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
Attacking through a blocker: targets that fall when the screen moves
The attacking x-ray sets your line piece against an enemy piece that hides behind a blocker on the same rank, file, or diagonal. Nothing lands yet. The trick is reading what happens the instant that intervening piece leaves or gets captured, because then the bigger piece behind it sits exposed to your rook, bishop, or queen. In these positions you often force the screen to move first. A check, a threat the blocker must answer, or a clean capture pulls it off the line, and the attack arrives on the piece you were eyeing all along. Plenty of back-rank shots work this way: your rook already eyes the king down the file, the screen on that same line steps aside, and the king has nowhere to run. While you solve, train yourself to look one square past the first piece on every open line. The target behind it is the whole point, and the move that clears the road is the answer.
Defending through an enemy piece: saves that hold the line
The defensive x-ray flips the idea. Now your own line piece guards one of your pieces through an enemy piece that sits between them, so any capture gets answered by a recapture and you come out level instead of down material. These are the saves that feel like cheating until you see the line.
File or rank guard. A rook behind an enemy rook still defends your piece on the far end of the file, because trading on that square leaves your rook ready to take back. Diagonal guard. A bishop or queen does the same job along a diagonal, protecting through the blocker. Back-rank hold. On the first or eighth rank, an x-ray defense can keep a square covered while a threat looms on the same line. I lean on the rating slider here, nudging it up to about 2400 when the defensive ones start clicking; the puzzles are real computer-verified positions pulled from real games, set to keep you near a 75 to 80 percent solve rate, so the defending patterns show up often enough to stick. Three free hints wait if a save hides too well: first the motif, then the piece, then the move.
Telling an x-ray from a skewer while you solve
Many sources blur these two, and that confusion costs you the right read at the board. Keep the line clean. A skewer hits two enemy pieces lined up on one line: you attack the front one, it moves, and you grab the piece behind it. An x-ray does not stack two enemy targets like that. Instead your piece sees or guards through a single intervening piece, friendly or enemy, and the action happens to whatever waits on the far side. The pin is a third thing again, since a pin freezes a piece in place rather than working through it. When a puzzle shows a long-range piece aimed down a busy line, ask one question: is the blocker friendly or enemy, and are there two enemy men you can win in sequence? Answer that and you tag the pattern correctly, which makes the solving move far easier to find on the next position of the same shape.