Solution 1

Possibility 3: g7-d4

White plays 1.g7-b4 and leaves Black 2 possibilities to recycle pieces: either 1b3 or 1e9-e5. In the first case White wins with 2.b6-e6;xGg4, in the second case with 2.e9-e5;xGg4. There's nothing Black can do about it

Check the initial diagram of Problem 27.
Possibility 1: 1.b6-h3 doesn't work because of 1f8-f6;x.
Possibility 2: 1.e9-e5 wouldn't be a smart thing to do because it offers Black and easy re-fill of his reserve.
Possibility 4: 1.g7-g3 isn't a win for the same reason as Possibility 1 didn't work: 1f8-f6;x.