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

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... 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 $5\sigma$.