2024/03/24 DPA: "The Backwards Pawn Saves The Day"

Black to move.
Piece count is the same but White has 2, connected, passed pawns on the Qside.
White's King is confined to the h file so it looks like we'll be seeking a checkmate.
If Black could play ... Rh8 while his g Rook was protected, it would be checkmate.
The f4 square is guarded by the Bishop.
Black has a Bishop but it looks to be blocked by the e pawn.
One obvious move is 1. ... Rh4+ but that allows 2. Kg3 and then 3. Kf3 and 4. Ke2.
Can Black sac the g Rook? 1. ... Rh8+ 2. Kxg4 Rh4+ 3. Kf3; no.
If Black sacs the Rook on f4 to the Bishop and the Knight recaptures, Black will control g2 and e2 with the Knight while e3 is controlled by the pawn - a partial mating net. But g4 isn't covered.
Trying to reposition the Knight with ... Nc3 then ... Ne2 fails since White controls c3.
1. ... Rh4+ 2. Kg3 Rbh8, intending to push ... g4 is too slow, as it gives White time for 3. Kf3.
How about an Intermezzo? 1. ... Rf4 2. Bxf4 Rh8+ 3. Kg3 Nxf4. Aah, but now that White's Bishop is gone, his Rooks are connected and White can contest the h file.
I'm pretty sure Black would rather have the Knight on f4 than a pawn, which doesn't control the light squares.
There might be a way to free the Bishop with ... f5 exf5 e4. Even better if the White King is on the b8-h2 diagonal so it comes with check.
Hmm, how about 1. ... f5 as a first move? It protects the Rook and threatens 2. ... Rh8#.
2. exf5. Now, it's premature to play 2. ... e4 because there is no gain of tempo with a check. 2. ... Nf6 protects the Rook and again threatens 3. ... Rh8#.
White cannot successfully interpose a defender: 3. Bxg5 [which does NOT come with check thanks to Black's trusty steed] Rh8+ 4. Bh4/h6 Rxh4/h6#.
White has no checks.
Moving either Rook of the Knight doesn't alter Black's control of the g file.
But this seems too simple for a Sunday puzzle so I'm probably missing something.
After 1. ... f5, can White do anything that either prevents ... Rh8 or forces Black to move the g Rook off of the g file? I see nothing save for 2. exf5, which removes the g Rook's defender. Every other move leaves the g Rook defended which means White has no escape along the g file. White must have the threat of Kxg4 so that Black can't play ... Rh8#.
Same goes for after 2. ... Nf6.
The only piece capture is Nxd6 but since it doesn't come with check, Black can ignore it.
White could re-order his defense with 1. ... f5 2. Bxg5+ Rxg5 and 3. ... Rh8# is still inevitable.
White also has 1. ... f5 2. Bxg5+ Rxg5 3. Kh4, attacking the Rook. But 3. ... Rg4+ and the Rook is again defended.
I think the solution will have White playing 2. exf5 because the requires the solver to find 2. ... Nf6; seeing 2. ... Rxg5 is much easier because the Bishop is checking
I was right.
I only realized at the end that Black's Knight was en prise. If I had realized that a priori, it would have made finding 1. ... f5 all that more difficult.
The key was realizing that the g Rook must stay on the g file to make Rh8 a credible mate threat. Since there is no safe square for the g Rook, it must be defended, which ... f5 did and it also freed up f6 for the Knight.

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There may be questions about why White didn't play a different move/idea but the point is that ALL opponent responses lose; it's only a matter of choosing which move the opponent makes and how to counter it.
The puzzle solution 3. f3 was played to attempt to scare Black into moving his g Rook off of the g file and giving White an escape. The puzzle also could have played any of the above ideas I listed.
The people who fixate on exactly which losing line the opponent should have played are missing the bigger picture: that by finding 1. ... exf5 and 2. ... Nf6, the solver has sealed the victory.