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Friday night Brain teaser

C

calbear2000

Golden Member
I heard this riddle back when I was in Berkeley... apparently not too many people have heard it, so this should be fun:


> There are 100 people on an island. These 100 people
> can't speak or
> communicate with each other in any way. 10 of them
> have blue eyes and 90 of
> them have brown eyes. But there are no mirrors or
> anything so no one knows
> if he/she is blue or brown-eyed. Then an ultimate
> being comes to the island
> and tells them that when each blue-eyed person finds
> out he/she has blue
> eyes, he/she must kill themselves that night at
> exactly midnight. The 100
> people are also very obedient so they will do as
> they are told The
> ultimate being doesn't tell them how many people on
> the island have blue
> eyes though. He just tells them that each blue-eyed
> person will kill
> himself when he finds out he has blue eyes.
>
> So what happens?
 
Something happens!


In response to Mani's Q in the other thread, assume these guys are drones and have no emotional reactions. So they can't communicate at all.

 
So the ultimate being says nothing more to them than, "When you find out you're blue-eyed, you must kill yourself at exactly midnight." Is that right?
 


<< So the ultimate being says nothing more to them than, "When you find out you're blue-eyed, you must kill yourself at exactly midnight." Is that right? >>



Correct.

BTW, the 100 people are smart enough to count.
 
The people look around, see that there's 90 brown eyes and 9 blue eyes, so they figure it's gotta be a nice number like 10, so they just figure they're blue-eyed. 🙂
 


<< dude tell me the answer so i can sleep >>



I'll pm it to you... I'd like to see if someone can get it in this thread though
 
If they haven't been able to figure out if they have blue or brown eyes in all the time they've been on the island, I see no reason why they'd all of a sudden get really creative just to kill themselves.
 
Solution: Don't read if you want to figure it out for yourself.



1. If only one person on the island has blue eyes then he can look around and see 99 pairs of brown eyes. Therefore, he knows that he must be the one with the blue eyes and kills himself that night.

2. If two people have blue eyes, then each can look around and see the other person's blue eyes along with the remaining 98 pairs of brown eyes. They both go to sleep that night thinking that the person they see with blue eyes will kill himself like in situation 1 above. However, when both wake up the next morning and see that the other person with blue eyes didn't kill himself, then they know that they themselves must have blue eyes also and therefore both blue-eyed people kill themselves on the second night.

3. If three people have blue eyes then the above reasoning can be used again except now two nights will pass and the three blue-eyed people will kill themselves on the third night.


So in general, all the blue-eyed people will kill themselves on the nth night where n is the number of blue-eyed people on the island.
 


<<

<< very good shooters >>


Thanks, but I must confess I've heard this puzzle before.

G'nite all. >>



At least you have the integrity to admit it 🙂

 
I've heard a variation to this riddle and I've been telling various friends this riddle for over 6 years and not one person in those 6 years has been able to solve the riddle.

This is a VERY tough riddle and if you can figure this one out by yourself, then you're brighter than anyone I've ever met. 🙂
 


<< I've heard a variation to this riddle and I've been telling various friends this riddle for over 6 years and not one person in those 6 years has been able to solve the riddle.

This is a VERY tough riddle and if you can figure this one out by yourself, then you're brighter than anyone I've ever met. 🙂 >>



A group of my friends got this... but these guys were CS gurus (it helps to think recursively) and plus we acted it out 🙂 But yeah, I've also never encountered anyone who got it completely right on their own without any hints. Its a tough problem.

Its a very cool riddle once the solution is understood
 
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