Abstract
Subtraction games are “simple” variants of the famous Nim game (Bouton, 1901). In this note we will show that in some subtraction games the sequences of Win/Loss states have superlinear period lengths. Our most prominent observation is: For all s with 1 ⩽ s ⩽ 26 the ( s, 4 s, 12 s + 1,16 s + 1)-game has the cubic period length 56 s 3 + 52 s 2 + 9 s + 1. Possibly, the ( s, 8 s, 30 s + 1, 37 s + 1, 38 s + 1)-games with s ∈ N have superpolynomial period lengths.
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