Blue Eyes Puzzle |
Wed, 11 October 2006 19:07 |
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Borrowed from here for your amusement and mental anguish. (btw the comic is good too )
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.
On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). Everyone on the island knows the basic rules -- everything in the first paragraph. 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 them their own eye color; it could be 101 brown and 99 blue. Or 100 brown, 99 blue, and the one could have red eyes.
The Guru speaks only 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 with 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, 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."
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Re: Blue Eyes Puzzle |
Fri, 13 October 2006 03:31 |
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Kotk | | Commander | Messages: 1227
Registered: May 2003 | |
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doh
[Updated on: Fri, 13 October 2006 03:32] Report message to a moderator
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Re: Blue Eyes Puzzle |
Thu, 19 October 2006 03:44 |
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mazda | | Lieutenant | Messages: 655
Registered: April 2003 Location: Reading, UK | |
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The maths behind the Monty Hall is very straightforward.
It is just that the answer is counter-intuitive (well for some it is).
You have the same problem with explaining Gamblers Ruin to most gamblers.
OTOH I'm not happy with this version of the blue-eyes/brown-eyes problem. In particular I'm not happy about the known initial conditions and the jump to the iterative process that says "on day one if no-one leaves the island ...".
I've seen a version of the problem where I thought it was phrased correctly, but this isn't it IMO.
M
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