Mate in 3: queen to e8 (e4·2)

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Boden's mate

Two bishops cross their diagonals over a king blocked by its own pieces.

Boden's mate crosses two bishop diagonals over a king blocked by its own pieces. The classic victim has castled on the queenside: its own rook and pawns have stolen the escape squares, and the bishops slash crosswise. The trigger is usually a queen sacrifice that blasts open the second diagonal. Whenever the enemy king is boxed in by its friends, ask whether both of your bishops can reach it on crossing diagonals.

Mate in 3

A forced checkmate in three moves.

Mate in three is a forced staircase: each of your moves narrows the opponent's choices, and the third one ends the game. Look for the start among checks and sacrifices — quiet first moves are rare in mating problems, but deliciously sneaky. Keep the tree in your head: every defense gets its own branch. Do not stop calculating after move two — see the final mating picture with your own eyes.

Counter-strike

Don't defend — answer the threat with a bigger one.

The counter-strike: instead of defending against the threat, you answer with a bigger threat of your own. While your opponent grabs a pawn, you deliver mate — the arithmetic favors you. Look for a counter when direct defenses fail: do you have a check, an attack on the queen, a mating threat? The beginner's error is meeting every threat with a reflexive defense without checking the counterattacking resources first.