2015/06/23 by Ho, Nhan Bao
#91A46 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1506.06961
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.