Lunchtime Logic Puzzle

[_Bat_]

I could not work this one out... see if any of you can.

 

The answer can be found using google if you can't work it out and get curious.

 

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."

[rolfea]

I think I have an answer, but can't find a definite answer on google.

 

link to an answer page if possible?

 

Edit: Found the answer I was wrong

 

the answer is here http://xkcd.com/solution.html for anyone interested

 

or "an" answer

Edited June 4, 2009 by rolfea

[AlexB]

Lunchtime puzzle? I think I need to talk to your boss on how long you get for lunch if you wrapped your head around that without looking up the solution in a lunch break!!

[gibbo_ap]

the person running the ferry, and every night

[gibbo_ap]

te other way to look at it logically is by reading a few bits

They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly

so there is a solution...yes...THEY get it straight away, they all leave. it doesnt ask how do they figure it out, just who and when.

 

so as they will figure it out "instantly" the answer [logically] is....

 

every one leaves on the 1st night

 

simple

[jamesb]

All of the blue-eyed people leave that night.

 

I think I've got the answer, but I don't want to spoil it for everyone else.

 

Bat, I'll PM you with it.

Edited June 4, 2009 by jamesb
Adding more

[gibbo_ap]

All of them, that night.

 

Except the Guru.

 

i was wondering about her too, tho goin by my reasoning she also has perfect logic

[rolfea]

thats what I thought, but supposedly i'm wrong

 

which (logically) makes you wrong

[jamesb]

i was wondering about her too, tho goin by my reasoning she also has perfect logic

 

The brown-eyed and green-eyed people are irrelevant to the puzzle.

[jamesb]

thats what I thought, but supposedly i'm wrong

 

which (logically) makes you wrong

 

Don't know what you're talking about. Edits to correct my answer once I'd actually worked it through in full, none here. Move along.

[Pottsey]

the answer is here Blue Eyes - The Hardest Logic Puzzle in the World - Solution for anyone interested

or "an" answer

That solution seems very flawed to me. I just cannot see a way for that solution to work. Well it works with low numbers but not the numbers we are given.

 

EDIT:

The more I think about it the more the solution seems wrong. According to the logic in the solution everyone will leave thinking they have blue eyes even if they have not.

 

I understand how the solution can work with low numbers, but say there are 11 blue eyed people. That means each blue eyed person see 10 other blue eyed people. No one can leave as they all see 10 other people with blue eyes. So the 11th person has no idea if their eyes are blue, red, green or whatever.

Edited June 4, 2009 by Pottsey

[Jamo]

That solution seems very flawed to me. I just cannot see a way for that solution to work. Well it works with low numbers but not the numbers we are given.

 

It does work with any numbers, but to explain why would give the puzzle away!

[rolfea]

Don't know what you're talking about. Edits to correct my answer once I'd actually worked it through in full, none here. Move along.

 

I don't know what your on about, I looked at the answer so I know I was wrong, and my answer was the same as yours!

[Pottsey]

Could someone explain via PM?

[tmcd35]

I've read the solution. It makes perfect sense to me - never would have come up with the answer in a million years! But, I'm now left feeling very sorry for the Guru...

[gibbo_ap]

cummon tis the ferry master, he leaves every night

[keithu]

But, I'm now left feeling very sorry for the Guru...

 

And the brown-eyed people; they're not going anywhere either.

[tmcd35]

cummon tis the ferry master, he leaves every night

 

Thank you, it never says anything of the sort, but makes me feel better none the less. lol.

 

And the brown-eyed people; they're not going anywhere either.

It never says what the guru does after the first people leave. It does say that the guru is allowed to speak once per day. The guru only has to say the wrong sentance, "I see brown eyes", for instance.

 

The guru on the other hand has different colour eyes to everyone else and no way of finding out what colour they are

Edited June 4, 2009 by tmcd35

[_Bat_]

Thank you, it never says anything of the sort, but makes me feel better none the less. lol.

 

 

It never says what the guru does after the first people leave. It does say that the guru is allowed to speak once per day. The guru only has to say the wrong sentance, "I see brown eyes", for instance.

 

The guru on the other hand has different colour eyes to everyone else and no way of finding out what colour they are

 

No, the guru can only speak once ever.

 

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island.

[rolfea]

No, the guru can only speak once ever.

 

this looks true.. which means the answer i read is not possible, so anything is back in the question!

 

Edit, re-read it and it works again!

 

And no, its not the ferry man

Edited June 4, 2009 by rolfea

[Jamo]

this looks true.. which means the answer i read is not possible, so anything is back in the question!

 

Because the guru can only speak once the solution is possible.

[rolfea]

It is possible yea, just had to re-read the solution.

 

I did edit my post afterwards haha

 

Good luck anyone trying to work it out though, the solution is almost as hard to work out as the puzzle!