Shrinking 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.