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Some Remarks on End-Nim
Joint Authors
Source
International Journal of Combinatorics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-12-29
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We reexamine Albert and Nowakowski's variation on the game of Nim, called End-Nim, in which the players may only remove coins from the leftmost or rightmost piles.
We reformulate Albert and Nowakowski's solution to this game.
We examine its misère version and a further variant where the winner is the player who reduces the game to a single pile; we call this Loop-End-Nim.
We show that the three games, End-Nim, misère-End-Nim, and Loop-End-Nim, all have the same losing positions, except for the positions where all the piles are of equal size.
We also give some partial results concerning the higher Sprague-Grundy values of the three games.
American Psychological Association (APA)
Cairns, Grant& Ho, Nhan Bao. 2011. Some Remarks on End-Nim. International Journal of Combinatorics،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-501088
Modern Language Association (MLA)
Cairns, Grant& Ho, Nhan Bao. Some Remarks on End-Nim. International Journal of Combinatorics No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-501088
American Medical Association (AMA)
Cairns, Grant& Ho, Nhan Bao. Some Remarks on End-Nim. International Journal of Combinatorics. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-501088
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-501088