1.
[
{F:B}{B:8/8/8/8/4kpP1/2K1b3/3P2r1/7B BLACK}
{V:This is one of my own compositions. Several grandmasters have been completely stumped by it, but GM Kindermann solved it in ten minutes, and anyone who beats his time (without looking at the hint!) should consider themselves expert solvers. Black to move. Helpmate in 4.;e4e5;Correct;Incorrect.;It may help if I reveal that I have a fondness for geometrical themes. It is also worth noting that White could mate by d4 and Bxg2, except for the annoying pawn which can interpose on f3. If only the bishop could get round to the other side of the king, then Black wouldn't have this defense.}]

2.
[
{F:B}{B:8/8/8/8/4kpP1/2K1b3/3P2r1/7B} 
This is a really tough problem, firstly because the mating position is not at all obvious, and secondly because there are a lot of near-misses, i.e. mating positions which could, theoretically, be reached in four moves, but fail for reasons of move-order. One example is 1...Bd4+ 2 Kc2 Kd3?? 3 Kd1 Re2 4 Bc6 Re4 5 Bb5 mate, although this takes four moves, there is no move-order without an illegal move in the middle.]

3.
[
{F:B}{B:8/8/8/8/4kpP1/2K1b3/3P2r1/7B}
Curiously, the actual mating position is perhaps the most obvious one - White plays d4 and mates with his bishop on the long diagonal. In order to avoid the defense ...f3, the bishop must deliver mate from the other side of the black king. At first sight this is impossible, because a maneuver such as Bg2-f1-a6-b7 takes four moves, leaving no time for d4. But this is where the geometry comes in ...]

4.
[
{S:e4e5}
1... Ke5
Black is going to need his rook, so the first move is to unpin it.]

5.
[
{S:d2d3}
2 d3
This point of this is to clear the second rank for the rook.]

6.
[
{S:g2b2}
2...Rb2
Black frees the bishop ...]

7.
[
{S:h1a8}
3 Ba8]

8.
[
{S:b2b7}
3...Rb7
... only to rebury it in the opposite corner. The idea is to block White's control of the long diagonal long enough to let the black king reoccupy
e4.]

9.
[
{S:d3d4}
4 d4+]

10.
[
{S:e5e4}
4...Ke4]

11.
[
{S:a8b7}
5 Bxb7 mate.]
