2024/04/21 DPA: "A Little Jiu Jitsu Goes A Long Way"
White to move.
Gee, another Queen and Knight combo: what a surprise [not]. 
White is down the exchange.
White's Queen is under attack but defended by the Knight.
This feels like another "order dependent" puzzle where it will be easy to go astry with the right move at the wrong time.
Can White run some sort of interference tactic? Are any Black pieces overloaded?
1. Rc6 just loses to 1. ... bxc6, which keeps the Queen on the back rank, defending the f Rook.
And the Knight can't deliver check [at least, not in one move].
No Knight move looks promising: say, 1. Nc7 Rxf6 2. Qxf6 Qxc7 3. Qf8+ Rg8 4. Qf6+ Qg7.
1. Qxc8 feels bad because it eliminates the tension between the Queens and between the Rooks. Solving these types of positions is often about deciding when to resolve the tension [this idea recurs throughout a game, even in the opening when deciding whether to capture a pawn with your pawn or to leave things "in situ"].
What about 1. Rf7, entering the lion's den?
It's not as bad as it looks since by moving the Rook, the Queen now pins the g Rook so it can't be used for capture.
- If 1. ... Rfxf7 2. Qxc8+, leaving White with Q+N v 2R, a winning scenario.
- If 1. ... Qxc3 2. Rxf8+ Rg8 3. Rxg8+ Kxg8 4. Nxc3, another winning line.
White also threatens 2. Qxg7#.
Black can defend with 1. ... Rfg8 so then White attacks again with 2. Ne7. But now White's Queen is undefended.
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Another idea is 1. Ne7:
- If 1. ... Rxe7 2. Rxf8^++# [discovered and double check and checkmate]
- If 1. ... Qxc3 2. Rxf8+ Rg8 3. Rxg8#
- If 1. ... Qd8 [staying on the back rank], how does White continue? Now that the Queens are no longer attacking each other, Black is free to play ... Rxf6
No, I don't think this will work.
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1. Rf7 Rfg8 2. Rxg7
- A) If 2. ... Qxc3 3. Rxg8+ Kxg8 4. Nxc3
- B) If 2. ... Rxg7 3. Qxc8+
- C) If 2. ... Qc6 [Queen is now defended] 3. Rxg8+ Kxg8 4. Qxc6 bxc6 5. Ne7+, winning the pawn [edit: "slightly" better is 4. Ne7+, a Royal Fork]
- D) If 2. ... Qd8 3. Re7^ [blocking the Black Queen's access to f6] Rg7 4. Qxg7#
No Black Queen move can stop the coming discovered check and guard g7. And once the Rook moves along the 7th rank, now 4. Qxg7# is on the board.
Line C seems to offer the best chance for White to err by playing 3. Rc7^ which allows Black 3. ... Qxc6 4. Nxc6 and White has R+N v R, which offers more counterplay than if the Rooks were traded.
They chose line A.
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The keys were discovering how to exploit Black's weaknesses:
- 1. Rf7 opened up the Queen pin of Black's g Rook, rendering it immobile
- It also attacked Black's f Rook, which also has to defend the Queen [Overloaded Defender]
- 2. Rxg7 won a Rook but also threatened 3. Re7^ and 4. Qxg7# [again, the g Rook is overloaded, defending both the Queen and g7]
- Finally, it was critical to play the 2nd Rook capture and then capture the Queen, not vice versa. The reason is that the Rook capture comes with check, gaining White the tempo to then recover the Queen. If White reflexively recaptures the Queen first, the Rook is lost and now Black is winning.
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Seemingly optimal for Black was 1. ... Rfxf7 2. Qxc8+, as Q+N v 2R, while winning, offers the opponent a lot of counterplay. But the engine disagrees: the puzzle line is actually optimal.
But I was fairly confident this would not be the solution because it would have been significantly easier to solve whereas the line chosen required White to then find 2. Rxg7 AND 3. Rxg8+ before recapturing the Queen.
For those wondering about why sub-optimal moves are often deployed in puzzles [for the opponent; never for the solver], check out the following blogs:
https://www.chess.com/blog/EnPassantFork/no-the-puzzle-is-not-wrong