Games of Nim with Dynamic Restrictions
Keita Mizugaki, Shoei Takahashi, Hikaru Manabe, Aoi Murakami, Ryohei Miyadera
Abstract
The authors present formulas for the previous player’s winning positions of two variants of restricted Nim. In both of these two games, there is one pile of stones, and in the first variant, we investigate the case that in k -th turn, you can remove f (k ) stones at most, where f is a function whose values are natural numbers. In the second variant, there are two kinds of stones. The Type 1 group consists of stones with the weight of one, and the Type 2 group consists of stones with the weight of two. When the total weight of stones is a , you can remove stones whose total weight is equal to or less than ⌊a /2⌋
Keywords
Combinatorial Game Theory restricted nim
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DOI:
http://dx.doi.org/10.19184/ijc.2024.9.1.5
References
L. Levine, Fractal sequences and restricted Nim, Ars Combinatoria, 80 (2006), 113--127.
R. Miyadera, S. Kannan and H. Manabe, Maximum Nim and Chocolate Bar Games, Thai Journal of Mathematics, accepted.
R. Miyadera and H. Manabe, Restricted Nim with a Pass, Integers , 23 (2023), # G3.
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ISSN: 2541-2205
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