Three-pile Sharing Nim and the quadratic time winning strategy

We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing then, topping up on a smaller pile provided that the destination pile does not have more tokens then the source pile after the move. We discover a situation in which each column of two-d...

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Bibliographic Details
Published in:arXiv.org 2016-05
Main Author: Nhan Bao Ho
Format: Article
Language:English
Subjects:
Periodic variations
Online Access:Get full text
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Summary:We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing then, topping up on a smaller pile provided that the destination pile does not have more tokens then the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague-Grundy values is a palindrome. We establish a formula for P-positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague-Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded.
ISSN:2331-8422