Deceptive mate-in-one problems

By convention, directmate problems are solved from White’s perspective, and over time the stipulated task of “White to play and forces mate in N moves” has become abbreviated to “Mate in N.” An even more basic convention requires problem positions to be legal, or reachable from the initial array. What if these two rules are at odds in a given problem, in the sense that the position is illegal solely because Black couldn’t possibly have played the last move? Ordinarily, when such a situation occurs by accident, the White-to-play problem is deemed invalid for breaking the second convention. However, a branch of composition has developed that bends the first rule by exploiting the seeming ambiguity of “Mate in N,” which doesn’t specify whose turn it is. In these problems, the position is carefully constructed so that Black couldn’t have made the prior move, and this fact – combined with the legality requirement – leads to the conclusion that White had moved last and it is Black’s turn to play in the diagram.

This sort of reasoning about how a position legally arose means that such directmates also fall under the heading of retro-analytical problems. In this particular retro type, solvers are generally not warned about the need to first deduce which side is to play (spelling it out would spoil half the solution). Once the “twist” that it must be Black’s turn is detected – the proof itself is often straightforward – the solution could proceed in one of several ways. Here we will consider the main sub-type: Black has a number of legal moves, and White executes the mate-in-N task against each one. (Another sub-type sees Black delivering the mate-in-N as the real solution.) Let us look at some economical examples of this deceptive idea where the goal is mate in one move.

We begin with perhaps the best-known problem in this unusual genre. If White is to play, there is no solution, but retro-analysis proves that Black couldn’t have just moved. The enclosed black rook has no square where it could have come from. The black king has only one vacant adjacent square, but it did not arrive from c8 where the piece would have been in an impossible triple-check. Therefore the position is legal only if White had just moved and it is Black’s turn. Black has three possible moves, each of which is met by a unique mating reply: …Kxc7 1.bxa8=S, …Kxa7 1.b8=S, and …Rxa7 1.Rc8. Thus we uncover two surprising knight-promotion mates in this classic miniature.

This composition is nearly identical to a standard mate-in-2 problem that appeared some 20 years later, in a peculiar case of anticipation. As shown in this database entry #35233, Cyril Kipping published a two-mover whose diagram differs only in that the white queen stands on e1, and its key-move 1.Qb4! brings about the same position as the mate-in-1 problem. Unfortunately, the initial position with the e1-queen is still illegal with White to play, for the reasons just mentioned. This illegality was overlooked by the composer, editor, solvers, and the judge who bestowed a 2nd Prize to the problem. When the flaw was eventually discovered, the invalidated problem was stripped of its prize. The impossible position could be fixed by adding a black pawn on b4, though such a correct two-mover would still be essentially anticipated by the earlier work.

If it were legal for White to move here, then 1.Sc7 would mate. The presence of such a thematic “try” or would-be solution is a desirable feature in this problem type, ideal for catching the unwary solver. For the retro-analysis, the black king obviously did not come from a7/b7, adjacent to the white king, and the black knight did not move from d7 where it would have been checking White on Black’s turn. Thus it must be Black to play, and the actual solution consists of three neat variations, …Sxa6 1.c7, …Sxc6 1.Bxc6, and …Sd7+ 1.cxd7.

White apparently has three ways to deliver mate, 1.Qf5, 1.Qe6, and 1.Qf7 – multiple solutions that if playable would make the problem unsound. But Black has no legal last move; the bishops and pawns have no potential departure squares, and the king cannot retract to f7 or f5 where it would be in an impossible double-check by White’s queen and a pawn. Therefore it’s Black to play, and each of the three possible moves prevents two of the queen mates to induce the third: …Kxg6 1.Qf5, …Bxg6 1.Qe6, and …Bxg4 1.Qf7. This is a curious rendering of the Fleck theme, an established idea in regular directmates. In two-movers, the theme occurs in this form: White’s first move creates multiple mate-in-1 threats, which are then individually forced by various black defences.

No thematic try is available in the next problem, but it shows four related variations. The black rook (which did not come from b8 where it would be checking White) has four possible moves in different directions, and they provoke distinct mating responses. Such a pattern is called a rook-cross: …Rxc7+ 1.Sxc7, …Rxb6 1.Sxb6, …Rxa7 1.Rxa7, and …Rb8+ 1.axb8=Q. It’s tempting to try to improve this composition by eliminating two small weaknesses: (1) the lack of a mate-in-1 try, and (2) the 1.axb8=Q/R dual (which is albeit technically insignificant). My attempts at such reconstruction led to some interesting results, which I will present in another instalment.

Our final selection includes two mating tries, 1.Re8 and 1.Qe7, one of which recurs in the actual play (not a tidy scheme). Black has no legal last move for familiar reasons, with all queen retractions to vacant squares placing White in check, while the king coming from e8 would mean an impossible double-check. In the solution, the black queen generates six precise variations: …Qxe6+ 1.Kxe6, …Qxg6+ 1.Kxg6, …Qf7+ 1.Qxf7, …Qg7+ 1.Qxg7, …Qh8+ 1.Qxh8, and …Qxh7 1.Re8. The protagonist queen is well controlled in both the retracting and forward play, especially in view of the light setting with no pawns. A quick quiz question: why does the problem become faulty if the position is rotated 180 degrees?