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

Note by Kaito Einstein
4 years, 3 months ago

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[SOLUTION 1 ] I go and tell to any one of the prisoner that "Go to the guard to demand leave and tell any other fellow prisoner to do the same ". Explanation : Let's call this person(to whom I speak ) as Mr A .Now , A does not know that his eyes are green . But once he goes to the guard , the guard will instantly know that his eyes are green , so he will let him pass. The other prisoner to whom he speaks will go to the guard and escape. Similarly , all of them will escape . [SOLUTION 2] I go the prisoners and tell them to demand leave when they see the guard . Meanwhile , I go and hit the guard and hide so that he cannot see his attacker. Explanation : The guard will come to find out who has attacked him . When he comes , he will find out that all of them have green eyes . Then the prisoners demand leave and according to the rules he has to let them go . Assumption : (This applies to both the solutions) The guard has sound eyes and does not suffer from colour blindness.

- 3 years, 9 months ago

atleast one of you have green eyes.

- 3 years, 9 months ago

One of you have brown eyes

- 4 years, 3 months ago

All of your eyes reflect violet,indigo,blue,yellow,orange and red.

- 4 years, 3 months ago

leave

- 4 years, 3 months ago