  We address the question whether the ILC can resolve the LHC Inverse Problem
within the framework of the MSSM. We examine 242 points in the MSSM parameter
space which were generated at random and were found to give indistinguishable
signatures at the LHC. After a realistic simulation including full Standard
Model backgrounds and a fast detector simulation, we find that roughly only one
third of these scenarios lead to visible signatures of some kind with a
significance $\geq 5$ at the ILC with $\sqrt s=500$ GeV. Furthermore, we
examine these points in parameter space pairwise and find that only one third
of the pairs are distinguishable at the ILC at $5\sigma$.
