Can you solve the famously difficult green-eyed logic puzzle? – Alex Gendler

Can you solve the famously difficult green-eyed logic puzzle? – Alex Gendler


Imagine an island where 100 people, all perfect logicians,
are imprisoned by a mad dictator. There’s no escape,
except for one strange rule. Any prisoner can approach the guards
at night and ask to leave. If they have green eyes,
they’ll be released. If not, they’ll be tossed
into the volcano. As it happens,
all 100 prisoners have green eyes, but they’ve lived there since birth, and the dictator has ensured
they can’t learn their own eye color. There are no reflective surfaces, all water is in opaque containers, and most importantly, they’re not allowed
to communicate among themselves. Though they do see each other
during each morning’s head count. Nevertheless, they all know no one would
ever risk trying to leave without absolute certainty of success. After much pressure
from human rights groups, the dictator reluctantly agrees
to let you visit the island and speak to the prisoners
under the following conditions: you may only make one statement, and you cannot tell them
any new information. What can you say
to help free the prisoners without incurring the dictator’s wrath? After thinking long and hard, you tell the crowd,
“At least one of you has green eyes.” The dictator is suspicious but reassures himself that your statement
couldn’t have changed anything. You leave, and life on the island
seems to go on as before. But on the hundredth morning
after your visit, all the prisoners are gone, each having asked to leave
the previous night. So how did you outsmart the dictator? It might help to realize that the amount
of prisoners is arbitrary. Let’s simplify things
by imagining just two, Adria and Bill. Each sees one person with green eyes, and for all they know,
that could be the only one. For the first night, each stays put. But when they see each other
still there in the morning, they gain new information. Adria realizes that if Bill had seen
a non-green-eyed person next to him, he would have left the first night after concluding the statement
could only refer to himself. Bill simultaneously realizes
the same thing about Adria. The fact that the other person waited tells each prisoner his
or her own eyes must be green. And on the second morning,
they’re both gone. Now imagine a third prisoner. Adria, Bill and Carl each see
two green-eyed people, but aren’t sure if each of the others
is also seeing two green-eyed people, or just one. They wait out the first night as before, but the next morning,
they still can’t be sure. Carl thinks, “If I have non-green eyes, Adria and Bill were just
watching each other, and will now both leave
on the second night.” But when he sees both
of them the third morning, he realizes they must
have been watching him, too. Adria and Bill have each
been going through the same process, and they all leave on the third night. Using this sort of inductive reasoning, we can see that the pattern will repeat
no matter how many prisoners you add. The key is the concept
of common knowledge, coined by philosopher David Lewis. The new information was not contained
in your statement itself, but in telling it to everyone
simultaneously. Now, besides knowing at least one
of them has green eyes, each prisoner also knows
that everyone else is keeping track of all the green-eyed people they can see, and that each of them
also knows this, and so on. What any given prisoner doesn’t know is whether they themselves are one
of the green-eyed people the others are keeping track of until as many nights have passed
as the number of prisoners on the island. Of course, you could have spared
the prisoners 98 days on the island by telling them at least 99 of you
have green eyes, but when mad dictators are involved,
you’re best off with a good headstart.

100 Comments

  • idk how 2 spell says:

    No

  • a crummy channel for a crummy person says:

    Couldn't you just say " thumbs up to everyone around you who has green eyes"

  • Bryan Fullbuster says:

    I was wondering why can't we just say "all of you have green eyes"?

  • Spotted Hyena says:

    Ok, so how does the dictator raise or even have kids when there is no mother present nor will the child protection Laws Still Need To Apply?

  • Who took the last pizza!!! says:

    How come they can’t spill water on the floor and look at it….?
    It works in cartoons!

  • JiminhasYESjams. MochiPanda says:

    Theyre blind.

  • Catrin Öhrn says:

    I solved it

  • Alpha Nogra says:

    How could they understand when they weren't allowed to communicate since birth?

  • Adelmund Oppo says:

    Easy
    Her: at least one of you has green eyes
    Me: sees other 99 green eye prisoners
    Me: BYE I'M LEAVING

  • Why Why says:

    You know you could just say that the person to your right or left has green eyes

  • skull jokes says:

    i would say to the crowd: “Cowards die a thousand deaths, but the brave only die once.”

  • GURDEEP SINGH says:

    This is originally a planet with green eyed dragons

  • Johnny Booi says:

    But that assuming everyone actually knows and thinks like that, if i heard that sentence, i would not be able to think of this.

  • FINfon228 says:

    High five someone with green eyes. Boom

  • Haughty Willow says:

    My proposed solution: there is at least 99 people with green eyes.

    If the prisoners know that I must say something that each one of the them already knows, then this is correct. This is because all prisoners know that there is at least 99 people with green eyes. Since all the prisoners can see that everyone else (99 people) has green eyes, and everybody knows this that means that everyone has green eyes.

  • Hotaru says:

    Everyone is concerned they may have brown not green eyes.
    Night one: If Adria saw two brown eyes, she would leave knowing that she must be the Green.
    She returns meaning she sees at least one green eye.
    I see two green eyes and if I have brown eyes Bill would see only Adria, one person, with green eyes.
    Day Two. When Adria returns on the second day Bill knows he has green eyes, because mine are brown. So Adria must have seen Bill's eyed as the one green and not left thinking Bill was the green eyes. At the same time, Adria sees Bill return and realizes as Bill has green eyes and I have brown that Bill must have seen her as the green eyed person.
    Therefore they would both leave the second night. …if I have brown eyes
    Day Three
    However since they both return the third day, they must not have realized they have green eyes.
    How? Well the answer is that If I have green eyes, Adria must have thought the same thing as me and expected Bill and I to leave, because she thought she was the brown eyes.

    Adria, Bill and I leave on the third night.

  • Squidney _ says:

    How would they know what green looks like

  • minieyke says:

    I'm pretty sure there's an illogical assumption in this. While having two individuals on the island, pretty straightforward assumptions can be made about what the other person sees, but once you go one green-eyed-person beyond that you cannot assume what motivates them. If they stay, you cannot think that it is because they witness two other green eyed people (or 4, or however many n+1 people on the island). As long as two more people than you have green eyes while the whole population is green-eyed, you cannot deduce that people are staying because YOU have green eyes as opposed to the other people who YOU KNOW and THEY KNOW have green eyes.

  • MaxDaledge says:

    is it just me or is the ‘at least one of you has green eyes’ redundant? Say there were only two on the island, they wouldn’t need to be given this information to figure out when to leave, same for 3,4.. people etc since they are born there they just need to be told which day to start counting so they are all on the same page, am I missing something?

  • Super Greyflash says:

    But they could just slap the person and point at their eyes. They would know that they had green eyes

  • 에슈르 says:

    두명까지는 이해했는데
    세명에서 이해하는데 좀걸렸네….
    진짜 재밌다

  • Ariel Wang says:

    If only they were scientists and know genetics…

  • Ben Izmailov says:

    Hi ted Ed

  • Adam Hennessy says:

    Could you say the person next to you has green eyes since you're saying it to all of them they know the person next to them was also told that

  • Girl Magic says:

    I thought they didn't know what the color green even looks like

  • Moraya says:

    Kiss every person you see with green eyes

  • emily says:

    if i saw everyone else with green eyes id take a chance and assume i also have green eyes

  • John Kurt Langrio says:

    Omg dont answer this logic
    Actually answer this
    There is a easy way to solve this logic though.

    The ANSWER:
    STOP IMAGINING!!!

  • Joshua V says:

    If I look around and see 99 people with green eyes, what you think I'm going to assume about myself? I'm leaving the first night.

  • Ace_de _Menace says:

    They lived there since birth, they all would've easily taught that everyone has the same eye color but themselves, since they're all perfect logicians they all would've taught it was themselves with green eyes which would lead them all to meet at the gates on the same night which would've then led them to realize that they all have the same eye color therefore leading them all to freedom… Just trying to think this through gave me a migraine ✌🤣

  • Evan Tazeris says:

    I don't understand 🙁

  • Tonya Fincher says:

    that gave me a headache

  • Fred Weasley says:

    Can’t you see your own reflection in other peoples eyes?

  • Alexey0795 says:

    I didnt understand why they need 100 days. 2 is enough

  • josephyzpan says:

    Poor the water out of the container and “accidentally” leave it out where everyone can c it

  • val masing says:

    Bad voice of narrator.

  • 美桜ん says:

    Couldn’t you have said, if all of you stand in a ring, the two people next to you will have green eyes?

  • Raidriar- gerechter Rächer der Geächteten- says:

    I dont get it. If at least one Person has green eyes how is that person suppose to know if he has green eyes even if nobody leaves for 99days?

  • Shen Support says:

    That was suppose to be hard?

  • Caleb Dutrow says:

    That’s new information

  • Bacon Bitz says:

    You can say you can see 99 green eyed people this isn’t new information since they already know that and if they realize it’s a general statement they can easily piece together that they have green eyes

    You could also say that if I were you I’d be happy to have green eyes since you state in opinion and they gather the information themselves

    You could also say I wish I had green eyes you guys are lucky

  • Karel Vecht says:

    My instinct was to have said 'at least two' and then they'd be all gone the first night. Mad dictators are generally not that smart…

  • Copyrighted Tree Yes says:

    If water is in an opaque container literally just spill it on the ground

  • Curtis Combs says:

    I don't believe its possible to tell if you have green eyes with the information given. Yes, logically you could deduce that everyone else has green eyes therefore I probably do as well, but there would be no sure way to tell with the information given.

    EDIT: It makes perfect sense now!!!! If there's only one person on the island with blue eyes they would look around and immediately know they could leave. If there were 2 blue eyed people they would wait to see if the other person immediately left telling everyone else they were the only one but because they both see a blue eyed person they would wait a day and realize there was another blue eyed person and logically deduce they are clearly the other blue eyed person. And for every additional blue eyed person they would have to wait an additional day to logically come to the conclusion that they themselves must be the other blue eyed person

  • Caleb Gee says:

    How would they know what the color green is? Also how would they be able to keep track of all the othe 99 people there?

  • Doobernator says:

    Just kill the dictator and liberate them.

  • matrixphijr says:

    "After much pressure from human rights groups, the dictator reluctantly agrees…"

    Oh wow, what power and influence from human rights groups!

  • arta9360 arta9360 says:

    I would just get a Gun and kill the Ruler. Boom Problem Solved.

  • kosoub says:

    I understand the whole reasoning but in my opinion since the prisoners are perfect logicians,no exterior help was needed.Everybody should have left the third day on their own.
    I will explain it shortly.Every prisoner should consider as common knowledge(understood by each prisoner's perspective) the following fact:
    "There are at least 98 green eyed prisoners"
    They should have chosen this number because it is the strongest between smaller numbers while still being perceived by everybody for sure.Then by following the reasoning on the video everybody should have left the third day of the dictatorship.

    The reason they cant consider the 99 is because they know for sure that anybody else sees at least 98 because everybody does not know his own eye colour.

  • Esteban Bernal Correa says:

    What about the number of people with green eyes is even?
    They would all leave first night

  • Chris Li says:

    I'm going to Cambridge to study maths and physics, but this is still mind-bending.

  • K3V!NG SPORTS says:

    They wouldn’t need 100 days to figure that out they could just split up into ten groups of ten people after ten days the realize that at-least nine of them have green eyes then each group will go into groups of fifty then after five days they realize 49 of them have green eyes and the sixteenths night is when they escape

  • jadekayak01 says:

    Or they could just write in the dirt and be done with.

    Its no forbiden in your rules

  • Phoenix Studioz says:

    Can’t you see reflections in other’s eyes?

  • Joe Plumber says:

    If all of their mouths are taped shut then how do they eat?

  • Vincent Hou says:

    This is a logic problem in elementary school math competitions in China.

  • MowgLy STAR says:

    easy peasy…puzzle…and for prisoner colore dont matter to scape from prisone it can be any coloure which you like

  • nibb_ nibb says:

    This doesn't make sense

  • PhantomLeGend says:

    Literally me in every video
    Video: can you solv-
    Me: NO
    Video: can you-
    Me:NOO
    Video: can-
    Me: NO NO NO, NOT THIS AGAIN!!

  • Baxter Manly says:

    How do they ask to leave if they can't talk

  • Hrabia Rak von Vrijheid says:

    If i will be the prisioner i will just risk.

  • Daniel Lopez says:

    he calls this a riddle because he is not smart

  • Wolfe The Elf says:

    How do they ask to leave if they can’t speak?

  • magicmulder says:

    I once sent the three-prisoner variant of this to everyone in middle management in my IT company. Only one of them was able to solve it, and she was the one most folks considered "less clever" (which was a pure confidence issue in her case).

  • Taliah Gucci says:

    But they would have to look into each others eyes anyways thus seeing the small reflection and their own green eyes

  • flap jack says:

    Yow what about this , If i had (green eyes) i would tell them " i can leave any time i want if i were one of you" . If i dont have (green eyes) i would say "if i were one of you i could never leave." Hmm ?

  • Podladog 00 says:

    One of the rules was you can't tell them new information, so telling them one of them has green eyes is new information.

  • Cptkirk1315 says:

    Nice clickbait title when you just give the answer away

  • Elizabeth Mary says:

    or simply look at your reflection through the eyes of your friend.

  • Klipklapklop • says:

    Y’all have green eyes

  • sunny singh says:

    I would say nobody is going to the volcano.

  • creschendoes says:

    "you'll definitely succeed if u ask"

  • Noah Clark says:

    I love how logical these videos are and how unintelligent the comments are.

    “Just crush him with the helicopter lmao”

  • llxX //¡ŚT Xxll says:

    Say gg while pointing to your eyes then tell them to do it to the others are the person that told the person and again and again..

  • Onkel Iroh says:

    The escape of area 51

  • Boussa Diagne says:

    I did it

  • Adel Boukabous says:

    I would say : " the dictator is gonna kill you tommorow"

  • Adi Burgos says:

    You could have said you all have the same eye color

  • Elizabeth Chavez says:

    Have you ever wondered why people with green eyes are so rare? That’s probably because they’re all in a prison held by a mad dictator.

  • AwkwardPanda 83 says:

    Watching teded high is wilddddd

  • Jenny Lin says:

    could’ve just said you all have the same eye color

  • Steven Hatfield says:

    Very faulty logic past two people.

  • Jake Knight says:

    The real question is: Is it worth it to leave the island?

  • Nope Nope says:

    How is this a puzzle. Just say "you all have green eyes" it is one statement and it is not new information as they can all observe this with their own green eyes. Am I missing something? I absolutely hate this hypothetical nonsense.

  • Pinchy Cheeks says:

    I would have been thrown into a volcano 🙁
    I have Hazel eye with some green soo…

  • ImNotAUsername says:

    Lol just look in the reflection of their eye

  • Lara Arnott says:

    I was still uncomfortable with this riddle until I saw it presented on Popular Mechanics. In that case, the statement is also added that the islanders are perfect logisticians. That made sense to me as I was trying to figure out how to predict what would occur on the 100th night if someone didn't leave because they fell in love and wanted to stay on the island, or had the flu.

    I'm an overthinker.

  • Imacookieboi Choc chip says:

    Pour the water on the ground and boom, mirror.

  • Amaya Thomas says:

    Maybe I missed the reason why this wasn’t possible but it said they couldn’t talk but they can all see that everyone around them has green eyes. If every person you see got green eyes Imma take my chances and assume I do too and bounce

  • Chris van de Vrande says:

    How is “at least one prisoner has green eyes” not new information? Clearly they didn’t have this information already or they would have escaped ages ago. I think the only solution that meets the criteria in the problem is to give them an instruction rather than a statement. Something like “jump up and down if you only see green eyed people “. Then after at least two people start jumping, everyone leaves night one.

  • PunchBug2012 says:

    just pluck an eye out then you'll know i mean you'll be down an eye but eh

  • akash patel says:

    say “the person next to you has green eyes”

  • ReyJ says:

    At least 99 of you have green eyes

  • Druva Kumar says:

    You could just tell them the gaurds can only see green colour eyes

  • Miso RR says:

    They got water can't they see their reflection in it?

  • Sayak Sen says:

    That's where this meme came from…

  • Nathanael McCooeye says:

    I would see (yes, the people around you do have green eyes). That’s not news, and it’s one statement, and everyone realizes that they are around someone, so they must have green eyes

  • Emma Holm says:

    "the person next to you has green eyes"

  • Chang Bronstien says:

    That answer is to complicated, I’d just say “everyone you see has green eyes”

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