Lesson
White to move. Main line: 1. Qb8#
Qb8# is a long-range contact mate. From b8 the queen attacks the king on a8 and controls a7 and b7. The black pawn on a7 occupies one of those squares, becoming part of its king’s cage.
The rook on b1 protects the queen up the open b-file, so Kxb8 is illegal. Because the queen is adjacent to the king, the check cannot be blocked; Black has neither a safe king move nor a legal capture.
Before sending a queen next to the king, trace the complete protection line. A distant rook or bishop can make the entry decisive, but a single intervening piece would make the apparent mate an unsound queen sacrifice.