Proof of a conjecture by Walter Deuber concerning the distances between points of two types in Rd

Theorem. (A) For equal numbers of black and white points in euclidean space the sum of the pairwise distances between points of equal color is less than or equal to the sum of the pairwise distances between points of different color. (B) Equality holds only in the case when black and white points coincide. Statement (B) was originally formulated as a question in 1998 by the late Walter Deuber (Bielefeld); his question implicitly includes the assumption (conjecture) that (A) is true.