Finding potential energy difference of two electronic system

1. Jul 13, 2008

withoutwax

1. The problem statement, all variables and given/known data
Suppose N electron can be placed in either of two configurations. In configuration 1, they are all placed on the circumference of a narrow ring of radius R and uniformly distributed so that the difference between adjacent electron is the same everywhere. In configuration 2, N-1 electrons are uniformly distributed on the ring and one electron is placed in the center of the ring. What is the smallest value of N for which the second configuration is less energetic than the first?

2. The attempt at a solution

$$\sum$$U of configuration 1 > $$\sum$$U of configuration 2

*deduced that number of electron in one of the system must be odd, and another is even.

So, by drawing some circles with different number of electrons to understand the pattern of the summation.

But then i failed to get any relevant equations.

I think there must be some much easier way to solve it.