Solution - the only one. :)
Here now the only solution, found by @greatwolf:
- Qxg7+! Kxg7
- f6+ Kh7
- b6! cxb6 (3. ... axb6 4. c6! with the same idea like in the main variation.)
- a6! bxa6
- c6 Qg4! (That's the only way to get some counterplay.)
- hxg4 h3
- c7 h2
- c8Q h1Q
- Qf8! (Now it's over because of the threat Qg7#.) Qe1+
- Kd8 Qd2+
- Kc8 Qc3+
- Kb8 ...
And now black has no reasonable check anymore:
12 . ... Qc8+ - Kxc8 a5
- Qg7#
Very nice chess problem which combines several ideas, like restricting the mobility of the opponent's pieces by means of a brilliant queen sacrifice, and a pawn break through with underpromotion into a new queen.