  Multiquark states have been advocated to explain recent experimental data in
the heavy-light sector, and there are already speculations about multiquarks
containing only heavy quarks and antiquarks. With a rigorous treatment of the
four-body problem in current quark models, full-charm $(cc\bar c\bar c)$ and
full-beauty $(bb\bar b\bar b)$ tetraquarks are found to be unbound. Thus their
stability should rely on more subtle effects that are not included in the
simple picture of constituent quarks. The case of $(bc\bar b\bar c)$ might be
more favorable if the naive color-additive model of confinement is replaced by
a string-inspired interaction.
