White to move and win

???? black can still move a7

In the final position(after 3.Be4), move the a-pawn loses due to 4.Nxb6+ Ka7 5.Bxb7 followed by 6.Nc8#. But what if 3...Bc6 instead?

3..Bc6 loses to 4.Kxc6! (Lol). White will just continue with a shortened form of the B+N mate, with the king already cornered on the right colour corner. I stopped the puzzle here because of that reply.

I've saw 4.Kxc6 too, but i thought that it would take more longer to checkmate with K+B+N vs K(luckily the black's K is in the correct corner to give mate). But then 4...Kb8 5.Ne7(covering c8) a6 6.Bf3 a5 7.Be4 axb4 8.Bf3 Ka8 9.Kc7#. Correct me if i missed something.

The king can still go to a7, no?

Following that line,

5..a6 is answered with 6. Kxb6 7. Bb7 etc...

5..a5 is answered with 6.Bf5, followed by setting a mating net with either the king on b6 and bishop on a6, or the king on c7 and the bishop on c8, depending on black's reply.

Smart one zugzwang

easy

I did not realize that b6 was a check... I wanted to mate and the knight refused to move :). Fortunately this does not mean I would have failed the problem had it been in the tactics trainer since with pieces that were willing to move I made the right moves...