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 thoughts on “Can you solve the famously difficult green-eyed logic puzzle? – Alex Gendler”

  1. I would have said, you all have the sam colour eyes. Then when would see that someone else on the island has green eyes, they know there eyes must be the same and they all can leave.

  2. we all know that the eyes also a mirror, if they noticed others' eyes so keenly, sure that they can see their own eyes colour through others's eyes.

  3. …can’t they all see that everyone else has green eyes during that gathering and make the assumption that they also have green eyes?

  4. There is a flaw in the riddle, all you had to do is look around.

    If I was a prisoner and I’ve noticed that everyone else had green eye, then I would’ve assumed that I had green eyes as well.

  5. I don’t know why I would have to make it hard on myself and these prisoners , I’d just tell them “everyone standing on the ground here excluding the guards is arranged in a way that each and every one of them has a green-eyed neighbour” and saved them 99 days of trouble

  6. He never told us how we could solve the riddle. Me being the type of guy to give blunt answers, I would of stated: You'll know theres 100 of you and only 1 of him. Ted-Ed never said they were in cells or confined or shackled by any means.There for they could charge him with what ever portable cover they can get. Riddles. They never say how your suppose to solve them, also after the guard is dead they can just what ever there is on the island to make a boat

  7. You could also say, "High-five someone who has green eyes."

    1. It is one statement.
    2. It is not NEW information as each person already knows they can see multiple people with green eyes. They know this already in their heads.
    3. Each person will get a high-five from someone, therefore revealing they themselves have green-eyes too. (You might high-five someone letting them know THEY have green eyes…eventually someone will high-five you letting you know YOU have green eyes. That someone who high-fived you will get high-fived from someone too.)
    4. You gave the non-verbal signal to do a high-five, so each person knows exactly what the high-five means so there is no confusion or misinterpretation. The high-five communicates that the person has green eyes.

  8. Can you at least tell them that the prison is in an island near Cuba but not run by Cuban? or is it not allowed by the riddle rules.

  9. 'And the dictator has ensured they cant learn their own eye color.There are no reflective surfaces.' When you said that there was sun glasses on the eyes of dictator.(0:36)

  10. But…. aren't they all aware that atleast one of them has green eyes? Being able to see eachother afterall, eve the 99 green eye oe

  11. In the video, it explains how Carl thinks if he has non green eyes.

    Can someone explain how Carl thinks if he has green eyes ?

  12. What if you said "Everyone around you has green eyes." ? If you told three people (1, 2 and 3) this; 1 would realize that everyone 2 can see has green eyes, including him. The same goes for the other two. This would work the same way for 100 people and they would all leave that night. But it isn't new info, because everyone knows that everyone else they see has green eyes. Please notice this, it might be the cleverest thing I've ever thought…

  13. The chance that all of them have green eyes and are all smart enough to understand this without communicating seems less likely than for people to even be stuck in this bizarre scenario.

  14. How is that all dont know each others eyes? are they in a delusion. Man if was among them i would indicate them that they had green eyes and vice versa by hand guestures if i can't talk. Simple all would know that evryone has green eyes and leave.

  15. Telling them at least 99 if them have green eyes tells them that if they didn’t have green eyes then everyone else would have gotten new info

  16. You could speed this specific problem up by saying “at least 99 of you have green eyes”. They’d leave after one day

  17. If only one of them has green eyes and they all have the same eye color then they all green eyed. LOGIC

  18. I’d just say “you can all ask to leave” cause it would imply that they all have green eyes but they already know they can ask (it doesn’t make a lot of sense but I’m not smart)

  19. If they are perfect logicians I would just say “ you can see That everybody around you has green eyes” then they know that they have green eyes cuz I’m referring to everyone

  20. Can I say "More than 99 of you can leave" or will I be tossed into the volcano by the fuming dictator?

  21. Why couldn’t he just give one of the prisoners a gun to shoot the dictator there were no rules against that

  22. "At least one of you has green eyes"
    I think it is a new information.
    It is because they weren't informed that anyone of them has green eyes

  23. alright everyone here is smart but i still dont GET IT. like for two people, it makes sense, but not with three.
    and why did these people need reassurance about one person having green eyes? didnt they already know that from before??? why didnt they try escaping before if they already knew that?

  24. 1. Shoot the dictator.
    2. Take the key.
    3. Hijack the copter.
    4. Fly to the island.
    5: Unlock the island.
    6. Release the prisoners.
    7. Realize that you don’t know how to fly a helicopter, and died somewhere around step 3. That combined the fact that you don’t know how to get to the island, and the prisoners would have no where to go after you released them, means that this plan was doomed from the start.

  25. Wouldn't it be simpler to say that everyone has the same eye color.
    Or more vaguely "the one next to you has the same color eyes as u"

  26. 2 rules, very easy. No info, one statement. The person to your left and right has green eyes. DONE. They all know the others have green eyes. They already know the person on their left and right has green eyes. When this statement is made, they will be aware that this applies to their counterparts obviously just as equally as it was a statement addressed to the entire mass.

    Did I just solve this riddle in 2 seconds? I guess I'll hit play.

  27. This is the coolest riddle i have ever seen. Also after knowing the answer one will think for minutes to find how it works..

  28. they were on an island….. the water in the sea wouldve been a reflective surface….THEY COULDVE JUST SEEN THEIR GODDAMN REFLECTION IN THE SEA AND GAZED UPON THEIR WONDERFUL GREEN EYES

  29. Everyone beside you has green eyes. The prisoners can already see that so it's not new information. The only thing it offers is that you are one of those green eyed people. Not sure if this breaks the new information rule or not.

  30. This seems wrong. I think when it gets to 3 people, it is impossible to figure out if the person himself has green eyes or not. From Bill's perspective, he knows Adria and Carl has green eyes, but not sure of himself. The next day comes Bill realizes that both Adria and Carl have not left. From Bill's perspective, he thinks Adria didn't leave because she sees Carl the only one with green eyes and doesn't matter whether Bill himself has green eyes or not. From Bill's perspective again, he also thinks Carl didn't leave because Carl sees Adria the only one with green eyes and doesn't matter whether Bill himself has green eyes or not. So they would all have the same reason for not leaving. THINK ABOUT IT!

  31. what if you said ''those who dont leave tonight have green eyes''. Then we can assume that everyone would wait to see if the others are going to wait a full night and once everyone sees that everyone waited, they all would assume that everyone else has green eyes and would they'd also think they're own eyes are green aswell because they waited like everyone else.

  32. So basically every person sees everyone else's with green eyes so when nobody leaves for the same amount of days as there are prisoners they can conclude that nobody left because they saw everyone else's green eyes.

  33. The part where the prisoners cannot see their own eye colour…
    Like the dictator literally has glasses, and the people can just pour some water, which will show their reflection

  34. The prisoners never would free themselves in reality because at least one of them wouldn't understand/ still feel insecure and therefore not leave the Island

  35. The solution makes sense, "they were told at least one of them has green eyes", but they cant be sure 100% which one of them has. Adria and Bill sees each other, and if at least one of them has green eyes, one of them would have left on the next day if the other don't but the fact that they still see each other the next day meaning themselves have green eyes. In Adria's perspective, she is assuming she does not has green eyes and if she does not has green eyes Bill would have left on the next day but Bill stayed meaning she has green eyes. Same with Bill's perspective. When Carl is added, same things apply, in Carl's perspective he would assume himself does not have green eyes, and if he does not have green eyes, Adria and Bill would just be looking at each other and figure out themselves. However, I do not understand how this rule can be apply to the 4th person and so on, imagining adding David, what is her perspective to understand the situation and realize that she has green eyes?

  36. Do they know what a green color is though? What if they don't know? Maybe the dictator told them the sky has green color and the grass is red and they accepted is as a fact?

  37. Can't we say that at least 99 of you have green eyes?
    Everybody knows this but when they realise that everybody is supposed to know this they would conclude that no one can see a non green eyed person and everybody will leave on the 1st night

  38. She said " at least one of you is green-eyed " then every person will think that "everyone have the same eyes probably its me who have diffrent ( green ) eyes " so every person on island will leave in one day

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