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A RESTRICTION OF EUCLID

Part of: Game theory

Published online by Cambridge University Press:  12 June 2012

GRANT CAIRNS  and
NHAN BAO HO
GRANT CAIRNS*
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia (email: [email protected])
NHAN BAO HO
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia (email: [email protected], [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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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 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.

Keywords

combinatorial game theorySprague–Grundy functionEuclid

MSC classification

Secondary: 91A46: Combinatorial games
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 506 - 509
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

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