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Interesting Puzzle (and analysis)

Link to puzzle below (have a go at it first, and then read the analysis below)
en.lichess.org/training/49941

Note: Black is down approximately a rook and gaining a queen for a rook is not sufficient for the puzzle

At first sight it seems that Re1+ is the correct answer (obvious continuation is Qf1 Bd4+ Be3 Bxe3 but now the rook is a defender of the queen. Thinking that Kh1 Nf2+ does not achieve much after Kg2 Nh3+ with no way to remove the rook defending the queen, I discarded the Re1+ variation.

So I went on and played Rd1+ as the first move, thinking that after Nxd1 I could play Re1+ and have the same continuation, except this time, the Rook cannot protect the queen due to the knight in it's way (even after the bishop is sacrificed)

However, this neat sacrifice is a trap and fails, can you spot why?. Also, can you spot the winning variation I missed starting with Re1+ ? Try solving it yourself and then see below for the solution.

**Solution below**

*Solution to why Rd1+ does not work:
After white blocks with bishop on e3 and black captures on e3 white can recapture on e3 with the knight, and the sacrifice on d1 has failed as now both the bishop and knight are not obstructing the view of the rook.
As for the solution to the puzzle, well, Re1+ actually does work. Checkmate follows after
1... Re1+ 2. Qf1 Bf4+ 3. Be3 Bxe3+ 4. Kh1 Nf2+ 5. Kg1 and Black plays Nd1+!! obstructing the rook and checkmate follows after capture of queen.
Great puzzle, i gave up after 20 minutes thinking and tried to take the queen with the rook. How much time did you spend in this puzzle?
I figured out the variations detailed above (excluding the solutions) in around 7 minutes (however I failed the puzzle as I played Rd1+)
194 secs but should have been less. The puzzle is nice but does not look hard for an average player.

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