Helpmates of the ‘distant’ future – Part 1

The helpmate was invented in the mid-19th century, and early examples of the form usually consist of a single line of play with modest thematic content. Over the years the genre evolves and the problems become more elaborate and varied. Now the modern helpmate (at least in two- and three-movers) typically involves two solutions that are strategically rich and interrelated. The trend towards greater complexity continues with the arrival of ‘helpmates of the future’ (HOTF). This is the name given to a scheme in which a problem contains not one but two pairs of analogous solutions. Helpmates of this sort are of course quite demanding to compose, and it’s probably not a coincidence that they came to prominence around the turn of the millennium, when computer-testing of problems became commonplace.

The British Chess Problem Society held a HOTF tourney in 2001-03, and the First Prize went to the problem shown below. It features two white indirect batteries (R + B on the file and B + R on the diagonal), which are utilised or dismantled in a variety of ways. The diagram position is solved by 1.fxe5 Rc5 2.exd4 Bc4 and 1.Rxd5 Bf4 2.Rxd4 Re3. The twin replaces the d4-pawn with a black queen, which converts the solutions to 1.Ke3 Bg6 2.Qf4 Bd4 and 1.Kc4 Rb8 2.Qc5 Rd4. While the two solutions of each pair show matching play, the two pairs are themselves strategically distinct – such an element of contrast is considered desirable or even necessary in HOTF. The judge of the tourney praised this work for its creative twinning, originality and harmonious play.

What could be the next step in this development of increasingly intricate and dense helpmates? One easy answer – which is anything but easy to arrange – is to have a problem incorporate three pairs of related solutions. We might call this type, ‘helpmates of the distant future,’ and a rare example recently appeared in The Problemist. The play of this superb composition revolves around two white batteries (R + P and B + P) aimed at the black king. In each of the three pairs of solutions, these batteries are exploited in analogous ways, to bring about a three-fold orthogonal-diagonal transformation.

1.Sb5 axb5 2.a4 c5 (A) & 1.Rh7 gxh7 2.g6 e6 (C).

1.gxf6 c5+ (A) 2.Kxe5 f4 (B) & 1.axb4 e6+ (C) 2.Kxc4 b3 (D).

1.Re8 f4 (B) 2.Rxe5 Bxe5 & 1.Qe2 b3 (D) 2.Qxc4+ Rxc4.

What makes this helpmate even more special is how certain moves recur in different solutions with new functions, to create another kind of pattern. In the three solutions listed on the left-hand side, the white pawn moves c5 and f4 (labelled ‘A’ and ‘B’ respectively) act variously as a first move and as a mating move, and a similar role reversal of e6 and b3 (‘C’ and ‘D’) occur in the right-hand group. That means the three solutions of each group, while showing different strategy, have a formal connection that enhances the coherence of the problem.

Helpmates of the ‘distant’ future – Part 2

26 Dec. 2014