Abstract
AbstractEuclid 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 entries are equal. We examine a further variation which we called M-Euclid where the game stops when one of the entries 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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
