A difficult riddle

[Fredy]

There's an island of ~300 very intelligent people. They are all (perfect) logicians and they also know that everyone else is a perfect logician.
There's no population growth and no one ever dies.
Additionally, the inhabitants of the island are either blue-eyed or brown-eyed.
As a tradition of their island, they aren't allowed to know the color of their eyes, and if they get to know it, they have to leave the next morning, which is also the only way for them to leave the island.
Every person knows the eye color of everyone else (but not themselves).
They have no mirrors and can't find out their eye color by themselves (they also don't tell anyone else their eye color).

One day a traveller comes to visit the island. At the end of his trip, he makes the following remark to all inhabitants:
"I really enjoyed my stay here and I'll hope to see such beautiful blue eyes again next year!" (note that he does not identify the person(s) who has/have blue eyes)
The traveller was telling the truth.

A year later the traveller comes back but is shocked to find that there is no one left on the island. They all left because they got to know their eye color.

Note that it does not matter how many of them are blue-eyed or brown-eyed, they would always leave within the year.

How?

This riddle can be solved with just the assumptions above and does not require additional information such as
"The traveller told everyone their eye color"

 

[Philip]

They made a mirror!



Im too retarded for this

 

[M]

The traveler came the first time and told them their eye colors.

 

[Tyla Jai]

Maybe they went on some family tree website and worked out whose parents had blue eyes and which parents had brown.

 

[Chrissy]

They are all mistaken and are partially colour blind, confusing the colour of someone with blue eyes for grey. They think they know their colour so they leave, when in actual fact they are incorrect.

 

[Alex_:D 3]

They realized the island had no dank kush so they left on a quest to find some clearly.

 

[Chrissy]

The traveler has a speech impediment and actually said "bluetiful eyes"

 

[JJannui]

~300 very intelligent people. They are all (perfect) logicians.

After a year, these intelligent people had long enough to figure out a way off/a way of working out the colour of their eyes?

EDIT: There was a 50% chance of guessing either blue or brown eyes so it shouldn't be that hard??

 

[Frank]

They all left because he said that they are beautiful, making them think it is blue maybe cause they didn't hear him say it right, cause they thought he said blutiful?

 

[Fredy]

I fucked it up,
the traveller said "I really enjoyed my stay here and I'll hope to see such beautiful blue eyes again next year!"

 

[Philip]

The lazorkid came there and killed them all

 

[TheFrozenMonkeyKing]

They all had blue eyes?

 

[M]

He told them collectively that they had blue eyes. They have no way of confirming what they are told, as tradition tells the inhabitants not to tell each other (and no mirrors), so they think they know their eye color and have to leave.

 

[Hayden]

Everyone already had the common knowledge that everyone knew that at least one blue eyed person was present.

 

[Philip]

They probably just got tired of it and told each other and went for some McDonald's?

 

[Frank]

As a tradition of their island, they aren't allowed to know the color of their eye, and if they get to know it, they have to leave the next morning, which is also the only way to leave the island.

How did he leave if his only way to leave was to know his own eye color?

 

[M]

, and if they get to know it, they have to leave the next morning, which is also the only way to leave the island.

The guy knows his eye color as it is the only way he has to leave the next morning, a second visit (of >24 hours???) is impossible.

 

[User0]

I fucked it up,
the traveller said "I really enjoyed my stay here and I'll hope to see such beautiful blue eyes again next year!"

The traveller just said that everyone has blue eyes and none are brown.

 

[Hayden]

They're all logicians so they can tell who has a certain eye colour

 

[Frank]

As a traveller, he took pictures and showed them to other people?
Or, took a small mirror with him.