Mystery Solved

On my second day at the University of Toronto in a course called Introduction to Proof (which really was a life-changing course that I heard they stopped offering) the Professor gave this question (actually a variation with 100 people and no aliens) and (owing to the fact that all math teachers are inherently creatures of pure evil) neglected to provide the answer.

In the dozen or so years it's been this is the first time I've seen that problem and so here's the answer. Now you don't have to wait quite as long as I did.