A RESTRICTION OF EUCLID
2012 ◽
Vol 86
(3)
◽
pp. 506-509
◽
Keyword(s):
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.
2012 ◽
Vol 2012
◽
pp. 1-11
◽
1960 ◽
Vol 12
◽
pp. 374-389
◽
1991 ◽
Vol 14
(3)
◽
pp. 457-462
◽
Keyword(s):
1961 ◽
Vol 5
(1)
◽
pp. 35-40
◽
2018 ◽
Vol 11
(04)
◽
pp. 1850056
◽
Keyword(s):
2021 ◽
Vol 14
(2)
◽
pp. 380-395
Keyword(s):