I come across "mind reading" games based on elementary number theory from time to time; e.g. http://www.digicc.com/fido/. It bugs me a bit when people are wowed by such tricks, but not enough to sit down and figure out the mechanics of the thing. But the surprise factor may make a good museum activity -- where the second part of the activity is teaching why the trick works the way it does.
In general, math-based magic tricks would be good for an interactive exhibit: http://mathoverflow.net/questions/9754/magic-trick-based-on-deep-mathematics