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#1 Foggel

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Posted 04 November 2008 - 07:47 PM

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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#2 Foggel

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Posted 04 November 2008 - 07:50 PM

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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#3 AAAsn888s

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Posted 04 November 2008 - 08:02 PM

So they do not know that there are 100 blue, 100 brown and 1 green- is that correct?
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#4 michael531

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Posted 04 November 2008 - 08:19 PM

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

from what i understand...
Spoiler for hint/spoiler

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#5 AAAsn888s

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Posted 04 November 2008 - 09:58 PM

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

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#6 MrCubbie

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Posted 04 November 2008 - 10:27 PM

Does the guru know the color of his/her own eyes?
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#7 new guest

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Posted 04 November 2008 - 11:12 PM

This has been posted before!!
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#8 telethar

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Posted 04 November 2008 - 11:14 PM

Spoiler for answer + explanation

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#9 ledger

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Posted 04 November 2008 - 11:36 PM

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

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Posted 05 November 2008 - 09:11 PM

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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