On the first sight it seems impossible for white to stop the black pawn.
But a king can move diagnonally and so the white king is capable
of approaching the black pawn while at the same time help its own
pawn to promote. So the first moves seem clear.
1. Kg7 h4 2. Kf6 Kb6
The white king is already near enough to support the white pawn.
So black cannot just play 2. ... h3 as the game would continue
3. Ke7 h2 4. c7 Kb7 5. Kd7 and both pawns promote at the same time.
3. Ke5
(see next diagram)
a
b
c
d
e
f
g
h
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
a
b
c
d
e
f
g
h
White has reached the ideal position. The white king is threatening
to catch the black pawn. Of course the white king is still
supporting the white pawn.
3. ... Kxc6
3. ... h3 is of no help. 4. Kd6 h2 5. c7 Kb7 6. Kd7 and both queens
appear at the same time.
4. Kf4 h3 5. Kg3 h2 5. Kxh2 ½ - ½
The main lesson to learn is that the king can move diagonally without
loosing speed. It makes no difference if the king approaches the
black pawn via Kh8-h7-h6-h5-h4-h3-h2 or
via Kg7-f6-d5-f4-g3-h2. Both routes need the same number of
moves. Keep this in mind when playing pawn endgames.