The N-body problem has no general solution for more than two particles. Various restricted solutions such as the equilateral triangle solutions of the three-body problem can, however, be found. Here, we discuss how to find and understand such restricted solutions. We do this using generalized coordinates and the Lagrangian method. We note that the restricted solutions can be viewed as solutions arising from the imposition of constraints that do not require any constraint forces. We also note that an N-body problem leads to a central force problem provided the distances between the particles are equal. In three dimensions this allows the particles to be at the vertices of an equilateral triangle or a regular tetrahedron. We present corresponding restricted solutions to the three- and the four-body problems, respectively.