  We analyze relations between various forms of energies (reciprocal
capacities), the transfinite diameter, various Chebyshev constants and the
so-called rendezvous or average number. The latter is originally defined for
compact connected metric spaces (X,d) as the (in this case unique) nonnegative
real number r with the property that for arbitrary finite point systems
{x1,...,xn} in X, there exists some point x in X with the average of the
distances d(x,xj) being exactly r. Existence of such a miraculous number has
fascinated many people; its normalized version was even named "the magic
number" of the metric space. Exploring related notions of general potential
theory, as set up, e.g., in the fundamental works of Fuglede and Ohtsuka, we
present an alternative, potential theoretic approach to rendezvous numbers.
