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
Reading the Pillsbury's mate chess puzzles board: rook on the g-file, bishop on the long diagonal
Start by checking the g-file. If it is open and your rook can drop onto g1 or g8 with check, half the pattern is already on the board. The enemy king usually sits on g8 (or g1 in the mirror), boxed in by its own f- and h-pawns.
In the diagram below, the rook is already on g1 and the black king is on h8. White plays Bg7+ Kg8 Bgxf6#: the bishop from g7 captures the knight on f6 and uncovers the rook’s check along the g-file. The bishop on f6 controls h8, so the king cannot return to the corner. The rook gives the mating check even though the bishop makes the last move.
Ask which rook line can check the king and which escape squares the bishop controls. Then calculate every legal capture, block and king move before calling the position mate.

Setting up the trap before you solve Pillsbury's mate chess puzzles
The mate rarely appears fully formed. Two things have to happen first: the g-file must come open, and the king's pawn shield has to crack. A captured g-pawn, a luring sacrifice, or a trade that peels back the defense all do the job.
This is where a queen sacrifice often shows up. Give up the queen to rip open the g-file, or to drag a piece off the long diagonal. The rook supplies the checking line while the bishop controls escape squares; a bishop move can uncover the rook’s final check. The first time I solved one of these from a real game, I sat on the queen offer for a while. It took me a moment to trust that a rook and a lone bishop would close the net. The trainer pulls computer-verified positions from real games, and you can slide the rating from roughly 400 to 2400 to keep your solve rate steady. Three hints wait if you stall: the first names the motif, the second points to the piece, the third gives the move.
Pillsbury versus Morphy: check the piece roles
When comparing mating patterns, separate the last move from the checking piece. In the pictured Pillsbury pattern the bishop moves last, but the rook gives check while the bishop controls the corner. Do not label it a bishop-delivered mate merely because the notation begins with B.
Read the actual confinement before choosing a pattern name: identify the checking line, every controlled flight square and every possible defensive reply. For this Pillsbury position, follow the rook on g1 and the bishop’s control of h8 rather than memorizing a claim that the bishop must deliver the final check.
The family is wider than two members. The opera mate is a near relative, a rook mate supported by a bishop on the long diagonal, and Anderssen's mate sits nearby too. A bishop landing on h6 before the strike is a telltale Pillsbury detail. Sort the cage from the killing piece and these positions stop blurring together.