  It is very elementary to observe that functions interpolating an extremal
two-point Pick problem on the polydisc are just left inverses to complex
geodesics.
  In the present article we show that the same property holds for a three-point
Pick problem on polydiscs, i.e. it may be expressed it in terms of
three-complex geodesics. Using this idea we are able to solve that problem
obtaining formulas and a uniqueness theorem for solutions of extremal problems.
In particular, we determine a class of rational inner functions interpolating
that problem.
  Possible extensions and further investigations are also discussed.
