2024/05/19 DPA: "Take My Rooks, I Insist!"

White to move.
Black's back rank looks adequately protected. And Black has the h7 escape square and it's controlled by the Bishop on c2 [don't forget about that Bishop!].
What could be a possible checkmate? The Knight on f6 and Queen on g8. But that's a far stretch from the initial position.
Trap the Queen? Unlikely, as it can always move to c4, protected by the d pawn.
And White has potential back rank issues also if he moves the Rook.
Are there any useful checks? No.
Captures? No.
OK, so we have to threaten something [or threaten to threaten something].
1. R7e2 pins the Bishop but leaves the Knight en prise.
White can't interfere with the Black Rooks' control of the back rank.
1. Re8+ Rxe8 2. Nf6+ gxf6 3. Qg4+ Bg6
1. Qf6 [threatening 2. Qxf7+] gxf6 2. Nxf6+ Kg7
1. Qf4 Rf8
Note that White is in no immediate danger.
Any BQM [Backward Queen Move]?
1. R7e2 Rxd7 2. Re8+: the Knight sac removed one defender of the back rank.
2. ... Rxe8 3. Rxe8+ [now White faces his own back rank checkmate if he's not careful] Kh7
1. Ne5 Kf8 2. Ng6 fxg6 3. Qxg7#. Of course, Black won't fall for that.
1. Rxf7 [threatening 2. Qxg7#] Kxf7 2. Qf4+ Kg8
1. Qf4 f6 [1. ... Rf8 2. Nxf8] 2. Qg4
What about 1. Qf4 f5 2. Qg3: same idea of hitting g7 but now the Bishop no longer controls g6 and h7.
1. Qf4 Bg6 looks solid for Black. It also removes the Bishop as a pin target.
1. Nf6+ gxf6 2. Qxf6
1. Rxf7 is the only move that opens up the position; other moves allow Black time to organize a defense.
At this point, an hour has passed with no significant progress so I'm going to pull out a physical board and start moving pieces around.
[more going over the same ground]
I see it: 1. Rxf7 [threatening 2. Qxg7#] Kxf7 2. Re7+!! Kxe7 3. Qxg7+ Ke6 [or Ke8] 4. Qf6+ [or Qf8+] Kxd7 5. Qf7#.
[Edit: note that 3. ... Ke8 is followed by 4. Nf6#]
.
The keys:
- Recognizing that no move, including Knight, accomplished anything [boy, I tried]
- Intuiting that 1. Rxf7 was a great starting point as it didn't give any time for Black to defend
- Seeing the 2nd Rook sac, which not only gives away another 5 points but also leaves the back rank open for a Black checkmate
- Calculating that forcing the acceptance of the Knight sac would lead to checkmate as all of the escape squares are blocked by Black's own forces or controlled by that previously insignificant c pawn
