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Solution:
1. g5!!! The reason of this move becomes clear in a few moves.
1. ......., hxg5 (only move)
2. Ke7! d2 3. f7 d1=Q 4. f8=Q+ Kh7 5. Qf5+!! Kh6
(Other moves lead to mate very soon:
5. ......., Kg7? 6. Qf6+ Kg8 7. Qf7+ Kh8 8. Kf8!! and mate)
6. Kf7!! Qh5+ 7. Kf6!
--See diagram below.
to here.
Black must guard both g5 and g6 with his queen, and only has pawnmoves.
7. ......., g4? 8. Qf4+ Kh7 9. Qc7+ and mate.
So the only move left for black is:
7. ......., d4 8. Qe4!! Black still can only move his d-pawn!
8. ......., d3 9. Qxd3 Qe8 (only move)
10. Qh3+ Qh5 11. Qf5!!
See next diagram.
The same situation as in the last diagram, but no d-pawn move for Black!
11. ........., g4 12. Qf4+ Kh7 13. Qc7+ Qf7+ 14. Qxf7+ Kh6 15. Qg6#
A real great problem , I think!