# Lunchtime Logic Puzzle

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• 4th June 2009, 01:11 PM
_Bat_
Lunchtime Logic Puzzle
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.

Quote:

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."
• 4th June 2009, 01:44 PM
rolfea

Edit: Found the answer I was wrong

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

• 4th June 2009, 02:14 PM
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!! ;)
• 4th June 2009, 02:15 PM
gibbo_ap
the person running the ferry, and every night
• 4th June 2009, 02:27 PM
gibbo_ap
te other way to look at it logically is by reading a few bits
Quote:

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
• 4th June 2009, 02:27 PM
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.
• 4th June 2009, 02:35 PM
gibbo_ap
Quote:

Originally Posted by jamesb
All of them, that night.

Except the Guru.

i was wondering about her too, tho goin by my reasoning she also has perfect logic
• 4th June 2009, 02:35 PM
rolfea
thats what I thought, but supposedly i'm wrong

which (logically) makes you wrong
• 4th June 2009, 02:49 PM
jamesb
Quote:

Originally Posted by gibbo_ap
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.
• 4th June 2009, 02:50 PM
jamesb
Quote:

Originally Posted by rolfea
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. :D
• 4th June 2009, 02:55 PM
Pottsey
Quote:

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

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.
• 4th June 2009, 03:11 PM
Jamo
Quote:

Originally Posted by Pottsey
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!
• 4th June 2009, 03:18 PM
rolfea
Quote:

Originally Posted by jamesb
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. :D

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!
• 4th June 2009, 03:22 PM
Pottsey
Could someone explain via PM?
• 4th June 2009, 03:24 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...:(
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