4th Prize Europe Echecs 1966-68
13+14. (AP) Mate in 2
Analysis: Black captured with axb, b3xc2, and the wKB at home. White captured the bQ and one bR by f6xe7 and h4xg5. When f6xe7 was played, the bKBP was still on f7.
Any possible last move by Black must have been preceded by a White move played with Ke1 or Rh1, so that White can't castle. There are two exceptions. First 0 ... Na3 -1. a3-a4 is possible, but once the a4 pawn is on a3, the wQR could only leave its SW cage after the wK leave e1: castling is still forbidden.
The other exception is if Black's last move was 0 ... f7-f5. Now White can retract -1. f6xe7 and retains his castling right.
Therefore, we can say that if O-O is possible, then the last move was 0 ... f7-f5 and then 1. g5xf6ep is legal. The A Posteriori rule allows us to pick this as a key move, provided White castles later. This is the solution of the problem.
Now after any Black move, White follows with 2. O-O#. 2. Kf2 (or other "checkmating" moves) would not suffice because White has to provide the a posteriori justification of his 1st move.
Observe that Black has no way here to forbids 2. O-O#. For him, preventing 2. O-O would have been a valid defense against any mate.