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All Journal Indonesian Journal of Combinatorics
Manabe, Hikaru
School of Informatics, University of Tsukuba, Japan
Computer Science & IT Decision Sciences, Operations Research & Management

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Games of Nim with Dynamic Restrictions Mizugaki, Keita; Takahashi, Shoei; Manabe, Hikaru; Murakami, Aoi; Miyadera, Ryohei
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.9.1.5

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⌋
Co-Authors Miyadera, Ryohei Mizugaki, Keita Murakami, Aoi Takahashi, Shoei