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Instead of 8.Nc7+ is 8.Bf1+ equally valid?
That was my first thought, but after b5 white takes a bit longer to finish the job. I think you have to play Nc7+ anyway, then Ka5 and now after Bc3, there is b4 before Bxb4# (mate in 11).
I thought the key move after spotting that Nb5+ was possible, was the discovered check 4. Ne8+ blocking the back rank cover provided by the rook on f8. After that it was just a case of finding the fast way to finish off the king hunt.
If 8. Bf1+? then 8...Rxf1+, although white is still winning easily because of the threat of Nc7+. For example after 9. Kb2 Rb1+ 10. Kxb1 Rxe8 11. Rxe8, the outcome is clear, but checkmate is delayed. If instead 9...Rf3 10. Nc7+ Ka5, white doesn't have 11. Bc3# because of 11...Rxc3, but white does have of course, 11. Rxh8, easily winning.
Oops, yes quite right I had forgotten all about rooks !!
A reminder to us all to check our analysis before committing oneself...
good but what about 6.Bxc8? threatening 7.Ba6# and 7.Bd7 and 8.Bxc6 checkmate.
6. Bxc8 allows 6...Rxe8. Any discovered checks by white allow 7...Rxd8 except for 7. Bb7+. In that case 7...Kxb7, and black appears to be winning being up a rook for a bishop with no forcing checkmate for white. If instead of 7. Bb7+ the white rook moves off of the eighth rank then 7...Rxc8 or perhaps 7...Rxe5. If 7. Rxe8 Rxe8, black's rook forks the white bishops at c8 and e5. In all of these variations black comes out ahead a rook for a bishop with no forcing checkmate for white.
6....Rxe8 7.Bd7 Rxd8 8.Bxc6#
Very nice, a quicker, yet tricky, missed two bishop checkmate for white by me. Since 6...Re8 could get black checkmated in eight moves then black could try 6...Rf1+ 7. Kb2 Rb1+ 8. Kxb1 Rxe8 9. Bd7+ Rxd8 10. Bxc6# making it longer than the puzzle checkmate in nine. Also, black can play 9...Kb7 delaying checkmate even longer as well as play 7...Kb7, in your line, delaying checkmate. Once again though, very nice checkmate! Thank you again.
Happy with this. Saw what was needed very quickly (unusually for me) in blocking black's rooks in order to bring white rook up to d8. The best way to do that is with the knight via a discovered check & then drive the king into the corner at a8. Wanted to move 1.Nb5 but couldn't see why black wouldn't take at b5 then saw the two-bishop mate. In some of these puzzles the moves seem to suggest themselves & I found it more or less plain-sailing until move 6 then undecided about taking bishop on c8 with rook or bishop ? But then you see the bishop capture doesn't work (gives black the chance to move the pawn at a7) so the rest of the moves fell into place. A good exercise in applied logic & wonderful for the morale
Fun mate indeed!