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Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games
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Game on groups (generalization of spinning switches puzzle)
I looked at a very similar problem in my dissertation, with mostly cosmetic changes and one substantive change (italicized):
Alice picks a subset $S$ of $S \subset \{1, 2, \dots, n\}$, and a sequence …