0
Akavall Posted 18 years ago
Jokes, Puzzles & Riddles

Blue Eyes Logic Puzzle

"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. If anyone has figured out the color of their own eyes, they [must] leave the island that midnight. 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."
"

http://xkcd.com/blue_eyes.html

It's a good puzzle. Unfortunetly, I thought that I misunderstood the puzzle and looked up the solution, but there is really enough information to solve the puzzle.
  

Top answer

0 The facts we have known are:02br 001. 02br 002. 02br 02br 00Then:02br 02br 00The one who was going to leave couldn't be the Guru herself, since no one had given her any information yet.

  • 0 The facts we have known are:02br 001.
  • 02br 002.
  • 02br 02br 00Then:02br 02br 00The one who was going to leave couldn't be the Guru herself, since no one had given her any information yet.
  • 02br 02br 00The ones who heard the Guru might have two kinds of thoughts, at most:02br 001.
  • Yes, I have seen blue eyes too.
Free · every Monday

Get the Weekly English Kit 📬

New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.

25 Answers
0
0 The facts we have known are:02br
001. The Guru said that she had seen some blue eyes.02br
002. Which made someone leave.02br
02br
00Then:02br
02br
00The one who was going to leave couldn't be the Guru herself, since no one had given her any information yet. It was someone who heard the Guru.02br
02br
00The one
0
0This riddle is hard to understand, let me try to clarify.02br
02br
001) There are 100 people with blue eyes and 100 people with brown eyes02br
002) When a person finds out the color of their eyes, they leave at night02br
003) They know that at least one person has blue eyes, the Guru said it at noon02br
004) All the people on the island ha
0
0 all of them left the island that night after the guru spoke to them thinking that he/she might be the one having the blue eyes but 'm not sure if the guru was left, i gues she was. 0-
0
0Nice try, but the people have to be 100% sure about the eye color they have in order to leave; they can't just leave if they only think their eye color is so and so.0-
0
0I GOT THE ANSWER02br
02br
00They all leave that night...02br
02br
00THEY ARE PERFECT LOGICIANS0-
0
0I have heard a variation to this riddle. Same set-up, except, the situation is a bit different.02br
02br
00There are people stranded on an empty island. They find and read a message that states "At least one person amongst the stranded has red eyes." The islanders now all know that at least one person DOES have red eyes. They can see the eyes of others, but not their own. Th
0
In the example with Red Eyes, from the perspective of any Red Eyed Person:

For 1 Red Eyed Person:
I know there is at least one person with Red Eyes.
I see no other people with Red Eyes.
Therefore, the Red Eyed person must be the one I cannot see (myself).
I leave on the first night.

For 2 Red Eyed People:
I know there is at least one person with Red Ey
0
A solution to this puzzle is there at

http://www.rawkam.com/?p=978
0
There seems to be a flaw in the puzzle. Maybe someone can explain it.

There are 100 people with blue eyes.
There are 100 people with brown eyes.
There is 1 person with green eyes.

The blue-eyed people see
99 people with blue eyes,
100 people with brown eyes,
and 1 person with green eyes.

The brown-eyed people see
99 people with brown eyes,

Related Questions