C.S. Kipping published this unusual problem in Chess Amateur in 1923. In each position, White is to mate in two moves.
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(a) White castles, threatening 2. Nc7#. Black can capture the knight, but then 2. Rb8 is mate.
(b) After 1. Rxe3, Black can’t escape 2. Re8#.
The point is that in (a) both sides can castle legally, and in (b) they can’t. (In chess problems castling is deemed legal if king and rook stand on their original squares and it can’t be proven that either must have moved in a hypothetical game.) In (a) White needs to castle because the mere 1. Rf1 allows 1. … d2+, and 1. Rxd3 also won’t work because then it’s Black who can castle to safety. In the reflected position both sides lose the castling expedient, so a new solution becomes possible.
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