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Well, recognizing that a particular solution is impossible (and then proving it) is part of mathematics, as LorenCobb says. For example, you could think of the Riemann hypothesis as requiring a proof of impossibility, and if you could come up with a solution for that you'd be quite famous.


I realize that. However, after everyone said it didn't appear possible, I was hoping that there was actually a solution which would surprise us all. It would have been neat outcome.
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