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)