The balanced maximally diverse grouping problem with attribute values and varying group sizes (BMDGPAVVG) searches for the best balanced solution amongst all optimal solutions of the corresponding instance of the maximally diverse grouping problem with attribute values and varying group sizes (MDGPAVVG). We describe the set of optimal solutions of MDGPAVVG which allows us to use a short integer program presented in the literature to solve the BMDGPAVVG.