  We report on a study of a finite system of classical confined particles in
two-dimensions in the presence of a uniform magnetic field and interacting via
a two-body repulsive potential. We develop a simple analytical method of
analysis to obtain ground state energies and configurations. We prove
analytically the minimum energy configurations are independent of the nature of
two body interaction and the magnetic field. In particular we prove that the
first transition from a single shell occurs when the number of particles
changes from five to six. These results are exact.
