Sure, you don't absolutely need to know the problem to be able to derive an answer on the spot, but the problem with a widely known question like this is that candidates who already know it will have an almost insurmountable advantage over those who have never heard of it before, which makes it in essence a "know it or not" question.
There is very little you can do to distinguish between the candidates who knew the question beforehand but feigned ignorance versus those who actually managed to figure it out on the spot.