Queen vs Rook and Rook Pawn: The One-Square Win

Apply the chapter's criterion: how many squares does the defender's pawn protect for his rook?

One square. The h7 pawn protects only g6. A rook pawn simply has no second diagonal, so the defence never has a spare safe move. That is the whole reason Black is lost here, while the same setup with a d-pawn (c6 and e6 both protected) is a draw.

How the win goes. Restrict, do not check at random. Zugzwang forces the rook away from its king, and once it is loose a queen fork or skewer wins it: in the main line White finishes Qc7+ Kg8 Qb8+ Kg7 Qb7+, checking the king on g7 along the seventh rank while the b7-g2 diagonal picks up the loose rook on g2.

Do not lose the seventh. One warning while you squeeze: do not let the rook pawn slip forward to the sixth rank by mistake. If the defender ever gets to push it a rank with tempo, you can drop straight into the drawn version of this same fight. Keep your king coming and your queen cutting, and the zugzwang stays yours.

In this drill the conversion is long. Tighten the box one square at a time and watch for stalemate near the corner.