Some Remarks on End-Nim. (29th December 2011)

• Record Type: Journal Article
• Authors: Cairns, Grant; Ho, Nhan Bao
• Other Names: Hattingh Johannes Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2011(2011)
• Publication Date: 2011-12-29
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2011/824742
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : 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.