For the logicians, the dictator problem!!

Hi guys, it's been a while.

Here's the problem:

Imagine there's an island somewhere in the world that's controlled by a mad dictator who keeps one hundred people imprisoned. The island is swarming with guards, and the waters are filled with sharks. There's no way these people can just escape their fate, except they are all free to leave every night!

The rule is that any prisoner can approach the guards at night, and ask the leave, but only if they have green eyes. Since there are no mirrors on the island, and they are unable to communicate amongst themselves, the prisoners do no know their own eye color. The trick is that all of the one hundred prisoners have greens.

As human rights organizations world wide try to get the prisoners freed, you alone are selected to try and find a way to save all those people. The dictator allows you to to speak to the prisoners just once, but there are rules:

You can only make one statement.
You cannot tell them any new information.

What do you tell the prisoners to help them escape that awful island?

image credit: DreamWorks Pictures

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For the logicians, the dictator problem!!

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