How far can Nim in disguise be stretched?

Details How far can Nim in disguise be stretched? How far can Nim in disguise be stretched?

1998-09-16

arxiv.org/abs/math/9809079v1

Mathematics

Combinatorics

To appear in J. Combinatorial Theory (A)

Scientific paper

A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question which moves in the class can be adjoined without changing the winning strategy of nim. The results apply to other combinatorial games with unbounded Sprague-Grundy function values. We formulate two weakened conditions of the notion of nim-sum 0 for proving the results.

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