Mate in 3: knight to e7 (g6)

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Corner mate

Driven into the corner, the king runs out of squares.

The corner mate catches a king driven into the corner, where it has only three neighboring squares — all of them taken away or blocked. The corner is the worst home for a king, because the attacker needs to control the fewest squares there. Herd the king toward the corner with checks and never let it slip back toward the center. Cut off the escape routes before the final check, and the mate practically assembles itself.

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.