A reflex mate is an inverse mate problem (i.e. you force
the opponent to checkmate you) where both sides must checkmate (by
reflex) whenever a mate in one is possible.
In retros, the reflex condition applies to any proof game. This is
an additional constraint on legal proof games because they have to avoid
situations where a mate in one is possible.
Here is an example:
404 - N. Plaksine
Europe Echecs 283, 07/1982
In memoriam Roger Diot
6+13. Reflex mate in 1
Here the forward stipulation is easily answered with 1. Bb2!
forcing the reflex 1 ... Qa2xb2 mate.
The interesting problem is to find how the position can be reached
by a legal game without any earlier mate in one opportunity. Only the
last few moves are problematic. See
full solution if you cannot
The first reflex problem was published by B. G. Laws in a 1893
British Chess Mag. issue. I don't know who first used the
reflex condition in retros.
There exists a direct reflex stipulation (as opposed to
inverse), recently invented by Jean Zeller. Here the goal is
checkmate, but whenever it is possible (for any side) to play a so-called
helping move that grants the opponent with a mate in one oportunity,
one is under the obligation of playing it "by reflex" (unless
one can already mate in one).