Let D be a convex subset of the n-dimensional space, and suppose that D′ is obtained from D by applying a positive central dilatation and then a translation. Suppose also that the sum of the volumes of D and D′ is 1, and D \cap D'\not\equal{} \emptyset . Determine the supremum of the volume of the convex hull of D∪D′ taken for all such pairs of sets D,D′.
L. Fejes-Toth, E. Makai combinatorial geometryadvanced fieldsadvanced fields unsolved