2023/09/28 DPA: "The Zombie Dilemma"
A) White would like to play Nxf7# but the Rook on c7 is protecting that square.
B) He could also play something like 1. Rg8+ but that only works if 1. ... Kxg8 2. Qg2+ Kf8 3. Qg7+ Ke8 4. Qg8#. But Black can capture with the Rook. Still, don't discard that idea just yet.
The Queen can't check. White might have time for a setup move since Black poses no immediate threat.
1. Qg2, threatening Qg7# is too slow due to 1. ... Qxf6.
C) What about 1. Qc3, to deflect the Rook away from guarding f7? Obviously, if 1. ... Rxc3 2. Nxf7#. How can Black counter? 1. ... Rac8 [he doesn't have time for 1. ... h5, giving an escape].
But now White can play 2. Nxf7+ Rxf7 3. Qxc8 Rf8 4. Qxf8#.
The Rook has nowhere to go on the 7th rank and no way to protect it with the Queen. White will win a Rook but won't checkmate since Black now has time for 2. ... h5..
White has the choice of 1. Qc3 or Qc2: which is better? Qc2 allows the Queen to still slide over to the g file to form a battery; Qc3 does not. [c1 is bad because it gives Black the option of 1. ... Rxc1+: this move comes with check so White has no time for 2. Nxf7#.]
1. ... Rg8 2. Rxg8 Kxg8 3. Qg2+ [not 3. Qxc7 Qxf6] Kf8 4. Qg7+ Ke8 5. Qg8#.
1. ... Rf8 2. Qxc7 Qxf6; not very convincing. What about 3. Rg8+ Rxg8 4. Nxf7+ Kg7 5. Ne5 discovered + Kh6 6. Ng4+, with a Royal Fork [if 5. ... Kf8 6. Nd7+, another Royal Fork].
Hmm, but Black can play 5. ... Kh8 and what does White do now?
Even worse, Black has 3. ... Kxg8, which ruins White's beautiful Royal Forks.
Go back to 1. ... Rf8 2. Qxc7 Qxf6 3. Nd7 Qe7 4. Qe5 f6 5. Nxf6.
It might be that I'm overthinking and the puzzle will end with 2. Qxc7.
Turns out line C was the puzzle solution.

The first move was the toughest to find: not only did you have to figure out to attack the Rook but you had to know which square to move to [I didn't note that 1. Qa5 is also a possibility but fails for the same reason Qc3 does] but what to do after Black defends.
Black faced the "Zombie Dilemma": he is trapped in a room with doors with no locks at either end and the Zombies are closing in. He can't block both doors simultaneously just like Black can't defend both f7 and the Rook on c8 simultaneously.
But I don't think that was the sturdiest defense.
Here are Stockfish's top lines:

I did anticipate these, which is why I was not completely convinced that 1. Qc2 was the right first move. But I couldn't see anything better.
For all who say that the puzzle is flawed because the opponent didn't play optimally: puzzles do not always show the best opponent moves. It always shows the optimal solver moves. Once you understand that, you'll be able to solve puzzles better.
In this case, the solution was chosen to highlight the concept of switching attack motifs: White begins by threatening the Rook that guards f7 and then switches to a back rank checkmate. Black tried to defend the Rook and prevent checkmate but that was an error, one that we've likely made in the past and will make in the future.
If Black played the optimal 1. ... Qxf6, we wouldn't have gotten this great tactical lesson.
https://www.chess.com/blog/EnPassantFork/no-the-puzzle-is-not-wrong