(untitled) (Latakia University Journal -Basic Sciences Series, 2023)
Fibonacci NIM is an impartial combinatorial game, usually played with a single pile of stones, Its analysis involves the Fibonacci numbers and the Zeckendorf representation of a natural number. In this paper we will deal a study and a mathematical analysis of the case of 2-pile and 3-pile with the condition that the stones are deleted from exactly two piles, and we find Grundy values for two piles (n1, n2; r1, r2) and the winning strategy which amounts to understanding positions of Grundy value 0, and we will calculate all the positions of Grundy value 0,1,2,3, and use Fibonacci words to calculate all Grundy values for any position in which r1 is 1,2,3,4,5.