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

Here’s the thing why can’t they write? That is legal

The dictator has reflective sunglasses

Wooooow this is very good when you understand it😅
Thank you TED-Ed❤

I would say(( you all should open your eyes so that the guard see them .))😂

I've heard of this logic and the methods themselves, of hyperrationalism are perfect, but not at all realistic.

You though long and hard-

I mean props to the dictator finding 100 green eyed babies. Mustve been hard

Couldve just spilled water on the ground and boom reflection

just pour the water on the ground

Imagine if one person just waited even though they knew they had green eyes

Wait... if a person could see that all 99 others have the same eye colour, he would be assumed that he's got the green eyes. If every person could see another person's eyes everyone would assume that they're the ones. So, the next night everyone sould sould leave. They just chilling 100 days in that island prison...🏝️🏝️

so this is where all the memes comes from

My friend told me this

My answer would be: “all of you DO HAVE the ability to leave this island” idk if the dictator would allow it, but to me if i said this, i would be satisfying the dictator’s rules. Its true, they all have the ability to leave the island, they have the freedom to ask to leave, this isnt new info. But for me to be a person from the outside, understanding their rules saying this confirms that they can in fact all leave the island without dying when i emphasise the word “DO HAVE”. Dictator didnt say anything about tone lol

Why would it be illegal to say “everyone else on the island has green eyes”? Perfect logicians would know that since you couldn’t give new information, such a statement must be information everyone already knew and come to the conclusion that everyone must have green eyes? Also you could just give a statement like “follow the pattern” and smart people would figure it out

Lol i did what I normally do and got the right answer in the dumbest way. I thought to wait 99 days and then gage reactions at the mornings headcount. If people were shocked to see that no one has left, then that would mean that everyone is seeing what Im seeing, all green eyes. That must mean that my eyes are green and we would leave that night. Im sure there are wholes in that but fk it, I lived.

but since nobody's leave on the first day then it should take atleat 101 days.

I think this is actually impossible. With more than two people a simple „Just may start“ should suffice. But in a way this gives information, indeed by extension any addressing them would provide that information/their cue to start their winning strategy.

So, the simple answer? Stay on the island for a number of nights that equals the number of green eyes you see. If anyone leaves before you do, you know you have yellow eyes. Let’s walk through the logic with 4 people.

Assume 1/4 people have green eyes
Assume person A has green eyes
Person A sees that everyone else is yellow eyed
Person A knows that, because at least one person is green, this must make him the green one. He is safe. He leaves after 0 nights (on night 1)

Day 2:
B, C, D see that person A left. The only way he could confidently leave night 1 was if everyone else was nongreen. They know they are all nongreen so they stay on the island

Now assume 2/4 people have green eyes
A and B have green eyes
A and B ignore C and D, because C and D cannot be the one with green eyes

Day 2:
A and B see that the other hasn’t left. A knows that if B had seen him as yellow, B would have left on night 1 because everyone else would have appeared yellow to B (like in the 1/4 situation). But he didn’t, so A knows himself to be green. B knows also knows he is green for the same reasons. A and B leave after one night (on night 2)

Day 3: C and D see that A and B left the second night. The only way A and B could confidently do this is if they saw both C and D as yellow. C and D stay on the island

Now assume 3/4 people have green eyes:
Assume D is yellow eyes

A, B, C, D all wait out day 1

Day 2:

A B, C, D, notice that nobody has left. This means that more than 1/4 people have green eyes

They all wait out day 2

Day 3: A, B, C, D notice that nobody has left. This mean that more than 2/4 people have green eyes.

A, B, and C have noticed D has yellow eyes. Now they know that more than 2/4 people have green eyes, and less than 4/4 people have green eyes. D is the one with yellow eyes, so the rest know that they must be green. All but D leave on night 3.

Day 4: D realizes that everyone else left without him. He must be the only one with yellow eyes. He stays on the island.

Now assume 4/4 people have green eyes (this situation is reality, but they don’t know this going into it)

Everyone waits out nights 1, 2, and 3

On day 4 everybody realizes that nobody left on nights 1, 2, and 3. This could only take place if all eyes were green. They all leave night 4.

This still feels like such a logical paradox to me even writing it out 😵‍💫

I think the key element is that saying “at least one person has green eyes” implies that everyone should start this logical process, and to start it at 1/4 people having green eyes. Otherwise they wouldn’t know when to start or whether they should start at 1/4, 2/4, or 3/4. If you just said “at least a few of you have green eyes”, and the logicians didn’t have an agreed-upon value for a few or didn’t all default back to one, they wouldn’t be able to escape even though your statement necessarily implies that at least one person has green eyes.

This only works as long as each prisoner is only witnessing one new set of eyes each day. If on day 1, during morning head count, each prisoner takes the time to look at all 99 of the others, then everyone leaves on day 3.

God I want that 4.minutes of my life back.

so....i don't need speak. they will konw then 100 bay later

I hate puzzles that are this contrived.

With due respect, if we think that all are perfect logicians, then they must just wait one night and not 99 nights. All of them must escape the second night. Reason is this👉 if for the first night no one escaped meaning there is not a single person who saw 99 people with non-green eyes and henceforth nobody escaped.. Because even if one person had seen 99 non-green eyes, he would have escaped. Now everyone might have assumed himself as non-green eyed, so you may think that he needs to wait for 99 nights.. But no, because cumulating the logic of all 100 people there, the obvious perfect logic would be that everyone is green eyed. So they need not wait 99 nights, but only one night (since all of them are perfect logicians)

Take for example, the case of three people on island. If on first night no one escaped, then it means EVERYONE knows that EVERY OTHER person out of the three of them has seen at least one green eyed person. Now for three people to assume at least one of THE OTHER TWO is green eyed, concludes everyone is green eyed (Given all of them are perfect logicians ). So all three should escape the second night itself and not wait for one more night.

It's a logic puzzle but does it have any application in real life.

Why did the 100 need the person to tell them "at least one of you has green eyes"? Don't they already know that?

Actually, Adria and Bill can both leave on the first night. As soon as you say your statement, they will realize that they both have green eyes because otherwise, it will be new information to the other.

Another answer: Take out one of your eyes from its socket, see what color it is, then leave with only one eye left.

IF THERES WATER IN OPAQUE SURFACES, JUST SPILL THE WATER AND LOOK AT IT!!!! SO MUCH FOR BEJNG PERFECT LOGICIANS YOU GREEN EYES MORONS

well when you notice that everyone else on the island has green eyes than it is pretty safe to assume you do too right?

Ok…slow guy here. Still not understanding. Night 1: Alice sees two green but thinks hers might be brown. She gets into the heads of Bob and Charlie and imagines they might see one brown and one green. So they can’t tell their own color. Night 2: same story applies. Bob and Charlie might be seeing one brown and one green or two greens . No one can leave. Night 3: same story. What am I missing?

I mean, why didn't they use the water to look at their eyes. The water wasn't opaque, the container was!!!!!!

so does nobody of the prisoners knows what colour is green

This is very similar to a puzzle I had presented to me. It was aliens and hats. But the line of logic was comparable.

Why cant you say you all have green eyes?

the riddle that started a whole lotta jokes

Imagine being the one brown eyed person on the island, you’re waiting, kinda getting excited at the prospect and the day before you think you might get to leave, you show up and you realize everybody got to leave except for you.

To everybody who said something along the lines of. Everybody next to you has green eyes or that everybody can only green eyed people. You are giving new information. The new information is that you didn't know that applied to everybody else

But doesn't it add information?
Let's put the 2 people example, there you add information because each person doesn't know whether the other person knows there is at least one person with green eyes. Let's put it from the perspective from one of the logicians, you know the other one has green eyes, but you could not have green eyes, so the new information is knowing that the other person knows for sure there is at least one person with green eyes. It's getting the information about the knowledge of the rest of the people. In the 100 case example is the same thing, but in a nested loop, as in that statement makes you know that everybody knows that everbody knows that everybody knows that everybody knows... (In summary an extra nesting for each extra person) that there's at least one with green eyes. The thing is that this information is so complex you need to see the behaviour of the other people to decode it, but it is information nevertheless. I'd like to think the dictator is not a perfect logician so he fails to see this is actually new information.

What about everyone around you has green eyes

The green eyed prisoners got totally drunk which turned their eyes red . Then they stormed the dicktaters palace captured him and made him wear colored contacts with one green eye and one red eye . They tied him up to a traffic light which caused a massive pile up turning all of the drivers eyes red .
so they could no longer see green thus creating a permanent traffic jam .
the drivers finally left their cars in the road and bought e bikes which allowed them to filter through the parked cars . eventually when they calmed down all of their eyes turned blue and world peace was achieved .

What a weird dictator

I’d tell them “At least 50 of you have green eyes” 😊

I would've dipped off the island as soon as the first 10 or so people got out with no problems.

Why not say “At least 2 of you have green eyes” instead. I feel like that helps the prisoners know their own eye color quickly

Imagine all of this but some of randomly asks to leave as a guess and screws everyone

If I were you, I would ask to leave.

If Adria and Bill have green eyes and Carl has brown: on the 1st morning, Adria and Bill EACH would conclude that the other 2 people didn't see 2 people with brown eyes, or else they would have left knowing they are the only person with green eyes. So they would leave on the 2nd night. But I think brown-eyed Carl would leave, too?

Probably not

I thought they all went to the dude and were like “do I have green eyes? Let’s find out!”