k-Welter - a generalization of Welter's game
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 \(k+1\).
scientific article; zbMATH DE number 4001895