The Retrograde Analysis Corner
A Maximummer is a problem where Black is under the obligation
of always playing the (geometrically) longest legal move. (He picks
one of the longest when he has a choice.) There also exist Double-maximummers,
where the rule applies to both sides.
This fairy condition was first used by T. R. Dawson in 1913. It is
mostly used in selfmate problems.
Technically, the length of a move is the euclidean distance of the
displacement. E.g. a Knight's move counts as sqrt(5). Castling involves
the addition of two displacements, so that O-O counts as 4.0, and O-O-O
Checks are not fairy: the wh. King is under check
even if capturing him would not be Black's longest move. Thus all moves
in a Maximummer are legal moves in the usual sense.
In retros, the maximummer condition applies to any proof game. This
is a severe additional constraint on legal proof games and retro-composers
can use it to great effects.
Here is an example:
L. A. Garaza
Thèmes 64, Jan. 1962
12+9. (Maximummer) Mate in 2.
(a) diagram; (b) Pd5 -> c3;
(c) Pd5 -> c2
Here, it can be shown (in the (a) position) that
under the Maximummer condition, castlings
are mutually exclusive. So that 1. Rf1? O-O-O!
fails, while 1. O-O! forbids Black's O-O-O and forces
him to follow with the longest 1 ... Rd8 allowing 2. f7 mate.
See full solution for the maximummer
retrograde analysis establishing mutual exclusion between castlings,
and for the solutions of the twins.