

Terry Tao: The blue-eyed islanders puzzle - kkim
http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/

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cawel
Yay, I believe the narrative on that one was poor. It lacks some details and
makes you ask yourself lots of questions that are not actually part of the
enigma.

xkcd has the same enigma, with a better wording (with no ambiguities):
<http://xkcd.com/blue_eyes.html>

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yters
Seriously, the author says there are 2 "plausible" arguments. Obviously, he
got it wrong the first time and won't let it go!

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aston
Well, the problem is fundamentally that the people should've been playing the
game before anyone said anything, so there's some confusion as to why the game
only starts when the guru mentions a fact that's already self-evident.

That's a problem in both the grandparent link and xkcd's story.

~~~
zoltz
That's exactly the interesting point here: the foreigner states something
self-evident (there is someone who has blue eyes), and yet it will kill all
blue-eyed people, who would otherwise have been fine. Without the foreigner,
the inductive chain cannot start at n=1.

~~~
aston
Also, this problem isn't solved by induction. It's solved by recognizing the
pattern. You don't need to establish the base case via the outside observer.
All you need to know is that the day-based formula works for any number of
islanders.

It'd be like proving x^2 - 1 = (x+1)(x-1) for all x by starting with 1 and
walking up the integers... Which is to say, not a bad way to prove it, but not
necessary when you can logic it out otherwise.

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DaniFong
Since consensus seems to elude the discussion here, I've made a bit of effort
to distill the analysis.

If you don't want to spoil it, don't follow the link.

[http://daniellefong.com/2008/02/10/blue-eyed-islanders-
now-i...](http://daniellefong.com/2008/02/10/blue-eyed-islanders-now-in-
puzzle-format/)

~~~
zoltz
I agree with you that the original wording should have rigorously ensured
_common knowledge_ among the islanders _of their logicality and devoutness_ ,
since common knowledge (of a different fact) is what the puzzle is about. But
that's a subtle point and not the source of the previous disagreements here.

~~~
DaniFong
I don't know about _should have_. The subtle ambiguity in the wording is what
makes this version of the problem interesting.

