I said there MIGHT be. Never said for sure.
But I think it's possible for even those which we think are unanswerable to have some solution.
Think Laelaps and the Teumessian Fox. Whereas mortals thought the uncatchable fox would be caught by the dog that always catches his prey (or that the dog who always catches his prey would be unable to catch the uncatchable fox, in some unending cycle), Zeus said "F*ck it." and turned them both into stone.
“…Judge not what a man has done, but judge what he could have done if he was a different bloke altogether. For art thou a leper? And a leper can changeth his spots…” --Rudy Wade, Misfits (Series 4, Episode 8)