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Blue Eyes Logic Puzzle

math.ucla.edu

1–10 of 94 posts

Re: Blue Eyes Logic Puzzle

#3

Randall Munroe has a much more thorough write-up on (a variation on) this puzzle: http://xkcd.com/solution.html (Though you might want to click his link to the problem description first since his is a variation.)

And for an even more detailed examination of the underlying philosophical issues:

http://en.wikipedia.org/wiki/Common_knowledge_(logic)

http://plato.stanford.edu/entries/common-knowledge/

Re: Blue Eyes Logic Puzzle

#4
Taking the 'dramatic effect' argument further: if all the blue-eyed people kill themselves, would the brown-eyed people all simultaneously know they have brown eyes and also have to kill themselves?

Re: Blue Eyes Logic Puzzle

#5
Here is the part that people seem to miss:

> If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness.

Emphasis mine, of course.

You can think of this clause as specifying the clock speed (one cycle per day) of the logical machine that is the island.

Re: Blue Eyes Logic Puzzle

#8
post #4

Taking the 'dramatic effect' argument further: if all the blue-eyed people kill themselves, would the brown-eyed people all simultaneously know they have brown eyes and also have to kill themselves?

This is the missing element from most explanations I see of this problem. We all look at the n cases from the POV of a blue-eyed person. An outside observer with brown eyes has the same level of information available to him, so it seems to me just as likely that after the first day, each person, regardless of eye color, could reason that nobody left the previous day, so the visitor must have been referring to me. So either eventually everyone dies, or they all realize the paradox and forgo the ritual.

Re: Blue Eyes Logic Puzzle

#9
I think the foreigners statement is ambiguous enough to render the proof in argument 2 incorrect. "... another blue-eyed person", to me, implies a singular person in the tribe has blue eyes. All of tribespeople will see multiple tribespeople with blue eyes, and therefore assume the foreigners statement was wrong, rendering no effect.
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