A restriction of Euclid
Combinatorics
2012-02-22 v1
Abstract
Euclid is a well known two-player impartial combinatorial game. A position in Euclid is a pair of positive integers and the players move alternately by subtracting a positive integer multiple of one of the integers from the other integer without making the result negative. The player who makes the last move wins. There is a variation of Euclid due to Grossman in which the game stops when the two entrees are equal. We examine a further variation that we called M-Euclid in which the game stops when one of the entrees is a positive integer multiple of the other. We solve the Sprague-Grundy function for M-Euclid and compare the Sprague-Grundy functions of the three games.
Cite
@article{arxiv.1202.4597,
title = {A restriction of Euclid},
author = {Grant Cairns and Nhan Bao Ho},
journal= {arXiv preprint arXiv:1202.4597},
year = {2012}
}