A student society at a university campus decides to
create a pool of bicycles that can be used by its mem-
bers. Borrowed bicycles can be returned to the resi-
dence, the library, or the athletic centre. On the first
day, 200 marked bicycles are left at each location. At
the end of the day, at the residence, there are 160 bicy-
cles that started at the residence, 40 that started at the
library, and 60 that started at the athletic centre. At the
library, there are 20 that started at the residence, 140
that started at the library, and 40 that started at the
athletic centre. At the athletic centre, there are 20 that
started at the residence, 20 that started at the library,
and 100 that started at the athletic centre. If this pat-
tern is repeated every day, what is the steady-state dis-
tribution of bicycles?