After
- Kg3 Qg1+
- Kh3 Qxh2+
- Qxh2 Qxh4 is not possible. In case you mean Qxa4, then
- Qg2 Rd8 -> What now?
Interesting is also:
- Kg3 Qg1+
- Kh3 Qxh2+
- Qxh2 Qa3 -> What now?
After
- Kg3 h6
- Qxa8+ Kh7
- g6+ Qxg6+
- Nxg6 Qg1+ -> What now?
The last sequence (1. Kg3 h5) is accepted, but please check your notation again (4. Kg3 is not possible).
By the way, just as a hint: chess software is not allowed to solve my problems (apart from some exceptions where I explicitly inform the competitors). I am sure you are aware of that, are you? :-)
I mention that because your variations are very accurate without any small typical human errors ... I didn't say you are using chess software - just wanted to state the rules again, just in case ... :)
Edit: Sleeping time for me: I will check all remaining answers tomorrow. Good night for now. :)
4.. Qg2 Rd8 -> What now?
5.. Rxd4!! This move took me a long time to see it
If Rxd4, Qa8#
If Qxd4, a8=Q winning the game.
3.. Qxh2 Qa3 -> What now?
4.. Qg2 (attacking the Rook again) Rd8
5.. a8=Q Qd6
6.. Bb2+ Kh8
7.. Nf7+ Kg7
8.. Nxd6+ Kh8
9.. Qd8#
4.. Nxg6 Qg1+ -> What now?
5.. Qg2 Qe1+
6.. Kh3 Bxa7
7.. Rf8!!
I'm very sorry if I made you doubt. Chess is my favorite sport and I always try to do my best.
Don't worry! I had to ask that. It seems you are very talented & engaged solving my chess problems. :)
I will put an official solution now with a few selected variations.
I hope you had solving this chess riddle which cost me quite some time to compose. :)
tnx for resteem