Behind Blue Eyes...
Alternate Title: Brown-eyed girl.
Sorry to disappoint you guys, (or in a few cases a...ppoint? i don't if that's how that word works), but this entry is about math, not music.
Or, more accurately, it's about logic. Which is just math, but with more numbers.
So, I recently rediscovered the blue eyes puzzle, in all of its mystical wonder.
The problem goes a little something like this: (quote stolen from Randall Munroe. Please don't sue me.)
The answer to this problem is a lot harder to find, and a lot weirder than you would initially think. Think about it for a while, if you solve it before you crack and look at the spoiler below then you're one of the best logicians in the world. Good job.
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. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. 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. Everyone on the island knows all the rules in this paragraph.
On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). 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 him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.
The Guru is allowed to speak 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 who has blue eyes."
Who leaves the island, and on what night?
All 100 blue eyed islanders will leave on the 100th night after the Guru speaks.
I can hear you through your computer screen.
"What!?" you say, speaking aloud instead of typing like a normal person. "This Eeko guy doesn't make any sense? He's terrible at logic!"
Well, you're right. I'm not making any sense, and I'm pretty bad at logic. But it's still right.
However, this is not actually what this entry is about.
This entry is about the follow up question:
"What new information did the Guru give?"
This question is a little easier to find, but a little harder to prove definitively.
When you think about it, the Guru doesn't seem to give any new information. I mean, everyone one on the island can see blue eyed people, so why does having the Guru say it change anything?
So here is my challenge to you guys and girls.
Answer the above question.
It's much easier to solve it than the first question. (I was able to after much thought and a little hair pulling.)
I'll post the answer tomorrow.
Or maybe the day after, to give y'all more time.
I thought it was fun to work through, so you should give it a shot.
P.S. I think this is the most words I've had in a blog post before. Woohoo.