  We consider a one-dimensional model allowing analytical derivation of the
effective interactions between two charged colloids. We evaluate exactly the
partition function for an electroneutral salt-free suspension with dielectric
jumps at the colloids' position. We derive a contact relation with the pressure
that shows there is like-charge attraction, whether or not the counterions are
confined between the colloids. In contrast to the homogeneous dielectric case,
there is the possibility for the colloids to attract despite the number of
counter-ions ($N$) being even. The results are shown to recover the mean-field
prediction in the limit $N\to \infty$.
