The 100 Green Eyes
On an island, 100 people, all perfect logicians, are trapped on an island and imprisoned by a mad dictator. If they approach the security guards at night and ask to leave, and if they are green eyed, they will be released. Otherwise, they will be thrown into a volcano. Apparently, all of them have green eyes. But there are no reflective surfaces on the island, and they've been there since they've been there since birth. And they are NOT allowed to communicate with one another. Finally, one day you are allowed to go on the island and make one statement without providing them with new information. What do you say?