(1) Tony Lewis - Chess
White to play and mate in 2, 1952

All Black's available moves are already provided with a white mate, for example if the b5-knight moves, then Nd4#, or if the d6-knight moves, then Qe4#. Thus if White had a pure waiting move, then the problem would be solved. However, there is no pure waiting move, for example 1 Bb3 would give Black the extra possibility of 1...a2. The solution is 1.Qd1Black is again in zugzwang, but some of the mates are different. If the d6-knight moves, then instead of Qe4# we have Qxd7#. Likewise, 1...g3 is met by 2 Qh5# (rather than 2 Qxh3#) and 1...Bg2 by 2 Qxg4# (rather than 2 Qh5#). *

(2) M A Karimov - Mladi autori
White to play and mate in 3, 1952

Here is a more complex problem. In a solving event, to get full marks you have to not only give the key move, but also all the variations leading to mate. When there are several variations, it is easy to miss one and thereby drop a point or half-point. 1.Qa3The threat is 2 Qxc5+ Be5 3 Qxe5+. 1...Bd6 [1...Be52.Rg5+Kf63.dxe5#
; 1...Be42.Bg4+Rxg43.hxg4#
; 1...Re42.Rg5+Kf63.R8g6#
; 1...Rxd42.Qe3
threat Qg5# 2...Bf4 (2...Rf43.Qxc5#
) 3.Bg4#
; 1...cxd42.Qxe7
and Black cannot meet the many threats of mate in one] 2.Qc1threat 3 Qg5# 2...Bf4 [2...Rg43.h4
; 2...Rf43.Ng3#
; 2...Rh53.Qxb1#
] 3.Qxb1#My first idea was indeed to play 1 Qa3, but for a long time I couldn't see how to mate after 1...Re4. I then tried some other first moves, and after wasting some time I suddenly realised that this blocked off the bishop on b1 to allow a mate on g6 after 2 Rg5+ Kf6 3 R8g6#. *

(3) Walther Jorgensen - Die Schwalbe
White to play and mate in 4, 1950 [Nunn,John]

In this problem, the key move is far from obvious. Black will play ...hxg1 and will have a choice of four promotion pieces; note especially the choice of a rook, by which Black attempts to stalemate himself. The key idea is to focus on the most awkward promotion and see if that helps to determine the key move. To start with I looked at the rook promotion, but it turned out that there were several ways to cope with this. Then I looked at the knight promotion, and realised that the threats of ...Nxe2 and ...Nxh3, freeing the g1-square, meant that this was the promotion which White must must take most care about. The possibility of 1...hxg1N, 2...N somewhere and 3...Kg1 suggested that the final mate would be by Nf3#, and this led to me to suppose that the key was 1.d5to free d4 for a knight. This key is surprising as if Black promotes to a queen or bishop, then there will be a check after a capture on f2. Then the variations could be worked out one by one, although there were still some tricky moves to find, such as 1...hxg1R 2 Qb1!, lifting the stalemate. 1...hxg1Q [1...hxg1R2.Qb1Kxe23.Nd4+Kd2 (3...Kf14.Qd3#
) 4.Qc2#
; 1...hxg1B2.Nbc3Bgxf2+ (2...Bh23.Nb1or (3.Ne4
) ) 3.Qd4Bxc34.Qxf2#
; 1...hxg1N2.Ned4Nxh3
or any other move 3.Qe2+Kg14.Nf3#
] 2.Nbd4Qh2 [2...Qxf23.e7
] 3.Nb3and 4 Nd2#. The large number of complex variations caused several solvers to drop points on this problem. *

(4) Horst Boettger - Die Welt
White to play and mate in 6, 1994

Although there is only a single line of play, and Black's moves are almost all forced, this problem defeated a number of solvers, including former champion Jonathan Mestel. Black is in stalemate, so White's first move must allow the black king to move. Then, to prevent Black's pieces coming out, White must immediately force the king back to c5. The question is how White can make progress while keeping Black bottled up. I realised that the g5-pawn is the key feature of the problem. Why is it on the board? The answer must be that White starts with 1 Rh8 and 2 Rh4+, the g5-pawn being present to prevent the alternative 1 Rg8 and 2 Rg4+ (problems must have a unique solution). This logic allowed me to ignore possibilities such as 1 Bd5 and 1 Nd6, which don't work and on which I could have wasted a lot of time. 1.Rh8Kd42.Rh4+Kc5With two moves determined, it is now much easier although some imagination is still necessary to see the conclusion. 3.Rh6Kd44.Rd6+Kc5The transfer of the rook from d8 to d6 means that the bishop is no longer required to defend c6, and so White can sacrifice it. 5.Be2!dxe26.d4#
*

(5) Ilja Mikan - Die Schwalbe
White to play and selfmate in 5, 1935

In this problem White must force Black to deliver mate in 5 moves (White starts). Long selfmates can be very difficult to solve but a good start is to spot a possible final mating position. Here Black has only three legal moves, and after 1...Bxb7 I saw the plausible line 2 something exf3 3 Qd3+ Rc3 4 something Rxd3 5 Bd5+ Rxd5#. The obvious problem here is that there are three unknown White moves, which have to be used up somehow. Then the idea occurred to me of moving the b8-rook on the first move. After 1 Rb8-somewhere Bxb7 2 Rb8 exf3 3 waiting move Qd3+ it all works as planned, and the surprising fact that there is only one waiting move, namely 3 Ng7, led me to believe that this idea was correct. It only remained to work out where the b8-rook should move to, and this was determined by the line 1...Bb5 2 b8Q exf3 3 Qxc4+ Kxc4 4 Nd2+ which works after 4...Kc5 5 Qb6+ cxb6#, provided only that the black king cannot move to d3. This shows that 1 Rd8! was the key, and it only remained to tidy up the loose ends to provide the full solution: 1.Rd8exf3 [1...Bb52.b8Qexf3
transposes to the main line; 1...Bxb72.Rb8exf33.Qd3+Rc34.Ng7Rxd35.Bd5+Rxd5#
] 2.b8Q+Bb5 [2...Bb73.Qd3+Rc34.Rc8Rxd35.Bd5+Rxd5#
] 3.Qxc4+Kxc44.Nd2+Kc55.Qb6+cxb6#
*