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Without answering the question directly, the key to the B+N vs K ending is to know several key methods and positions. Right here, White obtains the position that Pandolfini memorably calls “the lock”: Bc4! Kb7 Nd5! Ka7 (or wherever) Bb5!. Now the Black King is locked in. The next step is for the Bishop to take over the a6-c8 diagonal, with help from the White King (which hones in via c7, either directly or after wasting a move.) Mate is then only several moves away.
Hi,
1. Bc4 Ka7
2. Nd5 Kb7
3. Bb5 Kb8
4. Ba6 Ka7
5. Bc8 Kb8
6. Nb4 Ka7
7. Kc7 Ka8
8. Bb7+ Ka7
9. Nc6#
if 3. … Ka7
4. Kc7 Ka8
5. Ba6 Ka7
6. Bc8 Ka8
7. Nb4 Ka7
8. Nc6+ Ka8
9. Bb7#
So I believe white needs 9 moves and black decides whether bishop or knight mates.
Jakob
1. Bc4 Kb7
2. Nd5 Kb8
3. Ba6 Ka7
4. Bc8 Kb8
5. Nb4 Ka7
6. Kc7 Ka8
7. Bb7+ Ka7
8. Nc6++ mate.
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