Solution

The solution is given in Genius in Chess (J. Levitt, 128 pages, Batsford, 1997, £12.99 ISBN 0 7134 8049 1)

1.h6+ Kg8

The alternative leads to immediate mate: 1...Kh7? 2.f6+ Kg8 3.h7 Mate.

2.h7+! Kxh7

Ditto 2...Kg7? 3.f6 Mate.

3.fxe6+ Qd3!

This avoids 3...Kg8 4.exd7 Ra8+ 5.Kb3, when White is winning.

4.Bxd3+ Kg8
5.e7

5.exf7+? Kxf7 6.Bf5 Nf2 is not good enough.

5... Ra8+

The situation is still delicate: 5...Re8? 6.Bb5 or 5...Rc8? 6.Ba6 are both winning for White.

6.Kb1!!

A deep move, leaving the a4-d1 diagonal open for later exploitation as becomes apparent on move ten.

6... Be5

6...Ra1+? 7.Kc2 does not help Black, while 6...Bc3 is just ignored with 7.Be4.

7.Be4 Re8!

7...Rc8? 8.Bb7 Re8 9.c8Q Rxc8 10.Bxc8 wins for White.

8.Bc6 Bxc7
9.Bxe8 Bd6
10.Ba4! Bxe7

10...Nc3+ 11.dxc3 Bxe7 is even easier for White to draw, since the b-pawn is no longer passed.

11.Bxd1 Bxg5
12.Kc2

The position is drawn; the d-pawn gives sufficient counterplay in this final position. Like many chess positions, this one admits no 100% clear-cut demonstration - the best you can do is give some plausible variations and reduce the doubt about your conclusion to an acceptably low level:

12...f5 13.Be2 Kf7 14.d4 Ke6 15.Kc3 f4 16.Kc4 Kf5 17.Kb5 Bd8 18.Kc6 Ke4 19.d5 Ke3 20.Bb5 f3 21.Kd7 Bf6 22.Kc7 Bd4 23.d6.
12...b5 13.Kc3 Be7 14.Bc2 Kg7 15.Kd4 Kf6 16.Kd5 Kg5 17.d4 b4 18.Ke5 Bf8 19.d5 Bg7+ 20.Kd6 f5 21.Kc5 Bc3 22.d6.

These two lines ‘demonstrate’ the draw as best I can.