Games of Nim with Dynamic Restrictions

Mizugaki, Keita (School of Engineering Science, the University of Osaka, Japan)
Takahashi, Shoei (Faculty of Environment and Information Studies, Keio University, Japan)
Manabe, Hikaru (School of Informatics, University of Tsukuba, Japan)
Murakami, Aoi (School of Engineering, Kwansei Gakuin University, Japan)
Miyadera, Ryohei (Keimei Gakuin)

Indonesian Journal of Combinatorics
Vol 9, No 1 (2025)

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⌋