• flannel jesus
    2.9k
    I found this online many years ago. Don't look up the answer!

    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."
  • T Clark
    15.2k
    Guru leaves immediately.
  • T Clark
    15.2k
    They all get off the first night.
  • T Clark
    15.2k
    Everybody but the Guru gets off the first night.

    I think I can justify all of them, but I think this is probably the best
  • flannel jesus
    2.9k
    none of these match the canonical answer but I would love to see your justifications anyway
  • Shawn
    13.5k
    Every night at midnight, a ferry stops at the island.flannel jesus

    Is this the crux of the puzzle?
  • Shawn
    13.5k
    Because the quoted is true, I can only deduce that some people have found a way to identify each other and they are being taken away.

    I watched LOST a lot.
  • flannel jesus
    2.9k
    every detail given is part of the solution. The fact that they all have the opportunity to leave exactly once a day is relevant to the final solution - the answer to the solution will involve specifying what night they leave eg first night, second night etc.
  • T Clark
    15.2k
    none of these match the canonical answer but I would love to see your justifications anywayflannel jesus

    All the people except the guru have a pretty good idea what color their eyes are. After all they can count. So that night they go to the boat and get on. You haven’t said how they verify whether or not the person knows their eye color. Let’s assume that the guy who is running the boat asks them. They tell him what they figured out. If they’re right, they get on the boat and go. If they’re wrong then they definitely know what color their eyes are so they get on the boat and go.

    One possible problem with this is that each person making the decision might be wrong and might have red eyes or some other color. But they know that isn’t true, because everybody showed up at the boat. They wouldn’t have all showed up if one of the people had red eyes. If that happened, they couldn’t be sure they didn’t have red eyes too.
  • flannel jesus
    2.9k
    All the people except the guru have a pretty good idea what color their eyes are. After all they can count.T Clark

    They can count, but... so what? What's the logic? From the point of view of any person showing up to the boat, how has he logically deduced the colour of his own eyes?
  • T Clark
    15.2k
    They can count, but... so what? What's the logic? From the point of view of any person showing up to the boat, how has he logically deduced the colour of his own eyes?flannel jesus

    You’re right, their ability to count doesn’t matter and I shouldn’t have put it in there but it doesn’t make any difference. The guy running the boat tells each person whether or not they got their eye color correctly. If they did they get on the boat. If they didn’t on their first try, then they know and can get on the boat.

    They know they don’t have some color other than blue or brown, because if they did, no one would’ve showed up at the boat
  • flannel jesus
    2.9k
    nah the solution doesn't need to involve any work arounds like guessing and failing. There's a clean solution.

    I included this text from the author at the bottom:

    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."
  • LuckyR
    635
    Great puzzle. I think that...
  • flannel jesus
    2.9k
    that colour thing didn't work. I was wondering if this forum has SPOILER technology
  • flannel jesus
    2.9k
    [spoiler] testing testing [/spoiler]
  • flannel jesus
    2.9k
    maybe base 64 encode your post and I can base 64 decode it
  • flannel jesus
    2.9k


    QW55d2F5LCB5ZXMgdGhhdCdzIHRoZSBhbnN3ZXIhIFlvdSBmaWd1cmVkIHRoYXQgb3V0IHdpdGhvdXQgbG9va2luZyBpdCB1cD8gSW1wcmVzc2l2ZQ==
  • LuckyR
    635
    I don't know what that means, I'll just delete it.
  • flannel jesus
    2.9k
    it means paste your reply into this website and click encode

    https://www.base64encode.org/

    And send me the result that comes out below

    There's a DECODE button at the top of the site to do the reverse process
  • LuckyR
    635
    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
  • unenlightened
    9.8k
    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
  • flannel jesus
    2.9k


    You two guys are good, I actually couldn't figure this one out myself.
  • flannel jesus
    2.9k
    Now @unenlightened @LuckyR, here's the more tricky part - what new information did the Guru give them that they didn't already have?
  • Michael
    16.4k
    I was wondering if this forum has SPOILER technologyflannel jesus

    [hide]this is hidden[/hide]
    

    Reveal
    this is hidden
  • flannel jesus
    2.9k
    oh wow! you're a true hero
  • unenlightened
    9.8k
    Now that is indeed tricky.
    Reveal
    It seems like no new information, because they could all see multiple blue eyes already, yet after 99 nights they knew something new that the guru hadn't told them, from the reactions of the others. So the new information was not what she told each one, but that she told them all at the same time. She set the clock ticking
  • flannel jesus
    2.9k


    Reveal
    I've heard it said that the new information is in iterative referential knowledge. If you look at the case with only one person with blue eyes, him saying "I see someone with blue eyes" doesn't give any new information to people without blue eyes, but to the person with blue eyes it does.

    If you look at the case with two blue eyes, everyone knows "there's someone with blue eyes" before the guru speaks, but after he speaks, now you can say "everyone knows that everyone knows that there's someone with blue eyes" - two people didn't know that already.

    And -- somehow, I forget how -- that everyone knows that everyone knows that ... keeps propagating upward, maybe after each passing day or something.
  • Michael
    16.4k


    Reveal
    If they're perfect logicians then on the first day that they arrived on the island, even before the Guru speaks:

    1. The Guru knows that 100 blue-eyed people each see either 99 or 100 blue-eyed people and either 100 or 101 brown-eyed people and that 100 brown-eyed people each see either 99 or 100 brown-eyed people and either 100 or 101 blue-eyed people.

    2. Every blue-eyed person knows that 99 blue-eyed people each see either 98 or 99 blue-eyed people, either 100 or 101 brown-eyed people, and either 1 or 2 green-eyed people, that 100 brown-eyed people each see either 99 or 100 brown-eyed people, either 100 or 101 blue-eyed people, and either 1 or 2 green-eyed people, and that the Guru sees either 99 or 100 blue-eyed people, either 100 or 101 brown-eyed people, and either 0 or 1 green-eyed person.

    3. Every brown-eyed person knows that 99 brown-eyed people each see either 98 or 99 brown-eyed people, either 100 or 101 blue-eyed people, and either 1 or 2 green-eyed people, that 100 blue-eyed people each see either 99 or 100 blue-eyed people, either 100 or 101 brown-eyed people, and either 1 or 2 green-eyed people, and that the Guru sees either 99 or 100 brown-eyed people, either 100 or 101 blue-eyed people, and either 0 or 1 green-eyed person.

    Using the reasoning given by unenlightened, on day 100 every blue-eyed person would leave knowing that they have blue eyes, every brown-eyed person would leave knowing that they have brown eyes, and the Guru would stay knowing that they have neither blue nor brown eyes.

    The Guru doesn't need to say anything; her saying either "I see at least one blue-eyed person" or "I see at least one brown-eyed person" provides no new information and is a red herring.
  • flannel jesus
    2.9k
    Using the reasoning given by unenlightened, on day 100 every blue-eyed person would leave knowing that they have blue eyes, every brown-eyed person would leave knowing that they have brown eyes, and the Guru would stay knowing that they have neither blue nor brown eyes.Michael

    What's the reasoning for brown eyed people? Unenlightened gave reasoning for blue-eyed people
  • Michael
    16.4k
    What's the reasoning for brown eyed people? Unenlightened gave reasoning for blue-eyed peopleflannel jesus

    The same, just change "blue" for "brown".
  • flannel jesus
    2.9k
    It's not the same though. The reasoning for blue eyed people specifically works because the guru said he sees blue eyes. He didn't say that about brown eyes. So what's the reasoning?
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