for a given small set of chess pieces, write a computer program that will play the endgame perfectly (in game value, not requiring the most efficient way to win) for arbitrary sized boards. (probably start with square and rectangle boards, but much generalization possible.) because board size is arbitrary, tablebase is not a possibility.
proving the correctness of a program across all board sizes will be challenging. perhaps run a contest among programs. allow the defending program many attempts, starting at what it believes are interesting corner cases.
or formal proof.
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