What mate in 1 chess position can be reached in the fewest number of moves? Half move before Fool's Mate.
What mate in 2? Etc. In other words, of all mate in 2 positions, which has the shortest proof game? Note that the opening position is not a mate in 2 (despite Fool's Mate): this is not a helpmate construction task.
What if chess960 opening positions were permitted? What's the largest N for which the shortest proof game is known?
Solving mate-in-N is an interesting programming problem, with many opportunities for optimization.
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