A restriction of Euclid

Authors

  • Grant Cairns La Trobe University
  • Nhan Bao Ho La Trobe University

Keywords:

combinatorial game theory, Sprague-Grundy function, Euclid

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. 10.1017/S0004972712000391

Author Biographies

Grant Cairns, La Trobe University

Department of Mathematics and Statistics Associate Professor

Nhan Bao Ho, La Trobe University

Department of Mathematics and Statistics Phd student

Published

2012-10-22

Issue

Vol. 86 No. 3 (2012)

Section

Articles
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