I think: Yes. As long as the problem is representative of the types of problems that the candidate will be required to solve if hired for the job. Naturally the problems should be within the candidate's claimed areas of expertise.

I like to pose problems that have been solved a while back, but was the subject of some considerable debate. Given a whiteboard, I am more interested in how the candidate approaches the problem and the questions they ask, the concerns they raise. In other words, demonstrating a mature approach.