In a “mate in 2” puzzle White makes a move, Black replies however they like — and with the second move White mates. The first move of the solution is called the key. Play on the board: the program answers for Black with the most stubborn defence and accepts any move that still forces mate. Every puzzle has been verified by a computer: mate is unavoidable whatever the defence, and the key is unique (except in puzzle 2).
1. Queen sacrifice
White to move. Mate in 2
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1. Qg8+ Rxg8 2. Nf7# — the king cannot take the queen — the knight guards g8. The rook takes the queen and locks in its own king: smothered mate.
2. The ladder
White to move. Mate in 2
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1. Ra7 Kf8 2. Rb8# — one rook cuts off the seventh rank, the other mates on the eighth. 1. Rb7 works just as well.
3. Damiano's mate
White to move. Mate in 2
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1. Qh7+ Kf8 2. Qxf7# — the pawn on g6 protects the queen on h7 and on f7. The king goes to f8 and is mated.
4. Boden's mate
White to move. Mate in 2
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1. Qxc6+ bxc6 2. Ba6# — the queen is sacrificed to remove the b7 pawn. Two bishops on criss-crossing diagonals deliver mate: the bishop on a6 gives check, the bishop on f4 covers c7 and b8.
Want something harder? “Mate in 3”.