Glossary
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 as 5.0.
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 3rd Prize
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.
