For a change, a problem involving light retroanalysis. A basic
chess problem convention is that the diagram position should be
legal, in other words one that could be arrived at in the course of
a hypothetical game. The solver’s task here is to prove that
there is only one square on which the black king can legally stand
mated.
The mated king cannot stand on the eighth rank because
White’s mating move would have had to be g7xh8=R, but all
8 white pawns are still on the board. A number of squares such
as h6 and d5 are ruled out because in each case no white move
could have delivered the double check. If the king stood on e4
White's mating move would have had to be either d2-d3, which is
illegal because the bishop from c1 could not have moved to f4
earlier, or e2xd3, in which case the bishop from f1 could not
have come out earlier to be captured at h5. The king must stand
on d4, White having just double-checked by d5xe5 e.p., after
Black’s last move e7-e5.