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arXiv · 1202.4597

A restriction of Euclid

Grant Cairns·Nhan Bao Ho
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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.

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Grant Cairns, Nhan Bao Ho. 2012-02-21. A restriction of Euclid. https://arxiv.org/abs/1202.4597

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