Helpmates

The directmate problems we have examined in the previous articles represent the most traditional form of chess composition. They are akin to an actual chess game in that the aim is to force mate and the two sides act in opposition. Among the less conventional problem types, the most significant and popular is the helpmate. In this genre, the two sides cooperate to enable White to mate Black, achieving this in the specified number of moves. All the normal rules of chess still apply here (e.g. checks cannot be ignored) – only the players’ motives have changed from the usual competitive mode.

Black generally plays first in a helpmate. The solution of a two-move problem, for example, comprises four single moves that run: 1.Black begins, White moves, 2.Black moves, White mates. This also illustrates how the method of writing helpmate solutions differs from normal practice, in that a black move appears first after the move number. Another characteristic of helpmates is that each solution consists of a precise sequence of moves, so that the play lacks variations in the manner of directmates. Variety is achieved, instead, through the use of multiple phases of play, such as stipulating more than one solution.

Let us look at our first example, 25, a helpmate in two moves. The black king initially has two flights on b5 and b6, and the eventual rook or bishop mate in each solution is likely to cover one of these squares. Black has to take care of the remaining flight by blocking it, with a piece that does not interfere with the mate. This is possible only by means of a self-pin. 1.Rxe6 Rg6 (White shuts off the black bishop) 2.Rb6 d4. The second solution is perfectly analogous to the first: 1.Bxd3 Be2 (cutting off the black rook) 2.Bb5 e7. The two parts show an orthogonal-diagonal transformation. That is, the strategic effects that take place on orthogonal lines in one phase are seen again in another, but they are changed to occur on diagonal ones, and vice versa.

Problem 26 stipulates for a set play to be found, in addition to the actual play. Set play in helpmates refers to a move sequence that solves the problem, but which is commenced by the player who normally moves second. So in a two-move helpmate, this extra sequence goes like this: 1…White begins, 2.Black moves, White mates. The set line is always shorter than the actual play, typically by a single move. In the diagram position, the black king has a lot of freedom, which suggests that the piece may step into a more confined area during the course of play. White facilitates this plan by sacrificing a piece in the set line: 1…Qxd4+ 2.Kxd4 Bc3. In the actual play, Black has no waiting move that would allow this set line to work again. Instead, the black rook captures the other white piece so as to vacate d5 for the king: 1.Rxa5 Qc8 2.Kd5 Qf5. The paradoxical capture of the white force is a motif oft-seen in helpmates.

The twinning device, to generate multiple positions for solving, is used much more frequently in helpmates than in directmates. Problem 27 consists of four parts – a “quadruplet” – where the positions are created by a unified method: substituting a piece in the diagram with a new one. The initial setting, part (a), in which a white rook stands on h7, is solved by 1.Ke2 Re7+ 2.Kd1 Re1. For part (b), replace the rook with a white bishop, and the solution is now 1.Kg2 Bf2 2.Kh1 Be4. Part (c) begins with a white knight on h7, leading to 1.Kg4 Kg7 2.Kh5 Sf6. Finally, for part (d) use a white pawn instead, and the solution becomes 1.Ke4 h8=Q 2.Kd5 Qe5. The four solutions taken together produce a geometric effect: an extended star pattern formed by the black king’s moves.

Yet another way for a problem to include more than one phase is the duplex, a type mostly found in helpmates. This condition means that a problem’s task has to be fulfilled twice: once normally, and once again with White and Black exchanging their roles. So in a duplex helpmate, an additional solution is called for in which White plays first and is mated by Black. Problem 28 has four parts in total, two solutions for each of the duplex halves. When Black begins, White mates with 1.e1=R Bc6 2.Rh1 Rg2, and 1.Kh1 Kh3 2.e1=B Bc6. And when White starts, Black mates with 1.Rg4 e1=S 2.Bh5 Sf3, and 1.Rg3 e1=Q 2.Bh5 Qxg3. The black pawn promotes to four different pieces, making this economical helpmate a remarkable demonstration of a theme known by its German name, Allumwandlung.

Another masterful work but in a very different style, Problem 29 features spectacular captures of white pieces as the main effect. The first capture in each solution is motivated by the need to unguard a square that the black king wants to access. A second white piece gets sacrificed with the king move itself. 1.Qxc8+ Rd8+ 2.Kxc4 Qd4, and 1.Qxh8+ Bg8+ 2.Kxd4 Rc4. Note that the mating piece in each solution becomes the captured piece in the other solution. Such a reciprocal change of functions between two white pieces is termed the Zilahi theme (also shown in Problem 26).