  We extend earlier discussions of the balance problem for two black holes and
study stationary spacetimes containing an arbitrary number of $n$ aligned
rotating and (possibly) charged black holes. For these hypothetical equilibrium
configurations, we obtain the most general form of the boundary data on the
symmetry axis in terms of a finite number of parameters. Hence future
investigations of $n$-black-hole configurations can be restricted to studying
properties of these finite families of solutions.
