1 ... Rb3 2 Bxb3 Rxb3 3 Qxc4 (or Qd2 or Qe1) then ... Rxg3+
Now a bit tricky If 4 hg3, then ... Qh1# is simple
If 4 Rg2 Rxg2+ and if the white queen went to c4 or e1, black will mate
If the white queen went to d2, then 5 Qxg2 Bxg2 and white can either take the bishop and lose the rook on c1
Or save the rook and play bishop and rook against queen and rook, which should lose, but white gets to keep playing
Did I get it? Or miss it entirely?

Oh wait, after Rg2 to block, the queen on d2 hangs, so ... Qxd2, Rxg3 Qxc1 and so on

I'm really lazy... after see Rb3 exploring Rxg3+ plus Qh1 I missed Bxb3 completely! if there weren't two rooks I would have failed ... Solving too many puzzles encourages us to look for themes\patterns\motifs instead of calculating variations.

...Rb3 wins; there's no defense. I'm not sure what difficulty you see.

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