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wouldn’t they all leave on the second day when there’s two blue eyed ppl? They would all assume they also have blue eyes no?

And if the visitor lied and everyone had brown eyes, they would all leave on the first day 😂😂😂

There's actually only one correct answer I can see to this since they are perfect logicians, and that's no-one leaves. There's no rule saying brown-eyed people can't leave, so if everyone wanted to leave then they would have, but they didn't so they obviously want to stay. They also know that introducing any new information will cause some people to leave, which could include themselves since they don't know if they're blue-eyed or not. Therefore, any stranger on the island would be immediately killed (or otherwise removed) before the stranger can say anything. They are perfect logicians and thus all know that any new information leads to people having to leave the island; the only logical choice is to prevent any new information from entering the island and disrupting their perfect society.

Can they speak? Do they know how many people have blue eyes in total (as we know) or not? Do they know when somebody leaves the island? Can they re-check everyone each day? Can the stranger repeat the statement or say anything else? This riddle is so badly specified it is painful…

before watching: by knowing there is at least 1 blue eyed person. if a villager sees a blue eyed person they will assume they are not blue eyed and will not leave. if they see none, then they will leave themselves as they are going to know they are the blue eyed person. if they see N number of blue eyed people, but the blue eyed people didnt leave immediately after N number of days, they will know they are also blue eyed and will leave the island. now ima watch and see if i got it right. Post video: i was 100% correct. all the blue eyed people will always leave the island in N+1 days (where N is the number of blue eyes people they see.) meaning if N = 0 N+1 = 1 meaning day 1, zero other blue eyed people, plus themself will leave the island or if N = 99 N+1 = 100 meaning day 100, 99 other blue eyed people, plus themselves will leave the island. as an example.

Brown eyed guy: those 10 people didnt leave, so there must be an eleventh blue eyed person! The brown eyed person then proceeded to leave the island

Wait! After all the blue eyed-people leave, wouldn't the others know they didn't have blue eyes therefore knowing they have brown eyes, also causing them to leave????

Imagine being a brown-eyed person during all of this, having to spend 10 days with all these blue eyed freaks hanging around in blatant disregard of the rules, and not being allowed to tell them off.

Oh I actually got it, feel so dumb it took me extra minutes. So basically 1 blue eye will leave on the first night, which is obvious. 2 will see each other on the following day, question why the blue eye guy didn’t leave and realise they both have blue eyes. Same goes to 10 people, after 9th day it would be obvious for 9 people to leave, and since they didn’t, there must be 1 more, which is You. I also was wondering why brown eyes wont leave, but yeah, pretty much same reason. They wont leave cuz amount of spent nights will never be higher than amount of blue eyes left. Circle will be ended all at once, all blue eyes will leave at the same day

What does the stranger's statement gotta do with it though? They already know that somebody is blue eyed, it's literally in front of them. And they know the rules.

So you know exactly how many days you have to wait to decide. This is fun, but would be terrifying

I remember this from Ted ed

Dr sean, i have a correction to make, in the second "part" of the video, the last point was "everyone follows the rulles. and all of this is common knowledge", if that was true, it means everyone know there are 10 people with blue eyes and, so, every blue eyed islander would know they are blue eyed because the know there are 10 and the can only see 9, so, they all would leave at day 1 with or without the stranger coment.

Solution: they unalive the stranger and pretend nothing happend.

10 second answer: Yes, it would cause someone to leave the island. 1) On the surface it feels as though it shouldn't cause anyone to leave the island 2) The question is being posed in a video 3) People post videos with the intention of receiving positive attention 4) It would be anticlimactic if it really was that simple 5) Anticlimatic videos don't receive positive attention 6) The people posting this video wouldn't have posted it unless the answer was yes.

I saw this concept explained on an animated Ted ed video!

Yeah but what happens if you’re the one with brown eyes, you see everyone hasn’t left yet and then assume you must have blue eyes? If the stranger says “at least one” person, they don’t know how many people actually do have blue eyes, right?

Well the first night all the blue eyed people would leave brcause they know there is atleast 10 blue eyed people, but they can only SEE 9, therefore they know they have blue eyes.

This is missing a VITAL piece of information: there are a limited number of people on the island, a small enough amount that it’s feasible to see everyone’s eyes, not just possible

I know this riddle from a similar puzzle, from Professor Layton 2

Wouldn’t this be the same from a brown eyed person’s perspective?

Unless the stranger doesn't say how many have blue eyes a brown eyed person may think they have blue eyes also since nobody left

Stretching the "perfect logical" definition. If there are quite a Number of people with Blue eyes,the perfect logical villagers will understand that they could have Blue eyes before the stranger arrives. What will happen then? They will probably find a (perfectly logical) way to understand. They are probably 'just' "mathematically logical"

These perfectly logical people who exile their friends and family for having a different eye color

Surely it wouldn't take long for people to tally how many blue eyed people there are. If they see everyone's eyes and count 10 people with blue eyes, then they must have brown eyes. If they only get to 9, they must have blue eyes.

Behold, i have created surreal theory. This theory primarily focuses on dividing by 0. Currently, the size of surreal theory is 1 comment(not actually used in surreal theory) Ok, Surreal Theory states that 0 should be treated as an expression or place-holder rather than a number. We can still use it in basic arithmetic operations but it will be a bit limited. Next, we state that 0/0=0 because 0×0=0 and also because multiplication is the inverse operation of division. Also, note that we only defined 0/0 and not 0/n (n>0). Using this knowledge, we can pinpoint the value of certain 0/n. I'll update this comment to show my progress!

Omg, just talk

The stranger is completely irrelevant to the situation. They would all behave in this fashion (leaving the island after some number of days) starting from the moment they all arrive on the island. There is no logical reason they would all decide to start counting from when the stranger shows up. The only cases it's necessary for are the cases of three or fewer blue-eyed people. With four or more, everyone knows that everyone sees at least two blue-eyed people, so no one thinks there could be someone who needs to be told that blue-eyed people exist.

But if they are perfectly logical and know that everyone is all the time. Why don't blue eyed people go up to a brown eyed person and ask if everyone leaves on night 9 or 10. And Brown eyed people do the same and ask 10 or 11. They would not have talked about eyecolor as by the rules and yet they would have their answer instantly. As by the rules that should be a completely fine question.

(tl;dr : To avoid misunderstanding : Word the problem in a way that islanders discover every other islander's eyes color at the time of the stranger's announcement) I have a bit of an issue with the way the puzzle is worded, because as it is, the answer and explanation given is wrong. Not because there is an issue with the mathematical reasonning presented in the video, which is sound, but rather for a more "pedantic" reason. I usually don't make such comment on those problems when anybody can fill the holes by themselves, but this isn't such a case, and I can notice in the comments that the explanation given feels wrong to some viewers. This is entirely justified, and I'll try to recontextualize in a way that could satisfy everyone. First off, and I've seen it in the comments : No, as long as 3 peoples or more have blue eyes, the stranger's announcement does not and can not add any new information : When at least 3 people with blue eye are on the island, everyone know that someone has blue eye, and also know that everyone else knows that too. The assumption that people will treat this assertion independently from what they already know is what enable the mathematical reasonning presented in the video : Islanders will ignore the fact that this isn't new information and will start reasonning upon it knowing that everyone else will do the same, which is what enable this sort of "timer" to start. The issue is the following. This assumption *IS* an additional hypothesis that is not stated. Whether islander are perfect logician doesn't imply on its own that they will treat this assertion that way. Someone used to do those logical problem will probably not notice this subtle fact, because the stranger's annoucement is *obviously* meant as a starting point for the problem. However less logic-literate people might not see it in such a light, because : 1/This hypotesis is not stated and thus, must be inferred. 2/Treating this problem as intended when worded as is, is acquired from experience and in fact far from normal human behavior. So it won't be inferred. My suggestion is the following : Keep the same rules, but word the problem in a way that islanders discover every other islander's eyes color at the same day of the announcement. This is a nice problem tho, and the explanation for the reasonning is great.

this is probably taken from tëd ëd

The funniest bit would be what would happen if the stranger tells an entirely brown eyed crowd he sees blue eyes. Gaslighting everyone into leaving on the first night.

I think I know why the brown eyed people wouldn’t leave. It’s because they will see that all of the blue eyed people left.

""It's common knowledge that every islander is a perfect logician who always follows the rules." In order for the problem to work, it must also be common knowledge that it is common knowledge that every islander is a perfect logician who always follows the rules. Furthermore, it must also be common knowledge that it is common knowledge that it is common knowledge that every islander is a perfect logician who always follows the rules. And it must also be common knowledge that it is common knowledge that it is common knowledge that it is common knowledge that every islander is a perfect logician who always follows the rules. And so on.

Why brown eyed people never think that they might have blue eyes?

so this is the logic question version of the highschool “do they know that i know that they’re gay, and do they know that i’m gay”

i don't know. it's not actually the stranger making the statement (except with just 1 blue eyed person) that triggers the logic chain. it's the existance of the rule that blue eyed people need to leave that does it

No the stranger did provide knowledge that wasnt previously known. He has implicitly stated that at least one person will leave the island in a finite number of days, which was not known before.

Isn't this just TED-Ed's green-eyed riddle?

I think some brown eyed people might leave on accident

ihave no idea what he talked about on the 10 blue eye one if i was one i would just think "huh they all didnt realize they were the blue eye person, oh well"

I see people with blue eyes *Everyone looks at said person with blue eyes unconsciously* Person with blue eyes *realizing whats happened* : well fuck.

Hmm my immediate thought is that, assuming the stranger is truthful, everyone would leave, if they were unable to observe someone with blue eyes. The fact they say or more means it never possible to conclude that you don't have blue eyes regardless what you see.

The important question is, where does this story fit in The Stormlight Archive? 😅

I personally hate the introduction of the stranger who provides (effectively) nothing new to this particular scenario. It in no way meaningfully changes the knowledge that there is at least one (and in this case multiple) perspn on the island with blue eyes despite it being upgraded from ninth order knowledge to common knowledge because all of the islanders are oerfect logicians who know the rules of the game. As soon as there are at least 3 blue eyed people on the island, the logic chain can immediately kick off without the stranger's common knowledge injection, because it is already knowledge of a high enough order to use the rules of the game to prove you also must have blue eyes when working with both your own and your fellow islanders' perfect logic. There should be no scenario where 10 people with blue eyes could accumulate over time before this logic chain kicked off and every blue eyed person left the island. Even if all islanders came to the island at the same time, and saw each other for the first time with 10 amongst them having blue eyes, the oerfect logicians would also have a synchronized point to kick their logic off from without the stranger's statement. Someone tell me where I'm wrong here

The stranger provides no new information, as everyone knows there are at least 9 blue eyed people.

There's a logic problem in my square space ad wtf

If they all are perfect logicians, then no stranger is needed. Those blues will just left island on day 10.

3:00 Someone help me. Either im misunderstanding or this logic puzzle is wrong. If Im one of the brown eyed people why wouldnt I also think that I might have blue eyes? Ive seen two people with blue eyes, neither of them leave. So maybe thats because they have seen me with my "blue" eyes.

Why the brown eyed people don't think "oh they didn't leave, must be me?" What is at stake her anyways? Is the brown island blue-eyephobic? Are they in danger or like get a prize? What is the brown eyed ppl thinking? Tell me!! So many questions