José Paluzie offered this chess poser in 1910. White is to move and mate in 1:

The key is to notice that the position is illegal: There’s no legal way for the black king to have arrived at a2. Black, desperate to avoid mate, must have put it there when White wasn’t looking.

Where did it come from? It doesn’t matter: White can place the black king on any legal square and mate in 1.

(From Burt Hochberg’s Chess Braintwisters, 1999.)