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Blue Eyes
Via xkcd.
Can you figure it out? I'll admit, I couldn't, but I wish I would've worked harder before I looked at the solution. The answer is very elegant, and it isn't any bullshit like they're blind or something. Like he says, it's not a riddle or lateral thinking puzzle, it's just a straight-up logic problem. So, do your worst. Also, please don't spoil it for others.
Can you figure it out? I'll admit, I couldn't, but I wish I would've worked harder before I looked at the solution. The answer is very elegant, and it isn't any bullshit like they're blind or something. Like he says, it's not a riddle or lateral thinking puzzle, it's just a straight-up logic problem. So, do your worst. Also, please don't spoil it for others.
Comments
Advice to the next guy: Read the puzzle and take a week to casually ponder it.
It's actually a really easy puzzle once you know it. As the note at the bottom says, this logic puzzle has roamed the world for ages. He just picked eye colours and an island. I've also heard the same logic puzzle with a line of prisoners all facing the same direction with either a green or a red hat on (or whatever two colours), and a version with a group of children where a certain number has dirty faces. It's quite simple once you know how to think. It took me some time to think up the proper method again and prove it to myself, but it didn't take me a week. MUAHAHAHAHA! That's what you get for studying Computer Science.
I do have to say she's a shitty guru. A real guru is wise and helpful, and would've said "I only see a person with blue eyes and a person with brown eyes." She's a bitch.
Two of the people (let's call them Rym and Scott), upon looking one another in the eyes, realise they could not bear to be seperated.
How, in keeping with the rules, should Rym ensure (with absolute certainty) they won't be seperated?
Note: This isn't difficult, and it is perhaps bending (albeit not breaking) the rules, but it is workable.
2. Eat Scott
3. ???
4. Profit
No! It's not useless, she has to say it for anyone to leave.I don’t understand how the guru’s hint gives the island people any more information then they already had. How does the hint start the hundred day count down?
What the guru does is bring the information into the realm of "common knowledge".
Consider a case with only two people having blue eyes. Before the guru said anything, if blue-eyed person #1 noticed there was only one other person (#2) with blue eyes, they would think "I know that someone has blue eyes". However, since from #1's point of view it's possible #1 doesn't have blue eyes, which would mean #2 doesn't see any blue eyes at all, #1 doesn't know whether #2 knows that someone has blue eyes. However, if the guru said "Someone has blue eyes", #1 can now think, "I know that #2 knows that someone has blue eyes".
Now, with that second bit of knowledge, the fact that the other blue-eyed person doesn't kill themselves on the first day means that #1 must deduce that they themselves have blue eyes.
In the case of 100 blue-eyed people, any given blue-eyed person #1 could before only say
"I know that #2 knows that #3 knows that #99 knows that someone has blue eyes"
but now they can say
"I know that #2 knows that #3 knows that #99 knows that #100 knows that someone has blue eyes"
That makes all the difference.