1.
[{B:n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8}
{V:The position is certainly congested, but most of the pieces don't move during the solution, so this problem is easier than it might appear. White to play and mate in six.;h5h1;Correct;Incorrect.;Black can only move his d-pawn, so after ...d4 and ...d3 he will be stalemated. This gives White two free tempi to do with as he pleases, before he has to worry about lifting the stalemate. If the pawn on a5 were missing, then White would be able to wait until Black played 2...d3, and then mate by 3 Bxb4 Kxf6 4 Bc3. At the moment the chain of black pawns on the queenside stops this idea by denying the bishop any squares on the e7-a3 diagonal. How can White use his spare tempi to unblock the queenside logjam?}]

2.
[{B:n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8}
The solution is more or less self-explanatory. Black is stalemated apart from his d-pawn, so White has two free moves before he has to worry about releasing the stalemate. On the other hand, it is hard to envisage a mating position since Black's king is virtually surrounded by his own pieces. The key idea is to leave the rook on f6 undefended at the right moment, forcing ...Kxf6, and then mate with the bishop along the long diagonal. The problem is that in the diagram the bishop has no useful moves because the four enemy pawns on the queenside prevent the bishop moving to d6, c5 or b4.]

3.
[{B:n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8}
{S:h5h1}
1 Rh1!
A mysterious rook move.]

4.
[{S:d5d4}
1...d4]

5.
[{S:h1a1}
2 Ra1!!
The mystery deepens. Why has White sent his rook to the furthest corner of the board when he is trying to mate the black king?]

6.
[{S:d4d3}
2...d3
Black's pawn moves are exhausted and now White must lift the stalemate.]

7.
[{S:a1a3}
3 Ra3!
This is the point of White's rook maneuver. White unblocks the queenside pawn structure and opens the diagonal for his bishop.]

8.
[{S:b4a3}
3...bxa3+]

9.
[{S:b2a1}
4 Ka1
Of course not 4 Ka2? stalemate.]

10.
[{S:a3a2}
4...a2
Everything is in place for the decisive maneuver, which involves the sacrifice of White's other rook.]

11.
[{S:e7a3}
5 Ba3!]

12.
[{S:g7f6}
5...Kxf6
All Black's moves are absolutely forced.]

13.
[{S:a3b2}
6 Bb2 mate]