Winning strategies for aperiodic subtraction games
Combinatorics
2011-08-10 v2
Abstract
We provide a winning strategy for sums of games of MARK-t, an impartial game played on the nonnegative integers where each move consists of subtraction by an integer between 1 and t-1 inclusive, or division by t, rounding down when necessary. Our algorithm computes the Sprague-Grundy values for arbitrary n in quadratic time. This solves a problem posed by Aviezri Fraenkel. In addition, we characterize the P-positions and N-positions for the game in mis\`ere play.
Keywords
Cite
@article{arxiv.1108.1239,
title = {Winning strategies for aperiodic subtraction games},
author = {Alan Guo},
journal= {arXiv preprint arXiv:1108.1239},
year = {2011}
}
Comments
6 pages, no figuress, added references, fixed typos, made proofs more efficient