P-positions in Modular Extensions to Nim

Tanya Khovanova; Karan Sarkar

P-positions in Modular Extensions to Nim

Combinatorics 2015-08-31 v1

Authors: Tanya Khovanova , Karan Sarkar

Abstract

In this paper, we consider a modular extension to the game of Nim, which we call $m$ -Modular Nim, and explore its optimal strategy. In $m$ -Modular Nim, a player can either make a standard Nim move or remove a multiple of $m$ tokens in total. We develop a winning strategy for all $m$ with $2$ heaps and for odd $m$ with any number of heaps.

Keywords

combinatorial game theory

Cite

@article{arxiv.1508.07054,
  title  = {P-positions in Modular Extensions to Nim},
  author = {Tanya Khovanova and Karan Sarkar},
  journal= {arXiv preprint arXiv:1508.07054},
  year   = {2015}
}

Comments

17 pages

Related papers

View all related →