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01 November 2009 @ 04:39 pm
I was cleaning up some old junk from boxes in my house, and came across this puzzle I was given in 1993.

Once upon a time, there lived 800 green-eyed people and 200 blue-eyed people on an island. No one on the island knew their own eye color, nor did they know the exact number of blue and green eyed people on the island. There was a local taboo against talking about eye color (which the citizens never violated), and there were no reflective surfaces on the island. There were absolutely no physical means for a person to determine his or her own eye color. The citizens on this island were all firmly committed to the belief, however, that if a person could figure out that he or she had blue eyes by using logic, the person had to commit suicide at midnight of that day.

Every day at noon, the citizens met in the town square to stare lovingly into each other's eyes. All was happy and gay. Then one day, day 0 to be exact, an oracle descended upon the island from the heavens and announced during the noontime meeting, "There are blue-eyed people on this island." The citizens promptly stoned and killed the oracle.

What happened after that day, and why? (Notice that the oracle said something all the citizens already knew.)

Enjoy. :)
Who, me?metageek on November 1st, 2009 11:45 pm (UTC)

Suppose I were a citizen of that island, and suppose some there were some predicate that could take the information available to me after the oracle's visit and prove that I had blue eyes.

But the oracle didn't introduce any new information, so that predicate would have offered the same proof before the oracle's visit. Since nobody committed suicide before that, nobody did afterwards, either.
(Anonymous) on November 2nd, 2009 02:27 am (UTC)
The oracle changes the situation.
(Anonymous) on November 2nd, 2009 02:39 pm (UTC)
perhaps upon making the statement, the oracle caused everyone to look at the nearest blue eyed person's near them and so you'd all of a sudden have 4 people in a particular vicinity looking at the same person and that person realizing "oh crap, they're looking at me because i have blue eyes!"

so all of the people who got stared at for even that short while knew they had blue eyes and committed suicide.
fuhm on November 2nd, 2009 03:33 pm (UTC)
It's a logic puzzle, not a riddle. So, no, nothing like that.
François-René Rideaufare on November 24th, 2009 11:40 pm (UTC)
It's just a variant of the classic problem of the "cheating wives", except with blue eyes instead of cuckold husbands.

Hint: the Oracle makes into Common Knowledge what was previously only Shared Knowledge. Grab your nearest course on epistemic logic.