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1. a3 Qxb3
2. Qc5+ Kg8
3. Qg5+ Kf8
4. Qg7+ Ke8
5. Qg8#
or
1. a3 Qxa3
2. Qb8#
or
1. a3 Qe1
2. Qxe1 Kg8
3. Qe5 g2
4. Qg5+ Kf8
5. Qg7+ Ke8
6. Qg8#
a3
1. Qe3!
A-1….h3. 2. Qh6+. Ke8. (otherwise mate at g7). 3. Qh8+. Qf8. 4. Qxh3 threatening mate at d7/c8.and black has to give up his Q for nothing to stave off mate on the move. Qc5+. 5. Kxc5. Kd8. 6. Kc6 amd mate next move.
B-1….g2. 2. Qh6+. Ke8. 3. Qh8+. Qf8. 4. Qh5!. (prevents Qc5+ and 5….g1=Q+). Qb4. (otherwise Qe5+, and Qb8#). 5. Qe2+. Kf8. 6. Qxg2 ..this is getting nowhere in this variation.
This is not working in some variation. Sat back to think how to dislodge the BQ from the a3-f8 diagonal which is the only saving move for black.?
So a3 wil help right at the start as the BQ is overworked having to cover the diagonal as well as b file.
Hence
1. a3.!
A-1…Qxb3. 2. Qc5+. Kg8. 3. Qg5+. Kf8 (otherwise Qg7#). 4. Qg7+. Ke8. 5. Qg8#
B-1…Qxa3. 2. Qb8#
C-1…Qc3+. 2. Qxc3. g2. 3. Qxa5!. Kg8. 4. Qg5+ etc as in A.
Phew.
I saw this problem last Fall on another site- yes the black queen is in a bad spot, and amazingly has no safe check on the open board white king- a3 dislodges her just enough to doom black.
Yes I assumed that my imagination wasn’t working because I wasn’t being playful enough but that wasn’t it, I was being a bit sulky and trying to shift responsibility away from myself with a kind of “things are really unfair for me so why should I have to bother with this” attitude and that worked out badly for me because I was thinking 1. a3 didn’t work and switched to 1. Qe3 and couldn’t see anything wrong with it because I was being irresponsible about updating moves.
Qe3!! and wins.