English

How far can Nim in disguise be stretched?

Combinatorics 2007-05-23 v1

Abstract

A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question which moves in the class can be adjoined without changing the winning strategy of nim. The results apply to other combinatorial games with unbounded Sprague-Grundy function values. We formulate two weakened conditions of the notion of nim-sum 0 for proving the results.

Keywords

Cite

@article{arxiv.math/9809079,
  title  = {How far can Nim in disguise be stretched?},
  author = {Uri Blass and Aviezri S. Fraenkel and Romina Guelman},
  journal= {arXiv preprint arXiv:math/9809079},
  year   = {2007}
}

Comments

To appear in J. Combinatorial Theory (A)

R2 v1 2026-07-22T17:59:59.158Z