  Studies of pairing correlations in ultrasmall metallic grains have commonly
been based on a simple reduced BCS-model describing the scattering of pairs of
electrons between discrete energy levels that come in time-reversed pairs. This
model has an exact solution, worked out by Richardson in the context of nuclear
physics in the 1960s. Here we give a tutorial introduction to his solution, and
use it to check the quality of various previous treatments of this model.
