Black&white Nim games
نویسنده
چکیده
We present a new family of Nim games where the rules depend on a given ‘coloring’ of the tokens, each token being either black or white. The rules are as in Nim with the restriction that a white token on top of each heap is not allowed. We resolve the winning strategies of two disjoint game families played on two heaps. The heap-sizes with black tokens correspond to the numbers ⌊βn⌋, where β > 2 is an integer for one of the families and irrational for the other, and where n ranges over the positive integers. In the process, new notions of invariant games are introduced.
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