Devise the most difficult mate in 2 chess problem, in which the mating move varies a lot depending on the opponent's previous move. The opponent has many defenses which force different finishing moves. It is a slightly tricky problem to determine the minimal set of mating moves (probably a variation of the set cover problem).
How can it be generalized to mate in 3? Sum of possible 2nd and 3rd white moves? Or total 2-3 combinations?
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