收缩环形Nim
Shrinking Circular Nim
AI总结：
本文提出了一种名为 Shrinking Circular Nim 的 Nim 游戏新变体，其圆圈大小随游戏进程缩小，并推导了其获胜条件，解决了初始配置包含 5 堆或更少的情况及包含 8 堆的特定情况。
AI中文摘要：
Nim 游戏多年来众所周知，有众多变体。其中一种变体是 Circular Nim，石堆排列在圆周上，玩家每次从连续相邻的石堆中取石。本文提出了一种名为 Shrinking Circular Nim 的新变体，其圆圈大小随游戏进行而缩小。我们还研究了该变体的获胜条件。本文论证了对于初始配置包含 5 堆或更少的情况，Shrinking Circular Nim 已被解决。此外，我们推导出了包含 8 堆的特定情况下的获胜条件。
英文摘要：
The game of Nim, which has been well known for many years, has numerous variations. One such variation is Circular Nim, where piles of stones are arranged on a circumference, and players take stones from consecutive adjacent piles in one move. In this paper, we propose a new variant called Shrinking Circular Nim, in which the size of the circle decreases as the game progresses. We also examine the winning conditions in this variant. This paper discusses that Shrinking Circular Nim is solved for initial configurations with five or fewer piles. In addition, we derive the winning condition for the specific case with eight piles.
