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We study a variant of 3-pile Nim in which a move consists of taking tokensfrom one pile and, instead of removing then, topping up on a smaller pileprovided that the destination pile does not have more tokens then the sourcepile after the move. We discover a situation in which each column oftwo-dimensional array of Sprague-Grundy values is a palindrome. We establish aformula for P-positions by which winning moves can be computed in quadratictime. We prove a formula for positions whose Sprague-Grundy values are 1 andestimate the distribution of those positions whose nim-values are g. We discussthe periodicity of nim-sequences that seem to be bounded.

Three-pile Sharing Nim and the quadratic time winning strategy