Winning and Losing Positions and Some Grundy Values for the Game of Exact-2-Fibonacci NIM

Authors

  • wajd ali Tishreen University
  • Hadeel Samir Barbara Tishreen University

Abstract

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}.

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Published

2023-02-23

How to Cite

1.
علي و, هديل سمير برباره. Winning and Losing Positions and Some Grundy Values for the Game of Exact-2-Fibonacci NIM. TUJ-BA [Internet]. 2023Feb.23 [cited 2024May13];44(6):93-107. Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/13086

Issue

Vol. 44 No. 6 (2022): Tishreen University Journal of Research and Scientific Studies - Basic Sciences Series

Section

Master student researches

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