A helpmate in 15 moves

Question

I recently came across this ChessBase India article on "engine defying problems." Here's a problem from the helpmate section. We need to reach the helpmate in 15 moves. I thought for a long time but couldn't come up with anything useful. Any idea on how to solve this?

[Title "Leonid Lyubashevsky & Sergei Tkachenko, Shahmatnaya Kompozicija 2nd HM, 2004, Helpmate In 15"]
[FEN "8/4p3/4P1p1/2p2pP1/1pP1pP1k/1Pp1Kp2/2P2P2/NB6 w - - 0 1"]

Answer 1

First Thoughts

1. White only has one move - moving the bishop between b1 and a2. Whatever black does he better not take the bishop else stalemate.
2. Black is going to have to start by taking the knight on a1 followed by the pawn on c2 to let the light squared bishop out. Then the bishop could take the e4, f5 and g6 pawns, queen the g5 pawn and mate. Let's see how that would work:

First Attempt

[Title "Helpmate in a lot more than 15"]
[Startflipped "0"]
[FEN "8/4p3/4P1p1/2p2pP1/1pP1pP1k/1Pp1Kp2/2P2P2/NB6 b - - 0 1"]

1... Kh3 2. Ba2 Kg2 3. Bb1 Kf1 4. Ba2 Ke1 5. Bb1 Kd1 6. Ba2 Kc1 7. Bb1 Kb2 8. Ba2 Kxa1 9. Bb1 Kb2 10. Ba2 Kxc2 11. Bb1 Kxb3 12. Bxe4 Kxc4 13. Bxf5 Kd5 14. Bxg6 Ke6 15. Bf5 Kf7 16. g6+ Kf8 17. g7+ Ke8 18. g8=Q#

Now, that is the fastest that white can queen and white queens with mate and it's still not quick enough. That means that somehow white has to mate with just the bishop, king and pawns. That means finding a square on the board for the black king to get to where white can move the bishop to give check and mate, so it must be a white square. Maybe f5 with the g6 pawn still on the board to take away a flight square.

Let's try that.

Second Attempt

[Title "Helpmate in 15 or 16"]
[Startflipped "0"]
[FEN "8/4p3/4P1p1/2p2pP1/1pP1pP1k/1Pp1Kp2/2P2P2/NB6 b - - 0 1"]

1... Kh3 2. Ba2 Kg2 3. Bb1 Kf1 4. Ba2 Ke1 5. Bb1 Kd1 6. Ba2 Kc1 7. Bb1 Kb2 8. Ba2 Kxa1 9. Bb1 Kb2 10. Ba2 Kxc2 11. Bb1 Kxb3 12. Bxe4 Kxc4 13. Bxf5 Kd5 14. Bd3 {Have to let the king take e6 as that's the only way to get to f5} Kxe6 15. Bf1 Kf5 16. Bh3#

That's mate in 30 ply, 15 black moves and 15 white moves.