Meisterwerke

a)

Black's last move can't have been c6-c5, because this would imply a retroplay like -1. ... c6-c5 -2. Qc7-b6 b6xNa5 -3. Be4-f3 Kg2-g1 -4. Bd3-e4 Kg1-g2 and now the only way to open the northwest cage is to uncapture a darksquared black bishop on b4, bring it to f8, and retract e7-e6; but then both black rooks would be caught in the cage. Thus the last move was c7-c5 with a retroplay like -1. ... c7-c5 -2. Qc6-b6 b6xNa5 -3. Kd1-e1 Kf1-g1, also showing that white can't castle. The only solution is 1. b5xc6 ep#

b)

Now the last move could be c6-c5, with retroplay like -1. .. c6-c5 -2. Qc7-b6 b6xNa5 -3. Be4-f3 Kg2-g1 -4. Bd3-e4 Kg1-g2 and the cage is opened by retracting the white rook to h8, the white queen to d8, and the black pawn on c6 to c7, and then uncapturing c6xb7. So white may not capture en-passant. But this retroplay also shows it's possible to preserve white's queenside castling rights. So #1 with 1. OOO#

Solution by H. Juel