**Note: The two initial attempts to phrase this problem correctly were abject
failures. The following is a new (albeit related) problem.
**

Place four points on the surface of a unit sphere so that the sum of the reciprocals of the distances between distinct points is a minimum. What is that minimum value?

Note: This is related to the problem of minimizing the potential energy of electrons on a sphere.

**
The solution will be posted shortly.
**

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