hmmm. This sounds like the old barmoeter question:
http://wearcam.org/barometer.html
Namely, there are better ways to solve it than the way that the jerks who made the problem want you to. Were I in that camp, I'd just ask each kid if he'd been in the room. The threat of 12 years of math camp would keep them honest. Once all of them said yes, I'd declare and we'd go home.