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Author Topic: Blue Eyes - spoiler thread for those who know the solution.
The Famous Druid

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Icon 1 posted February 16, 2009 10:51      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
WARNING - Don't read this unless you want to see spoilers for the 'Blue Eyes' logic puzzle.
WARNING - Don't read this unless you want to see spoilers for the 'Blue Eyes' logic puzzle.
WARNING - Don't read this unless you want to see spoilers for the 'Blue Eyes' logic puzzle.

Ok, I've read the solution

I don't understand the role of the Guru in this.

Presumably, if The Guru had said "I can see someone who has brown eyes." then all of the brown-eyes would have left.

But everyone on the island knows that The Guru could have said either, so why does it matter what she said? Why did she have to say anything at all?

--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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Ashitaka

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Icon 1 posted February 16, 2009 11:45      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
SO the question really is, "what information did the guru give out"

I think, the information she gave out, was not so much a fact,but a point for the logicians to start counting from.

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"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

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Ashitaka

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Icon 1 posted February 16, 2009 11:49      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
spoilers- spoilers
spoilers- spoilers
spoilers- spoilers
spoilers- spoilers

SO I understand (sort of ) the logic of the answer for 1 2 and 3 people, but I want to know if anyone can point me to a mathmatical proof for n=x, where to say that for any given number of blue eyed people, they will leave on day n.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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The Famous Druid

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Icon 1 posted February 16, 2009 12:52      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.
Spoilers.

I've had a bit more of a think...

The solution given would work equally well for the brown-eyes, but you need to be playing one game or the other, it won't work if you're playing both at the same time.
The Guru's statement is not so much a point to start counting from, as an indicator of which game they're playing.

quote:
Originally posted by Ashitaka:

SO I understand (sort of ) the logic of the answer for 1 2 and 3 people, but I want to know if anyone can point me to a mathmatical proof for n=x, where to say that for any given number of blue eyed people, they will leave on day n.

Here goes...

Assuming we have N blue-eyed islanders...

When the Guru speaks, everyone counts how many blue-eyed islanders they can see, call that X.
If you have blue eyes, you'll see X=N-1.
If you have brown eyes, you'll see X=N.

You then wait X nights, and see if there are any blue-eyes left. This means the blue eyes will wait N-1 nights, and the brown eyes will wait N.

On the morning after the N-1th night, the blue-eyes know their value of X is the same as all the other blue-eyes, so they can deduce their own eyes must also be blue. The brown eyes are still waiting till tomorrow to be able to make that deduction.

--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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Ashitaka

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Icon 1 posted February 16, 2009 13:13      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
sort of double post, clow internet and I click twice.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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Ashitaka

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Icon 1 posted February 16, 2009 13:14      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
spoilers and such, spoilers and such, spoilers and such...


TFD, good point. Hadn't thought of that.

after reading that, I had just thought on the first day there would be 100 pissed off bown eyed people on the island (becuase they are playing the "blue eyes" game). Then I realized, none of them are going to realize that they don't have blue yes until 100 people leave.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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The Famous Druid

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Icon 1 posted February 18, 2009 18:09      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Um, in the process of typing my little bit of brilliance, I spotted the obvious logical flaw.

I still reckon the official solution is wrong, I just need to polish my reasoning a little.

--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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Agburanar
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Icon 1 posted February 21, 2009 16:01      Profile for Agburanar     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
Um, in the process of typing my little bit of brilliance, I spotted the obvious logical flaw.

I still reckon the official solution is wrong, I just need to polish my reasoning a little.

I'm feeling like I did when I first saw a 1=2 proof - there's a series of perfectly logical steps that reach an illogical conclusion. I just can't quite get where it's wrong.
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