This investigation concentrates on the numerical solution of the multigroup neutron diffusion equations by computer codes. For a realistic model liquid-metal fast breeder reactor, several benchmark problems in two and three space dimensions were derived and calculations were performed by eight different computer programs. The effect on keff and the neutron fluxes of the refinement of the discretization mesh is studied. Very good agreement (∼0.05%) of the results was found in those cases where the computer programs use the same discretization scheme of mesh-edged discretization formulas, although the codes employ different methods of solution. On the other hand, minor discrepancies remain between results obtained by codes using mesh-edged and mesh-centered discretization formulas, even for fine-mesh grids. The reasons are not understood in every detail. Fortunately, these discrepancies are very small and more of theoretical than practical interest. The effect of a simple group condensation scheme on keff was also investigated by considering several different energy group structures. Spatial mesh refinements and resolution of the energy range were found to be well decoupled. As the main result, one may take the fact that spatial and energetic mesh refinements may influence the results rather strongly, unless the mesh step is comparable to the minimum diffusion length and unless enough energy groups are used.