How did the logistics of this question work out? Did the interviewees work on the problem live, with you (or the interviewer) in the room acting as a sounding board or as some other resource?
During the interview, the interviewee worked on the problem live, and the interviewer stayed silent, except for questions. If they didn't come up for air after 30 minutes or so, I'd check in and see if they were stuck, offer help, etc.