Borrowed from here for your amusement and mental anguish. (btw the comic is good too )

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. If anyone has figured out the color of their own eyes, they [must] leave the island that midnight. 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.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). Everyone on the island knows the basic rules -- everything in the first paragraph. 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 them their own eye color; it could be 101 brown and 99 blue. Or 100 brown, 99 blue, and the one could have red eyes.

The Guru speaks only 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 with 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, 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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Protest:

Because the sentence "everyone knows the first paragraph" was in second paragraph they all know that all are perfect logicians but they dont know IF all are aware that everyone knows it!!!

On that case "no one leaves" is correct answer.

On case there is mistake in puzzle wording and ... all know that all know that all are perfect logicians ... (recursion is present) ... the solution is too trivial to be called "The Hardest Logic Puzzle in the World".

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Because the sentence "everyone knows the first paragraph" was in second paragraph they all know that all are perfect logicians but they dont know IF all are aware that everyone knows it!!!
It doesn't matter whether or not each knows that the others know that all are perfect logicians. The fact that they each know that all are perfect logicians is enough.


the solution is too trivial to be called "The Hardest Logic Puzzle in the World".
a)Your solution is false.
b)The words are not mine. Follow the link and take it up with the author if you wish

[Updated on: Fri, 13 October 2006 00:32]

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gible wrote on Fri, 13 October 2006 07:31

It doesn't matter whether or not each knows that the others know that all are perfect logicians. The fact that they each know that all are perfect logicians is enough.

Or so you think.

Quote:

a)Your solution is false.

I know what the correct solution is but ... i havent posted it, so how you know my solution?

Quote:

b)The words are not mine. Follow the link and take it up with the author if you wish

Already did and he immediately changed the wording on his website.

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[Updated on: Fri, 13 October 2006 03:32]

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I take it that On that case "no one leaves" is correct answer.
isn't a statement of a solution then...I retract my statement...maybe you do have the correct solution

oh and fwiw, I didn't think it was that hard either

certainly less mind-bending than the Monty Hall problem

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[Updated on: Sun, 15 October 2006 17:55]

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mazda wrote on Tue, 17 October 2006 18:24

gible wrote on Fri, 13 October 2006 11:48 certainly less mind-bending than the Monty Hall problem You're kidding, right ?

I dont think he was kidding. I took coffe break at morning for experiment (Monty Hall is unknown name around here). It took me whole 15 minutes to explain Monty Hall problems solution (and to listen various funny protests) to group of my coworkers. Quite capable coworkers both in logics and statistics.

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