2023/12/08 DPA: "'One Way Or Another'..."

White wants to play Qg7# but he needs Rook support with Rg4 but the f pawn guards that square.
However, notice that if fxg4, the Bishop attack on h7 is now uncovered. That's probably significant.
White must be careful about giving Black any tempo to defend: ... Qd8 will attack the White Queen and Black would love to be able to play ... f6, allowing the Rook and Queen to control the 7th rank.
This means White can't play 1. Rg4+ fxg4 2. Qg5+ Kh8 3. Qh6, threatening 4. Qxh7#, because of 4. ... f6.
So White needs to keep his Queen on f6 for as long as possible to prevent ... f6.
1. Rg4+ fxg4 2. Rb4, threatening 3. Rxg4#. But Black has 2. ... h5.
Since White's Queen is not yet attacked, it can still maneuver freely: 3. Qg5+ Kh8 4. Qxh5+ Kg7 5. Rxg4+ Kf6 6. Qg5# [Dovetail Checkmate pattern].
Oops: I just spotted 2. Rb4 Bxd3 3. Rxg4+ Bg6.
So White needs to worry about the Bishop. If he captures first, 1. Bxb5, as long as Black recaptures 1. ... axb5, White can proceed. But what if Black plays 1. ... Qxc5? Now the idea doesn't work because the Rook lift to b4 is prevented by the Queen.
Could White rearrange the move order? 1. Rg4+ fxg4 2. Bxb5? No, Black still can play 2. ... Qxc5.
But I just saw something that I missed earlier: 1. Rg4+ fxg4 2. Qg5+ Kh6 3. Qh6 is a dual threat: 4. Qxh7# AND Qxf8#. So 3. ... f6 to allow the Queen to guard h7, fails due to 4. Qxf8#.

If 3. ... Bxe3 4. Qxf8#
If 3. ... R8[any] 4. Qxh7#
So I initially thought 3. Qh6 was too slow but I didn't see the dual checkmate.
This is a weakness of mine: even though I mentally moved the King to h8, my model still had the King on g8 guarding the Rook. I have to practice updating my model for what's possible and what's not.
I characterize this scenario as "The Zombie Dilemma": Black is in a room that has doors at both ends with no locks. Zombies are at both doors and Black can defend either door but not both.
https://www.chess.com/blog/EnPassantFork/2023-09-28-dpa-zombies-at-2-doors-but-you-can-only-defend-1