Shrinking Circular Nim

TL;DR

This paper introduces Shrinking Circular Nim, a new variation of the classic game where the circle of piles shrinks over time, and analyzes its winning strategies for small configurations.

Contribution

The paper defines Shrinking Circular Nim, solves it for up to five piles, and derives winning conditions for the case with eight piles.

Findings

Solved for initial configurations with five or fewer piles.

Derived winning condition for the case with eight piles.

Introduced a new dynamic variation of Circular Nim.

Abstract

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.