An unintuitive logic puzzle

[Flannel Jesus]

I found this online many many years ago. Don't look up the answer!

A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?


There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

[LuckyR]

Great puzzle. I think that the blue eyed people would leave on the hundredth day, everyone else would stay forever. Each blue eyed person would see 99 with blue eyes and the options are: if they have blue (100 total) or they don't so there's just the 99 with blue they see. In addition, for the 99 they observe with blue, the options are those can see 99 if the first one has blue, or 98 if they don't. Everyone knows that there isn't only 1 with blue, not only because they can see 99 or 100, but also because no one left the first night, which a logician who saw no one with blue eyes would do. Similarly they know there aren't 2 with blue because if 2 logicians saw 1 with blue and no one left on the first day, they'd know they had blue. Thus when no one leaves on day 99, each blue eyed person knows the blue eyed people they can see, don't themselves see 98, therefore they must have blue eyes. So they all leave the next day. The brown eyed people have no clue what their eye color is, they just know it isn't blue.

[Flannel Jesus]

[Impenitent]

the ferry driver leaves the island every night...

everyone leaves on the first night (if there are exactly 100 blue eyed and 100 brown eyed all you have to do is count- if you count 99 blue and 100 brown (other people beside guru) you must be blue #100 OR if you count 99 brown and 100 blue you must be brown #100)

-Imp

[Flannel Jesus]

Imp's probably just joking, but if he isn't, I'll give an answer:

[spoiler]wrong[/spoiler]
[hide]wrong[/hide]

Neither one of those worked? damn.

[Flannel Jesus]

Someone on another forum agreed with LuckyR's logic essentially, but disagreed that it's necessary for the Guru to say anything. Now, that seems like it should intuitively make sense - the guru wasn't saying anything anybody else didn't already know, so... why would the guru need to say anything?

But it seems as though the guru does need to say anything, because you can't really bootstrap the logic without it.

[Phil8659]

I can say one thing instantly. The person who posted this puzzle is illiterate.

Are there two types of Logic as intuitive and unintuitive? i.e., are those adjectival to logic? So, the real puzzle is, can an illiterate know if or not they posted a logical puzzle or not?

[Flannel Jesus]

I can say one thing instantly. The person who posted this puzzle is illiterate.

Are there two types of Logic as intuitive and unintuitive? i.e., are those adjectival to logic? So, the real puzzle is, can an illiterate know if or not they posted a logical puzzle or not?

If that's the only interpretation you can think of to the title, perhaps you're illiterate.

[Phil8659]

I can say one thing instantly. The person who posted this puzzle is illiterate.

Are there two types of Logic as intuitive and unintuitive? i.e., are those adjectival to logic? So, the real puzzle is, can an illiterate know if or not they posted a logical puzzle or not?

If that's the only interpretation you can think of to the title, perhaps you're illiterate.

Actually it is not. Since all information processing is a product of binary recursion, what is the function of the word logical? Is one grammar system logical, and another not?
Traditionally, one simply said, here is a puzzle. They did not embellish it with nonsense words, as you did.

Claiming that there is an intuitive or nonintuitive logic is a simple anthropomorphism.

[Flannel Jesus]

Anyway, gonna attempt to deduce the answer?

[Skepdick]

...

The blue-eyed people all leave on day 100. That's the day they all resolve their self-uncertainty given that nobody else with blue eyes left on day 99.

Which is what they all would've expected to happen if the split was 101 brown / 99 blue.

[Phil8659]

Anyway, gonna attempt to deduce the answer?

Not really. Working on a more important thingy. Aristotle. Been working on it for a while, using the most recent Oxford translations.
One part audio book.
One part on definition.
One part on demonstrating his use of Geometry.
Add that to my couple of hours of daily workouts, and housework, cooking, no real time for stupid and worthless puzzles.
Also, when I work, I either listen to music, or have movies or tv series on a monitor. I just re-watched Punisher 2004, and it seemed to me that the guy who played Frank Castle, also played Miller on The Expanse. Just checked it, got it in one.