Given integer $ n $ and $ k $ such that $0< k\leq n $ and $ n $ piles of stones, two player
alternate turns. By one move it is allowed to choose any $ k $ piles and remove exactly one …

We study remoteness function R of impartial games introduced by Smith in 1966. The player
who moves from a position x can win if and only if R (x) is odd. The odd values of R (x) show …

We consider the game of proper Nim, in which two players alternately move by taking stones
from n piles. In one move a player chooses a proper subset (at least one and at most n-1 n …

Abstract The Sprague–Grundy (SG) theory reduces the disjunctive compound of impartial
games to the classical game of NIM. We generalize this concept by introducing hypergraph …

© 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 …

We study the algorithmic complexity of solving subtraction games in a fixed dimension with a
finite difference set. We prove that there exists a game in this class such that solving the …

Simplicial nim games, a class of impartial games, have very interesting mathematical
properties. Winning strategies on a simplicial nim game can be determined by the set of …

We study the algorithmic complexity of solving subtraction games in a fixed dimension with a
finite difference set. We prove that there exists a game in this class such that solving the …

The classical game of Nim can be naturally extended and played on an arbitrary hypergraph
H⊆ 2V\{∅} whose vertices V={1,..., n} correspond to piles of stones. By one move, a player …

Given n piles of tokens and a positive integer k≤ n, we study two impartial combinatorial
games, Nim1 n, k and Nim1 n,= k. In the first (resp. second) game, each move consists of …