2023/11/30 by Keita Mizugaki, Shoei Takahashi, Mizugaki, Keita +7
Computer Science · Decision Sciences · Mathematics · #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Game Theory and Applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2311.18523
openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 half of a.