The Square of the Pawn

A pawn sprints for promotion; the enemy king gives chase. Will it catch up? There's a trick that answers instantly, no counting:

Draw a square from the pawn to its promotion rank, as wide as it is tall (highlighted here for the b5 pawn). If the defending king can step INSIDE that square on its move — it catches the pawn. If not, the pawn queens. That's the whole rule.