Here's a pretty easy one.
A new student (a male) was wandering down the hall of his new school looking for the boys' locker room. He asks a nearby student (who happens to be the school bully) to direct him. The bully says, "See those three doors? It's one of those, but I switched the signs around so they're all wrong! Ha ha!"
The new student looked at the three doors. They were labeled "Boys", "Girls" and "Cafeteria". Just then another student walked out of one of the doors.
The new student told the bully "Thanks" and proceeded to the correct door. How did he do it?
Answer
He saw a male student walk out of the door marked "Boys" - in this case, he either walked out of the Cafeteria or the Girls' bathroom. He must've exited the Cafeteria (because he cannot use the Girls' locker room). So one of the remaining doors must be the Girl's bathroom, but it can't be marked as such, so he picks the one marked "Girls".
Indeed, in general, the only case where one cannot deduce is when a male walks out a door marked "Girls" or when a female walks out a door marked "Boys".
If he sees a female exit a door marked "Girls", then she certainly was in the Cafeteria. This means he chooses the door marked "Cafeteria" (as opposed to the remaining door marked "Boys").
If he sees a female exit a door marked "Cafeteria", then she certainly was in the Girls' locker room. This means he chooses the door marked "Girls" (as opposed to the remaining door marked "Boys").
If he sees a male exit a door marked "Boys", then he certainly was in the Cafeteria. This means he chooses the door marked "Girls" (as opposed to the remaining door marked "Cafeteria").
If he sees a male exit a door marked "Cafeteria", then he certainly was in the Boys' locker room. This means he chooses the door marked "Cafeteria".
Of course, it's entirely possible he's been trolled by the clever bully into going into the Girls' locker room unintentionally.
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