2024/09/26 DPA: "Of Trapped Kings, Queen Flings, and Knight Springs"

Black to move:

White's King is stuck in the corner.

Black is down the exchange.

The Queens are in a staring contest.

I see a nice LQM [Lateral Queen Move] 1. ... Qa8+ but that can be blocked by 2. d5.  Yes, the Bishop is hanging but that gives White a tempo to play 3. Qe8+ Kh7  4. Qxh5+.

1. ... Nf2+  2. Qxf2 Qe4+  3. Rg2 stops the attack.

But I can use the idea by reversing the move order:   1. ... Qe4+  2. Qxe4 Nf2#.

.

The key was recognizing that ... Nf2 was checkmate so the Queen defender had to be removed but not by capture because that would allow the Rook to recapture and free up the critical g1 square for the King, something I didn't mention explicitly in my thought process but must have intuitively rejected.

Other options like 1. ... Qa8+ and 1. ... Nf2+ fail, which will lead the solver to discard them and look elsewhere.