters, Fibonacci numbers and the Zeckendorf representation characterize the winning moves.