Note that Peter's articles, follow a chess problem convention in using ‘S’ to represent the knight
(from the German word, Springer). ‘N’ is reserved for a fairy piece called the nightrider.

In directmate problems, the idea of changed play can be separated into two categories.

The more familiar one, changed mates, means that in two phases of play the same black defence leads to different white mating responses.

Problem 110 illustrates mate transference along with focal play.

The black rook in the diagram is ‘focusing’ on d5 and g4, the white knight’s mating squares.  If Black moves the rook, the focus is lost and one of these squares will be left unprotected, yielding the set lines 1…R- on rank 2.Sd5, and 1…R- on file 2.Sxg4.

However, the first move 1.Qa1! (waiting) pins the rook, and simultaneously unpins the black bishop.

The latter now takes over as the thematic defender, and when it moves, the piece similarly loses the focus and enables the knight mates to recur: 1…Be2/d1 2.Sd5, and 1…B- else 2.Sxg4.

There is by-play, 1…c4 2.Qxd4 and 1…d5 2.Qa6.

That these black moves are no longer playable makes the theme clearer, but mate transference can still occur when these defences remain legal.  And if these particular black moves compel White to deliver new mates after the key, the Rukhlis theme is produced.

Problem 111 presents such a scheme, a combination of mate transference and changed mates.  The set variations are 1…cxd3 2.Sb3 and 1…exd3 2.Sf3, in which White takes advantage of the simple unguards by Black’s pawns.

The key 1.Qxd7! (waiting) grants two flights to Black, and the ensuing king moves provoke the knight mates we have just seen, 1…Kc5 2.Sb3 and 1…Ke5 2.Sf3.

The key 1.d4! cuts off the a4-rook and a7-bishop, but neither knight mate is threatened because of the pin formed on the second rank.  White threatens 2.Qf3 instead, since the key-pawn has placed an extra guard on e5.

When Black defends with the h2-rook, the knight is released and so allowed to mate again: 1…Rh4 2.Se3 and 1…Rh3 2.Sf4, i.e. the knight mates are transferred to these unpinning defences.

Meanwhile, Black’s moves to d4 have changed their effects, from self-interferences to self-pins, and these errors are exploited accordingly with 1…Rxd4 2.Bc4 and 1…Bxd4 2.Rc5 – two pin-mates.

Also, 1…Rxg2+ 2.Bxg2, 1…Sxg5 2.Qe5, 1…Qe6 2.Qxe6, and 1…Qxe7 2.Qc6.

In Problem 113, the double-checks Sd4 and Se5 do not mate immediately because they interfere with lines controlled by the g1-bishop and g5-rook, respectively.  Black allows these double-checks to work in the set play, after self-blocking on b6 and b5: 1…Bb6 2.Sd4, and 1…Sb5 2.Se5.

Two more important set lines are 1…Qh2 2.Sxh2 and 1…Qd2+ Sxd2, making further use of the Q + S battery.  White starts with 1.Qb2! (threat: 2.Qb7), which observes b6 and b5 but relinquishes the battery set-up.

Now the knight mates are prevented for a different reason – direct guards by Black’s queen, hence the transferred mates when the queen tries to stop the threat by pinning White’s queen, 1…Qh2 2.Sd4, and 1…Qd2 2.Se5.