compose an initial chess position and sequence of moves which do not repeat positions (position includes player to move). how long of such a sequence can be constructed? it will be some huge number of moves, but finite because there are only a finite number of chess positions so positions must eventually repeat.
or, avoid repeating any position 3 times.
I think the task is more interesting (and simpler) permitting illegal positions (king left in check, or a player has zero, or more than one, king).
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