I think you answered your own question, though I would add the caveat: The problem being solvable or not isn't the issue, it's whether it seems solvable. Therefore it's in their interest to make problems look unsolvable through various means, and conversely when they refuse to solve something that is obviously solvable, they must give the appearance of making progress on solving it.
I think you answered your own question, though I would add the caveat: The problem being solvable or not isn't the issue, it's whether it seems solvable. Therefore it's in their interest to make problems look unsolvable through various means, and conversely when they refuse to solve something that is obviously solvable, they must give the appearance of making progress on solving it.