Chess notation cheat-sheet (for new readers)
Pieces: K king · Q queen · R rook · B bishop · N knight · (a pawn move has no letter)
Actions: x takes · + check · # mate · O-O short castles · O-O-O long castles · e8=Q pawn promotes to queen
Annotations: ! good move · !! brilliant · ? mistake · ?? blunder
Spotting the Y-shape before you solve
Find the swallowtail by its outline first. The enemy king sits somewhere in the middle of the board, not pinned to the edge, and two of its own pieces stand just behind it on the diagonal-retreat squares. Those two blockers fan out from the king like a fork, the splayed Y that names the pattern. Each sits a knight's-move away from where your queen wants to land.
Once you see that splayed pair, the solve narrows fast. The king already has two flight squares stuffed by its own men. Your job is to find the touch square right next to the king where the queen covers the rest. Train the eye to read the tail before counting moves, and the target square tends to announce itself. Look for the king boxed in by its own traffic, then ask which adjacent square your queen can reach safely.
Swallowtail mate chess puzzles: why the queen lands orthogonally, never on the diagonal
The whole solve turns on one choice of square. The queen lands orthogonally next to the king, directly above, below, or beside it, never on the diagonal. From that touch square she covers the three flanking squares plus the king's own, while the king's two blockers seal the diagonal-retreat squares behind it. Play the diagonal square instead and you have wandered into the dovetail setup, where the blockers sit elsewhere and the king walks out the orthogonal gap.
So at the board, count the king's open squares before you move. If the blockers are jammed on the diagonals behind the king, the mating square is the orthogonal one. If you see the queen drawn toward a diagonal landing, treat it as a warning that you are solving the wrong shape. Picking the right side of the king is the single decision that turns the position from check into mate.
Confirming the queen survives the quiet move in swallowtail mate chess puzzles
The last move here is usually a quiet step, not a capture, so confirm the queen will survive once she arrives. She has to be defended or otherwise out of reach, or the king just takes her and the attack collapses. In the common shape a rook covers her along the rank while the king's own two rooks jam its retreat. My habit is to lock onto the defender before committing to the touch square, since an undefended queen turns the mate into a blunder.
From there the checklist is short. Confirm the two friendly blockers are fixed behind the king, find the adjacent square that covers the rest, and trace the line that keeps the queen protected. A rook can finish the same job when other attackers cover the extra escape squares. The hints here name the motif first, then the piece, then the move, so you can nudge yourself toward the idea before the answer shows.