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Slow k-nim

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posted on 2021-01-21, 04:17 authored by V Gurvich, S Heubach, Nhan HoNhan Ho, N Chikin
© 2020, Colgate University. All rights reserved. Given n piles of tokens and a positive integer k ≤ n, we study two impartial combinatorial games, Nim1n,≤kand Nim1n,=k. In the first (resp. second) game, each move consists of choosing at least 1 and at most k (resp. exactly k) non-empty piles and removing one token from each of them. We study the normal and misére versions of both games. For Nim1n,=k we give explicit formulas of its Sprague-Grundy function for the cases 2 = k ≤ n ≤ 4; for Nim1n,≤k we provide such formulas for 2 = k ≤ n ≤ 3 and characterize the P-positions for the cases n ≤ k + 2 and n = k + 3 ≤ 6.

History

Publication Date

2020-04-13

Journal

Integers

Volume

20

Article Number

G3

Pagination

19p.

Publisher

Integers

ISSN

1553-1732

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