Can You Solve The Famously Difficult Green - Eyed Logic Puzzle?

Imagine an island where 100 people, all perfect logicians, are imprisoned by a mad dictator. 

There's no escape, except for one strange rule. Any prisoner can approach the guards
at night and ask to leave. If they have green eyes,  they'll be released. If not, they'll be tossed into the volcano.

As it happens, all 100 prisoners have green eyes, but they've lived there since birth, and the dictator has ensured they can't learn their own eye color.

There are no reflective surfaces, all water is in opaque containers, and most importantly,
they're not allowed to communicate among themselves. Though they do see each other during each morning's head count. Nevertheless, they all know no one would ever risk trying to leave without absolute certainty of success.

After much pressure from human rights groups, the dictator reluctantly agrees
to let you visit the island and speak to the prisoners under the following conditions:


you may only make one statement

 you cannot tell them any new information.

What can you say to help free the prisoners without incurring the dictator's wrath?


After thinking long and hard, you tell the crowd,  "At least one of you has green eyes." The dictator is suspicious but reassures himself that your statement couldn't have changed anything. You leave, and life on the island seems to go on as before. But on the hundredth morning  after your visit, all the prisoners are gone, each having asked to leave the previous night.

So how did you outsmart the dictator?

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