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Variations of the Game 3-Euclid
Author
Source
International Journal of Combinatorics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-06
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We present two variations of the game 3-Euclid.
The games involve a triplet of positive integers.
Two players move alternately.
In the first game, each move is to subtract a positive integer multiple of the smallest integer from one of the other integers as long as the result remains positive.
In the second game, each move is to subtract a positive integer multiple of the smallest integer from the largest integer as long as the result remains positive.
The player who makes the last move wins.
We show that the two games have the same P-positions and positions of Sprague-Grundy value 1.
We present three theorems on the periodicity of P-positions and positions of Sprague-Grundy value 1.
We also obtain a theorem on the partition of Sprague-Grundy values for each game.
In addition, we examine the misère versions of the two games and show that the Sprague-Grundy functions of each game and its misère version differ slightly.
American Psychological Association (APA)
Ho, Nhan Bao. 2012. Variations of the Game 3-Euclid. International Journal of Combinatorics،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-469565
Modern Language Association (MLA)
Ho, Nhan Bao. Variations of the Game 3-Euclid. International Journal of Combinatorics No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-469565
American Medical Association (AMA)
Ho, Nhan Bao. Variations of the Game 3-Euclid. International Journal of Combinatorics. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-469565
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-469565