The "add this and that" stipulation typically asks you to
add a given unit on the board so that certain explicit conditions are
met. E.g. "Add the Black King where it stands mated" or "Add a Pawn
for a mate in 2".
The implicit condition (where the retro-content lies) is that
one may only add units in a way yielding a legal position!
Polis-Tidningen 1/1, 1946
(I saw this in Problem och profiler)
11+1. Add a White Queen and then
mate in 1
(a) Diagram; (b) Mirror position
The retro-analytical trick here is quite simple. One just has to observe
that the original White Queen never left the 1st rank because the white
Pawns never moved. Also, no Pawn promoted into a Queen, so that we can
only add the original thing. Finally, the Queen and the King could not
cross, so that there are only three squares where a White Queen can
be legally added: a1, b1 or c1.
Solution: +wQa1 & 1. b3#
For the mirror position, the same reasoning applies. (The Kings now
are on e1 and f4.)
Solution: +wQc1 & 1. d3#