Assuming P $\neq$ NP, NP-complete problems are "hard to solve, but have answers that are easy to check." Does it make any sense to consider the opposite, that is, problems for which it's easy to compute a correct answer, but hard to verify an arbitrary purported solution?
I think such a problem would imply either:
Exponentially many "correct" answers for any given input, because otherwise verification could be carried out by simply computing all of the correct answers.
Some "correct" answers are easy to compute, but others are difficult to find.