Bittersweet Candy Bowl

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.”

How many people leave the island, of what eye color, 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.”

Bump

BLUE EYES WHITE VAGINA!

If the Guru says that she sees someone with blue eyes, social logic would state that most people would look towards someone with blue eyes, and since that statement takes logic, the citizens that are looked at will leave, which would be the one hundred people with blue eyes.

If I’m off and you are saying they have to KNOW then I have no idea how they could be exactly sure instead of just guessing with logic

She is not looking at anyone in particular.

@Scarfy
I taught him that… :3

@Taetchi
FUUUUUUUUUUUUCK.
YEEEEEEEEEEEEEES.

OK, let me have a shot at this. I’ll post whenever I’ve worked part of this out.

FIRST REALISATION:
The Guru and the Brown-eyes are not leaving the island at all. Rather like the old 4-people-wearing-hats problem, the Brown-eyes are disconnected from that information; since they don’t know the numbers of each, looking at a Brown-eyes doesn’t help either party.

SECOND REALISATION:
No-one leaves night 1. The only person worth considering, by the above, is a Blue-eyes. ( ) On the first night, he sees all the other Blue-eyes and thinks “They were probably the one referred to”, and can’t be sure he’s Blue also. However, EVERY Blue thinks this on BOTH sides of every comparison. That must be important somehow.

THIRD REALISATION:
There are actually between 2 and 101 pieces of new information for the islanders. First is the guru’s statement, but second is who leaves each night. Anyone who figures out the problem WILL leave, so the instant the problem is solvable to at least one person, everyone else will get that info.

That’s all I’ve got. Let me think for a few hours.

All the blue-eyed people leave on the 99th night. So that’s 100 people who leave.

All the brown eyed people leave the day after, on the 100th day.

Actually, 101th day.
On the 100th day, nobody would leave because they’d be waiting for the next blue eyes white dragon to leave, and if nobody left, it means that the person who’s guessing would have brown eyes.

Oh, thanks for that Radial. Forgot about that.

98 people leave. I don’t know why I just feel like saying it, I’M LISTENING TO MAH GUT!

The brown eyed people can’t leave. The puzzle is exactly the same if those guys are all brown eyes, or all green eyes, or split to 50 people brown, 50 people red. Hence there is not enough evidence to let any of them escape.

The only group with external information about themselves is the blue group.


After all, all anyone KNOWS is that there are at least 3 colours on the island. And the guru only knows of 2.

No. They dont know whether they have red/purple eyes or something of the like.

Hence AT LEAST. Meaning there could be more than three, but not less.