Computer Implementation of Multiple Fibonacci Nim

Abstract: In this paper a special combinatorial game with two players, called multiple Fibonacci Nim, is defined as below: There are n> 1 piles of chips. The number of chips in each pile is greater than 1. Two players take chips alternately. Each player in his turn first chooses one of the piles, and he can change his choice of piles in any his other turn. He then removes chips from the pile. The first player may remove any number of chips from the pile he chosen but not the whole pile. After that each player may remove at most twice as many as the previous player removed. The winner is the player who removes the last chip. Properties of general multiple Fibonacci Nim are researched. For n = 2 and n = 3, the algorithms or part of source codes to determine the P positions and to find the winning strategy are given. 1