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A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?

There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

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Posted · Report post

I just wanna say that I didn't write the riddle. I just figured that I'd share this with you.

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Posted · Report post

So they do not know that there are 100 blue, 100 brown and 1 green- is that correct?

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Posted · Report post

i have seen this before under the title the hardest logical puzzle in the world.

from what i understand...

you can a obtain the solution by thinking of small cases of the guru talking to one or two people and then gradually expand it using the based on the fact that everyone was told the same thing and everyone knows what color everyone elses eyes are, .....warning its a distinct possibility that your head will explode

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Ok - I think this is similar to the corporate test with three qualified candidates...

On the 100th night, the 100 blue eyed people leave....

Because - if there was only one with blue eyes - he would have left that same night (seeing no others with blue eyes, he would have deduced he was the only one.)

If there were two with blue eyes - both would have assumed the other to have left on the first night if they did not see anyone else with blue eyes - so both would leave on the second night.

I think this plays out all the way...

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Posted · Report post

Does the guru know the color of his/her own eyes?

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Posted · Report post

This has been posted before!!

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All Blue eyed people leave on the 100th day together

explanation:

People are named by a number, 1 is a noun representing a name.

A blue eyed person, 1, would see 99 blue eyed people.

So 1 knows there are 99-100 blue eyed people.

1 knows that every other blue eyed person sees 98-99 blue eyed people.

Assuming 1 has brown eyes they see 98 blue eyed people. Then 2 is thinking

I see 2 blue eyed people so everyone else sees 97-98.

Assuming they see 97, then I am not blue eyed and person 3 is thinking

I see 97 blue eyed people so everyone else sees 96-97.

Assuming they see 96, then I am not blue eyed and person 4 is thinking...

This logic can be followed all the way down to the last person.

Person 1 has blue eyes because the Guru said so.

So if they leave the first day only one person had blue eyes. Since no one leaves the first day, the assumption that person 2 did not have blue eyes is false. Now 2 knows he has blue eyes. On the second day no one leaves so person 3 must have blue eyes. on the third day no one can leave so person 4 must have blue eyes. Continuing on..

on the ninety-ninth day no one left so person 100 must have blue eyes.

Since all blue eyed people know that only 100 people can have blue eyes(the 99 they see + themselves) they all leave on the 100th night

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Posted · Report post

evryone with blue eyes leaves because everyone is hopeless they all might as well guess blue

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Posted · Report post

The guru does not know her own eye-color. She is in the excact same situation as everyone else. She is just allowed to say something once.

The solution is there. Just figured I'd mention it for those who want to find it out by themselves.

This has been posted before!!

Link? I searched the forum, but couldn't find it..

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