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ID 115957
Author
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 Sprague-Grundy sequence (or simply G-sequences) 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 G-sequences 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