k-Welter - a generalization of Welter's game
type: Item
instance of: scholarly article
title: k-Welter - a generalization of Welter's game
zbMATH Open document ID: 0617.90088
DOI: 10.1016/0097-3165(87)90073-2
author: Joseph Kahane
author: Aviezri S. Fraenkel
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: Finitely many coins are placed on distinct squares of a semi-infinite linear board ruled into squares numbered 0,1,2,.... Each of the two players alternately moves a coin to a lower unoccupied square, at most k squares from its present position, where k is an arbitrary fixed positive integer. The player first unable to move loses and his opponent wins. We give complete solutions for the case of two coins for any k; and for any number of coins when \(k=2^ m-1\) (m\(\geq 1)\). We also prove that, for any k, the Sprague-Grundy function of the game is invariant under translations of coins by \(k+1\).
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 4001895
zbMATH Keywords: Welter's game
zbMATH Keywords: semi-infinite linear board
zbMATH Keywords: Sprague-Grundy function
MaRDI profile type: Publication
full work available at URL: 0097-3165(87)90073-2
OpenAlex ID: W2042041839
cites work: Q3944542
cites work: Q4099541
cites work: Q5825669
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description: scientific article; zbMATH DE number 4001895