ID  115957 
Author 
Katayama, Shinichi
Tokushima University
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Koyama, Yuya
Tokushima University

Content Type 
Departmental Bulletin Paper

Description  Let p be an integer with p ≥ 2. We shall investigate the following two piles Nim games. Let S be the set of positive integers {1 ≤ i ≤ p − 1}. Each player can remove the number of tokens s1 ∈ {0} ∪ S from the first pile and s2 ∈ {0} ∪ S from the second pile with 0 < s1 + s2 at the same time. We shall identify (m, n) to a position of this Nim game, where m is the number of tokens in the first pile and n is the number of tokens in the second pile. We shall show the SpragueGrundy sequence (or simply Gsequences) gs(m, n) satisfy the periodic relation gs(m+p, n+p) = gs(m, n) for any position (m, n). We will call this two piles Nim Square Nim. In case m and n are sufficiently large, we will show that Gsequences gs(m, n) are also periodic for each row and column with the same period p. Finally we shall introduce several related games, such as Rectangular Nim, Triangular Nim and Polytope Nim.

Journal Title 
Journal of Mathematics

ISSN  13467387

NCID  AA11595324

Publisher  TOKUSHIMA UNIVERSITY

Volume  54

Start Page  93

End Page  104

Sort Key  93

Published Date  2020

EDB ID  
FullText File  
language 
eng

TextVersion 
Publisher

departments 
Science and Technology
