Mate in 3: queen to a7 (d4·4)

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Knight mate

The knight lands the killing blow from its unique angle.

In a knight mate the final blow comes from the knight — the only piece whose check can never be blocked. That makes it lethal against a cramped king: only a king move or capturing the knight itself can help. The sign: the squares around the king are occupied or covered, and there is a hop from which the knight checks while staying untouchable. Bring the knight over early — it is slower than the long-range pieces, but its strike cannot be parried.

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.