A difficult riddle

[JJannui]

Okay... so building on Chris' idea. He said the blue eyes remark to everyone and so everyone thought they had blue eyes, this meant that the actual people with blue eyes left the next morning and so everyone who didn't leave must have brown eyes because they are the only two on the island??? C'MON IT MAKES SENSE!!

If they had to have brown eyes then they now knew their eye colour so they left as well.
@Fredy ?!?!

 

[Philip]

just tell us already as no one here is smart enough to figure it out

 

[M]

Another traveler called @Jon Godinn came and told each one individually their eye color.

 

[Frank]

When the guys with the blue eyes left, the brown eyes noticed that they then had brown eyes because they didn't leave, making them leave aswell.

 

[Ezrider]

The traveler had no effect on them knowing their own eye color but instead they eventually found out their eye color within that year since their population was ~300.

 

[Philip]

Thinking logically though, wouldn't they be dead after 1 year on that island?

 

[M]

Who cares they're all probably fatasses. If it doesn't matter what color eyes they have and they're all leaving within the year what's the point in knowing their eye colors?

They all left because they got to know their eye color.

[DOUBLEPOST=1455143110,1455142998][/DOUBLEPOST]

They are all (perfect) logicians.

They have a sound understanding of genetics and worked their own circumstance out logically.

 

[BlitZKrieG]

Following him telling them that something something blue eyes something something they start entering a massive confusion of questions that leads to answers of everyone to each other of what their eye color is.

 

[Tyla Jai]

If we think out side the box here - they are really good logicians then maybe they just worked it out with logic and maths?

 

[Hayden]

Someone from the 300 people would make all of the blue eyed people leave. The rest would be brown eyed, and they would know that if the blue eyed people were sent away, they are the brown eyed people because they are left. So they would have found out and they would leave too

 

[JJannui]

So if two people are together, and one of them has blue eyes and the other doesn't. Then they will both be thinking that they both have blue eyes. When only one of them leaves the island then the other person will realise that they were wrong and then know they have brown eyes. So they leave the next night.
This happens around 300 times until everyone has gone. 365 days in a year and so it will be finished in a year?

 

[Murtsley]

They looked in the water, and noticed a difference; because there's only two options, the eyes that are darker are brown and the ones that are lighter are blue eyed?
[DOUBLEPOST=1455143999,1455143604][/DOUBLEPOST]Got it, all were told they had beautiful blue eyes everyone would assume that is their eye colour, blue eyed people and brown eyed, blue eyed would then knew their eye colour, ergo had to leave, remaining people knew they had brown eyes as that is the remaining option.

 

[Mathias]

They looked into eachothers eyes and managed to see a reflection?

I don't know my head hurts

 

[M]

Does the travelers remark imply to the logicians that at least one person has blue eyes, and therefor by further logic and observation provide a suitable basis for their own departure? (i.e. they know the traveler is not chatting shit)

This is not an attempt at a solution, this is a question.

 

[Deleted member 5920]

There was another traveller?

 

[M]

Based on what we know

• The traveler is truthfully implying that at least one person has blue eyes.
• The logicians therefore understand this concept that there are 300 ≥ n ≥ 1 people with blue eyes, taking there to be exactly 300 people on the island.
• They inspect the others for their eye color and subtract the number of brown eyes (n) from the total number of people on the island (300-n).
• Let n = 299 for the observation of one inhabitant, for example. The inhabitant sees 299 other inhabitants with brown eyes and therefore knows that - as the traveler is strictly telling the truth, he has discovered his eye color and must leave the island.
• Therefore you can derive a general rule...
• Let n < 299 for the observation of an inhabitant, for example, the inhabitant sees n other inhabitants with brown eyes, and therefore knows that there are 300-n with blue eyes IF HE IS TO HAVE BLUE EYES. He waits 299-n days to see if those with blue eyes leave (which would be true for a case of there are (300-n-1 = 299-n) blue eyes), and if those do not leave he knows that he has blue eyes and all of those with blue eyes have made the same observation and do not leave.
• Everyone else leaves the following day, observing that they have brown eyes.
• Therefore they all leave in under 365 days.

 

[John Daymon]

On the 365th day all people should have left.

So let's say there are two people with blue eyes and two people are staring at each other, they will realise; If this guy is the one with blue eyes he will leave by the night, they wait and realise by the next day that they were wrong and will think that they must be the person with the blue eyes, each leaves by the second night.

 

[Puma]

All of them were swimming one day, and they were bored af, so they watched the water below them. Reflections ftw.

This was easy lmao

 

[DarkShadow]

Someone from the 300 people would make all of the blue eyed people leave. The rest would be brown, and they would know that if the blue people were sent away, they are the brown people because they are left. So they would have found out and they would leave too.

 

[rogue]

We induct on n. When n=1, the single blue-eyed person realizes that the traveler is referring to him or her, and thus commits suicide on the next day. Now suppose inductively that n is larger than 1. Each blue-eyed person will reason as follows: “If I am not blue-eyed, then there will only be n-1 blue-eyed people on this island, and so they will all commit suicide n-1 days after the traveler’s address”. But when n-1 days pass, none of the blue-eyed people do so (because at that stage they have no evidence that they themselves are blue-eyed). After nobody commits suicide on the day (remember that n=1st) day, each of the blue eyed people then realizes that they themselves must have blue eyes, and will then commit suicide on the nth day.

I don't think suicide counts actually.