Lesson
White to move. Main line: 1. a4 Kg7 2. a5 Kf6 3. a6 Ke6 4. a7 Kd7 5. a8=Q
After the pawn’s first two-square move, imagine a square whose corners are a4, a8, e8 and e4. Black’s king is outside that square, so it cannot catch the pawn by moving diagonally toward it on every turn.
The replay confirms the count: Black takes the shortest route through g7, f6, e6 and d7, but White promotes on a8 one tempo before the king can reach the queening corner. No supporting king move is needed.
The rule works for an unobstructed pawn and king. Redraw the square after every pawn move, and remember that a pawn on its starting rank may advance two squares. Checks, captures and blocking pieces can override the shortcut, so use it as a fast first test rather than a substitute for calculation.