Delete Nim

TL;DR

This paper analyzes Delete Nim, an impartial game involving heap deletion and splitting, providing a method to compute its G-value using OR operation and 2-adic valuation.

Contribution

It introduces a novel approach to calculate the G-value of Delete Nim using OR operation and 2-adic valuation, advancing combinatorial game theory.

Findings

G-value of Delete Nim can be computed efficiently

The method involves OR operation and 2-adic valuation

Provides insights into the structure of the game

Abstract

In this paper, we study an impartial game called Delete Nim. In this game, there are two heaps of stones. The player chooses one of the heaps and delete the other heap. Next, she takes away one stone from the chosen heap and optionally splits it into two heaps. We show the way to calculate the G-value of this game by using the OR operation and 2-adic valuation.