  The possibility that like-charges can attract each other under the mediation
of mobile counterions is by now well documented experimentally, numerically,
and analytically. Yet, obtaining exact results is in general impossible, or
restricted to some limiting cases. We work out here in detail a one dimensional
model that retains the essence of the phenomena present in higher dimensional
systems. The partition function is obtained explicitly, from which a wealth of
relevant quantities follow, such as the effective force between the charges or
the counterion profile in their vicinity. Isobaric and canonical ensembles are
distinguished. The case of two equal charges screened by an arbitrary number
$N$ of counterions is first studied, before the more general asymmetric
situation is addressed. It is shown that the parity of $N$ plays a key role in
the long range physics.
