Not a paradox for a buddhist. Answering will make him open his mouth and lose his grip. Thinking about answering will cause the want, and the suffering as he can not answer without forfeiting his life.

The answer is unthinking- as in meditation, clear thoughts from the mind. It is designed to show how the right answer is no answer, in both senses!

With the proper understanding, there is no paradox. I agree with you that noticing a potential paradox is sometimes a souce of inspiration to learn, mostly when you can not show the way and when it must come by self discovery.

I do not know how familiar you are with Buddhism. If you want to keep learning, ask yourself: if Kyogen was asked 3 times, would he change his "answer" ?