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Show ALL Forums  > Science/philosophy  > Blue Eyes: The hardest logic puzzle in the world      Home login  
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 FrogO_Oeyes
Joined: 8/21/2005
Msg: 2
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Blue Eyes: The hardest logic puzzle in the worldPage 1 of 1    
Who leaves the island, and on what night?

The second-last person leaves, at midnight after the guru speaks. As the last person to not figure it out, this person had no way to know until the guru spoke. The guru is the last person, and has no way to deduce her own eye color, so is stuck there unless she decides to leave.

I see no requirement in the question that I explain how the OTHER 199 people figured it out, only that I explain ONE person.
 BlahGrim
Joined: 1/29/2004
Msg: 3
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Blue Eyes: The hardest logic puzzle in the world
Posted: 2/18/2008 6:15:33 PM
I had to cheat and look it up. I may have an actual reply in a few days when I think my way through this.
 FrogO_Oeyes
Joined: 8/21/2005
Msg: 4
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Blue Eyes: The hardest logic puzzle in the world
Posted: 2/18/2008 7:08:36 PM
The "standard" answer is a bit more complex and interesting. Having looked it up, I understand it, and it's distinctly different from mine. Given the way this particular version was worded however, I'm comfortable with my answer, even though the logic is drastically different.
 AwP
Joined: 12/31/2006
Msg: 5
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Blue Eyes: The hardest logic puzzle in the world
Posted: 2/18/2008 7:31:34 PM
I think that's wrong but close. The guru spoke to the islanderS, plural. There were at least two people besides the guru there. If one was a brown and the other a blue, then when the guru spoke they could look at each other and the blue eyed person could see that the blue the guru mentioned wasn't the other person, so it must be them. So I think it was the second last person (not counting the guru themself).
 AwP
Joined: 12/31/2006
Msg: 7
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Blue Eyes: The hardest logic puzzle in the world
Posted: 2/19/2008 7:12:34 AM
My best friend has dark brown hair and blue eyes. Me ex has blond hair and brown eyes. Try again.
 Wunderkindt
Joined: 1/3/2008
Msg: 9
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Blue Eyes: The hardest logic puzzle in the world
Posted: 2/19/2008 9:34:04 AM
I don’t see where the Guru spoke more than once: “… is allowed to speak once … on one day in all their endless years …”.

After “endless years”, I expect that 198 islanders had died of old age, and the last 2 raced for the boat when one flinched, after the Guru finally spoke; with at least one still having blue eyes.

(Even if the Guru spoke every day, he could be referring to the same individual with blue eyes over and over again, and therefore adding no new information.)

 scorpiomover
Joined: 4/19/2007
Msg: 10
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Blue Eyes: The hardest logic puzzle in the world
Posted: 2/19/2008 12:48:23 PM
Interesting puzzle, hdsa0irse.

Great answer, rune. Incredibly ingenious.

However, if I may add something:
So all 100 blue-eyed people would be able to leave after 100 days?
If there is only 1 blue-eyed person, he can see no other blue-eyed people, so he must leave on the night after the day of the Guru's statement.
If there are 2 blue-eyed people, they must leave on the 2nd night after the day of the Guru's statement.
If there are 3 blue-eyed people, they must leave on the 3rd night after the day of the Guru's statement.

Since there are 100 blue-eyed people, they must leave on the 100th night after the day of the Guru's statement.

So on the 100th day after the day of the Guru's statement, there are no blue-eyed people on the island. But the brown-eyed people and the Guru would still be there.

But this would all be true only if no-one wanted to leave the island.

However...if they all wanted to leave the island, all the blue-eyed people and the brown-eyed people could all leave on the night after the day of the Guru's statement.
A simple way to determine your eye colour would be to form everyone into groups of the same eye colour. You couldn't say what colour the other people's eyes were. But you would have to start somehow, so you approach someone and stand next to him, say someone with blue eyes. At this point, you would not know what colour your eyes were, so you could be in a pair of 2 blue-eyed people, or 1 blue-eyed person and 1 brown eyed person (you).

Then, if someone else approached you, then it would be no advantage to approach one blue-eyed person and one brown-eyed person, so that person would only approach 2 blue-eyed people, or 2 brown-eyed people. Then, if the person standing next to you has blue eyes, and you can see that someone is approaching you, then you would have blue eyes. If that person has blue eyes, you would encourage that person to join you, to make groups, so you would walk towards that person. So would the person next to you, because they have figured this out too. So the both of you would approach that person, and now you would have 3 blue-eyed people. If the person approaching you had brown eyes, then you would back off, and so would the person next to you, so you would both back off, and now he knows that he has brown eyes. So he would seek out 2 people with brown eyes.

If you had brown eyes, and you were standing next to the blue-eyed person, you would have no-one approach you. But that is not a guarantee. But everyone else would think the same, so eventually everyone else would pair off, just to get things moving.

At that point, you would not know what colour your eyes were, so you would split from your partner, look for a pair of blue-eyed people (or brown-eyed people) and try and join them, and so you would know what colour your eyes were and so would they. So then if you had blue eyes, there would be a trio of blue-eyed people (including yourself) and if you had brown eyes, you would look for a pair of brown-eyed people, who would figure out from your approach that they both have brown eyes, so they would accept you with your brown eyes, and there would be a trio of brown-eyed people. Eventually everyone would now be in trios of blue-eyed people and trios of brown-eyed people.

Then those trios would pair up in a similar fashion, and by midnight, there would be only 3 groups of people: 100 blue-eyed people, 100 brown-eyed people, and the Guru on her own.

The blue-eyed people would know that they all have the same colour, and by seeing the other people in their group, know they have blue eyes. The brown-eyed people deduce their eye colour similarly. The Guru is the only one who can never leave, because she is the only one with green eyes. She knows that she doesn't have blue eyes or brown eyes, because the other groups move away from her. But she doesn't know if she has red eyes, and no-one can tell her. So she cannot leave.
 nipoleon
Joined: 12/27/2005
Msg: 13
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Blue Eyes: The hardest logic puzzle in the world
Posted: 7/8/2008 2:47:47 AM
Couldn't they just all get together and let the guru divide everyone into 2 groups, blue eyes and brown eyes.
Then when the guru got to speak it would be, " All you people are blue and all you people are brown ".
Then everybody leaves, except the guru who has no way of knowing what his eye color is.
 maxxoccupancy
Joined: 2/5/2007
Msg: 14
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Blue Eyes: The hardest logic puzzle in the world
Posted: 7/9/2008 8:47:13 AM

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.


There are, then, 201 people on the island. Logically, the only way that the communication, "I can see someone who has blue eyes" can be effective is if only one individual is presenting himself for inspection. That individual then learns what color his eyes are, and that individual leaves at midnight that night, taking 200 days for completion. One never knows until tested by the guru what color their eyes are.

If, however, she can only speak generally, she is never offering new information. Unless islanders can hide themselves for the day, there's no way to determine eye color.
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