For the Hubbard model with infinite-range hopping, a sensible competition between hopping and Hubbard repulsion can only be found when U/t scales with the volume of the system. Only two electrons carry all the kinetic energy and so the variations in Hubbard repulsion are bounded by only 2U for an eigenstate. To be comparable with the kinetic energy this must be extensive. For this case we derive some exact eigenstates for the model. Our lowest energy solution is paramagnetic although the spin degeneracy energy scale is very small. The behaviour of this system appears to be very different to that for the shorter-range hopping systems and so little can be deduced about more physical models.