# Miscellaneous Problems

Solution

Niels Høeg
Tidskrift för Schack, 1924

5+1. Høeg-retractor. Wh. retracts 2 moves and mates in 1

The solution starts with White retracting -1. e6-e7 !!. This cannot be a capture, so Black does not get a chance to choose which bl. man was captured.

Now Black must retract a King move. The King could not have come from d4 or e5 (illegal double check). But whichever other square Black chooses, allows White to choose a wh. man that Black just captured, and to retract another wh. move such that he instead can mate Black with a forward move. It turns out that Black's choice of which bl. man white captured (if any) on White's second retraction makes no difference:

(Usually retracted moves are written like Kd5e4(R) to emphasize that Black chooses the square d5, after which White chooses the captured man, here a wR. But we shall just write Kd5xRe4.)
-1. e6-e7 Kd5xRe4 -2. Be7-f6, and forward 1. Qa8#
-1. - Kf3xRe4 -2. Bh4-f6, 1. Qh1#
-1. - Kf5xRe4 -2. h5-h6, 1. Qe5#
-1. - Ke3xBe4 -2. Be5-f6, 1. Qe1#
-1. - Kd3xRe4 -2. Qa2-a1 (or other moves), 1. Qe2#
-1. - Kf4xBe4 -2. Qa3-a1 (or other moves), 1. Qf3#

It is interesting, and indeed the point of the problem, that White should never choose that Black captured the strongest wh. man: a Queen. With another white Queen it is easy to mate, but Black chooses to resurrect a man that prevents the mate, e.g. -1. e6-e7 Kd5xQe4 (wQ??) -2. Qc2xQ/Re4 (bQR!!) and there is no mate.

There is hardly any retrograde analysis in this problem, but it demonstrates well the richness of variations that the Proca type rarely shows.

(Many thanks to Henrik Juel for suggesting this example and spelling out the solution.)