The term echo is sometimes used in the problem context to describe various types of repeated effects, but primarily it refers to a specific visual idea, namely the recurrence of a mating configuration.

In such a scheme, the black king at the end of two variations is attacked and confined in a similar fashion – its flights are controlled in the same way – but these mates take place on different parts of the board.

Thus the mating arrangement is in effect shifted from one position to another, and such an occurrence we call an echo mate.

Echoes are categorised in a variety of ways.  A chameleon echo, for example, results if the black king is mated on different coloured squares.  Another kind of classification relates to the preciseness of the echo.

The helpmate 63 is solved by 1.Qe4 Qf7 2.Sd4 Sc4 and 1.Qd5 Qg4 2.Sd6 Sd7.

The two final positions, apart from the white king, show a 90-degree rotation around the mid-point of e5.  Notice how Black’s first move in each solution unpins the white queen, a fact that determines the order in which Black’s moves are played.

Also, Black’s knight moves are self-interferences – they cut off the black queen’s control of the mating squares.

In Problem 64, White’s options are quite limited; it takes three moves to promote the pawn and the new piece has one remaining move to give mate, starting from a8, b8, or c8.

The white king is too far away to help arrange a mid-board mate, so Black has to prepare for a mate on the first rank, using the two rooks as blocking units.

1.Ba7 b6 2.Kf1 bxa7 3.Rf2 a8(Q) 4.Rae2 Qh1. 1.Bc7 b6 2.Ke1 bxc7 3.Rf2 c8(Q) 4.Rae2 Qc1. 1.Bd4 b6 2.Kd1 b7 3.Re2 b8(Q) 4.Rad2 Qb1.

The triple echo mates are enlivened by some variety in the play, viz. the change of promotion squares and the need for 1.Bd4! in one solution to shield the white king from check.

Multiple echoes are more frequently found in helpmates than other types of problems.  Especially by using the device of twinning to vary the starting positions, a helpmate can render a large number of echo mates.

Problem 65 incorporates six related parts, but remarkably without evoking twins.  Three pairs of exact echoes are brought about, and that they all stem from the diagram position makes this a rare achievement.

1.Re8 Sg4 2.Ke6 Kc6 3.Ree7 Sd4 and 1.Rd7 Se1 2.Kd4+ Kb4 3.Rdd5 Sc2.

1.Re4 Sd4 2.Ke5 Kc5 3.Rf6 Sd3 and 1.Re3 Sd3 2.Ke4 Kc4 3.Rf5 Sd2.

1.Ref5 Sg5 2.Ke5 Kc5 3.R7f6 Sd3 and 1.Rf4 Sg4 2.Ke4+ Kc4 3.Ref5 Sd2.