1.
[
{F:B}{B:8/8/2k5/4b2n/p7/pp6/rp5P/1K1n4 BLACK}
{V:In this problem, White's pawn sets off on mission impossible to single-handedly deliver mate. Black to move. Helpmate in eight.;e5h8;Correct;Incorrect.;White's king is totally imprisoned, so the h-pawn has to do all the work. The pawn can promote in five moves, presumably to a queen (a knight is worth a thought, but there is no mating position which can be reached in time). There is no mating position with a queen against just the king and minor pieces, so somehow the rook must be brought into the game ...}]

2.
[
White's pawn will promote in five moves, leaving just three to arrange the mate. No mate is possible in eight moves if White promotes to a knight, so we can assume that White will promote to a queen. Even so, no mating position is possible using just the black king and minor pieces. A mate is possible on the queenside, by playing Qxa3 and then marching Black's king in to a3, but this takes too long. The conclusion is that White has to bring the rook into the game. Fortunately, this is quite easy, because after promoting on h8 White can play Qxb2.]

3.
[
This is already White's sixth move, however, so White's seventh move will be to move the queen away. Black must then move his rook in such a way as to allow immediate mate. There are only two possibilities, either Black's king is on d1, when ...Rd2 will allow Qf1 mate, or Black's king is on h1, when ...Rh2 will again allow Qf1 mate. The first scheme fails because of the time element, if we add up Black's moves we find that playing the king to d1 takes five, the knight on d1 must move, the knight on h5 must move to allow the pawn to promote and the bishop on e5 must move to allow Qh8xb2, adding up to nine moves.]

4.
[
Thus the mate must be on h1. The last moves will be Qxb2 and Qf6 by White, allowing ...Rh2 and then Qf1 mate. Playing the king to h1 and ...Rh2 is six moves, and as before the h5-knight and bishop must move, so this plan is just possible. Now the problems start to appear. Where can the h5-knight move? Going to f6 or g7 blocks Qh8xb2, ...Ng3 stops the mate and ...Nf4 blocks Qf6-f1. It has been possible to proceed this far by logic alone, but logic can only take you so far, and then inspiration has to take over. It turns out that the only solution is for the h5-knight to be captured by the white pawn, but since the pawn must promote on h8, the bishop has to join the knight in a suicide pact.]

5.
[
{S:e5h8}
1...Bh8!!
The knight has to make way for the pawn, so this move must come right away.]

6.
[
{S:h2h4}
2 h4]

7.
[
{S:h5g7}
2...Ng7
Now everything is ready for h6xg7 and g7xh8.]

8.
[
{S:h4h5}
3 h5]

9.
[
{S:c6d5}
3...Kd5]

10.
[
{S:h5h6}
4 h6]

11.
[
{S:d5e4}
4...Ke4]

12.
[
{S:h6g7}
5 hxg7]

13.
[
{S:e4f3}
5...Kf3]

14.
[
{S:g7h8}{X:h8}{P:WQh8}
6 gxh8Q
Now that the knight and bishop have self-destructed, the decks are clear for the white queen.]

15.
[
{S:f3g2}
6...Kg2]

16.
[
{S:h8b2}
7 Qxb2+]

17.
[
{S:g2h1}
7...Kh1]

18.
[
{S:b2f6}
8 Qf6]

19.
[
{S:a2h2}
8...Rh2]

20.
[
{S:f6f1}
9 Qf1 mate.]
