  We consider a simple static extremal multi-black hole solution with
constituents charged under different $U(1)$ fields. Each of the constituents by
itself is an extremal dilatonic black hole of coupling $a=\srt$. For a special
case with two electrically and two magnetically charged black holes the
multi-black hole solution interpolates between the familiar
$a=\sqrt{3},1,\frac{1}{\sqrt{3}}$ and $0$ solutions, depending on how many
black holes are placed at infinity. This proves the hypothesis that black holes
with the above dilaton couplings arise in string theory as bound states of
fundamental $a=\sqrt{3}$ states with zero binding energy. We also generalize
the result to states where the action does not admit a single scalar truncation
and show that a wide class of dyonic black holes in toroidally compactified
string theory can be viewed as bound states of fundamental $a=\srt$ black
holes.
