1.
[
{F:B}{B:8/8/8/8/1k6/8/7q/R2NK3 BLACK}
{V:Remember that Black moves first in a helpmate, so here both sides play three moves, cooperating so as to help White mate Black. Black to move, helpmate in three.;h2b8;Correct;Incorrect.;The position of the king on e1 and the rook on a1 is bit of a give away, in a problem this almost always means that castling is involved  in the solution (although a few composers are fond of red herrings...). In helpmates, finding the mating position is 90% of the battle, so here you need to look for a mating position with White's king on c1.}]

2.
[
{F:B}{B:8/8/8/8/1k6/8/7q/R2NK3}
The position of the rook and king strongly suggests that White's first two moves will be a knight move followed by 0-0-0. Since it is not possible to mate with the rook on d1, the third and final move will be with the rook. It follows that White arrives at the mating position by Nb2, 0-0-0 and Rd3, with Black's queen on b4. One Black move is consumed by ...Kc3, which leaves two moves for Black's queen to reach b4. At first it seems that there are several possible routes for the queen, for example via b2, f4, h4, d6 or b8, but it turns out that only one of these works. Black cannot play 1...Qb2 because White's knight needs to move to b2, 1...Qh4+ delivers check and so prevents castling, while 1...Qd6 (1...Qf4 is the same) 2 Nb2 Kc3 3 0-0-0?? is illegal. So the only way is ...]

3.
[
{S:h2b8}
1 ...Qb8!]

4.
[
{S:d1b2}
2 Nb2]

5.
[
{S:b4c3}
2...Kc3]

6.
[
{S:a1d1}{S:e1c1}
3 0-0-0]

7.
[
{S:b8b4}
3...Qb4]

8.
[
{S:d1d3}
4.Rd3 mate.
When showing someone this problem, a good trick is to say '... and this is White's side of the board, but of course it doesn't matter since there aren't any pawns'.]
