  Consider a difference equation which takes the k-th largest output of m
functions of the previous m terms of the sequence. If the functions are also
allowed to change periodically as the difference equation evolves this is
analogous to a differential equation with periodic forcing. A large class of
such non-autonomous difference equations are shown to converge to a periodic
limit which is independent of the initial condition. The period of the limit
does not depend on how far back each term is allowed to look back in the
sequence, and is in fact equal to the period of the forcing.
