Black to move!
Happy New Year to everybody!!!
I love this analysis. Thanks, Yancey!! Happy New Year to you!!
The only thing I would add to Dave's analysis is that white can't save himself with 3.Ka1 since 3. .....c5! threatens the exchange of queens at d4 instead and white can't avoid it without getting quickly mated.
1...Qd2, 2. Qg7 Kc1+ (discovered check), 3. Ka3 Kb1! (threatening Qa2#), 4. Qh7+ Qc2, 5. Qh1+ Qc1+, 6. Qxc1+ Kxc1, 7. Ka2 Kc2, 8. Ka3 Kc3, 9. Ka2 c6!, 10. Ka3 c5!, 11. Ka2 Kc2, 12. Ka3 Kb1! (White is in zugzwang), 13. b4 (forced) cxb4+, 14. Kb3 Kc1, 15. Ka2 Kc2, 16. Ka1 b3, 16. c5 (forced) b2+ and Black b-pawn goes queening and mates White.
I don't have the time for a full analysis of this, but the position after 1. ....Qd2 2.Qd2 Kd2 is won for black fairly easily. So white would have to avoid trading the queens with 2.Qg7 or something like this, but white's king is in danger after 2. ...Kc1+ so white won't be able to avoid the exchange for long. I would have to look at the other positions where the queens gone, but the white king is on a3 and the black king is on c1 in one line I can imagine being played- that one also should be won, though I am a bit less certain of this.