Sharing Nim and Enumeration of Nim Characteristics

TL;DR

This paper introduces Sharing Nim, a variant allowing transfer moves with size restrictions, and develops new enumeration methods for Nim characteristics, including zero positions.

Contribution

It presents a novel Nim variant with transfer moves and provides new enumeration techniques for Nim characteristics, expanding understanding of game states.

Findings

Defined Sharing Nim with transfer rules

Enumerated zero nim positions in Sharing Nim

Developed new methods for Nim characteristic enumeration

Abstract

In this paper, we introduce and examine a variant of the game of Nim (Sharing Nim), where players can either remove or transfer objects from 1 pile to another. The only restriction is that players may not transfer objects from a pile of greater size to a pile of smaller size. We also find new methods of enumerating characteristics of Nim and Sharing Nim, including the number of zero nim positions.