(January 24th, 2013, 17:23)Jowy Wrote: @ The Island riddle:
Okay, I was not correct about the Guru speaking not giving any information. Without the Guru speaking, they can indeed tell that there are people with blue eyes, which is exactly what she says. But without the Guru saying it, the chain never starts. If there was just one with blue eyes, and there was no Guru saying that she sees blue eyes, then that one could not figure out that he has blue eyes, but if the Guru speaks, then he can. Basically, when there are 100 blue-eyed people, they are all the "100th" and have to wait until the 99th night before they know. Why? They see 99 others with blue eyes. But they could have brown eyes themselves, it's exactly what a brown eyed would see if there were only 99 blue-eyed. So if there were 99 blue-eyed, they would leave at the 99th night. But when they don't leave, it must mean that there are 100 blue-eyed people, and since you can only see 99, you are the 100th. Well, everyone with blue eyes is the 100th.
Everyone who has blue eyes knows from the beginning that there are either 99 or 100 blue-eyed people, and everyone who has brown eyes knows from the beginning that there are either 100 or 101 blue-eyed people. They know this, but to be SURE what color their OWN eyes are, they have to wait until the 99th or 100th night and see if people leave, then leave the next if they didn't.
(January 24th, 2013, 17:23)Jowy Wrote: @ The Island riddle:
Okay, I was not correct about the Guru speaking not giving any information. Without the Guru speaking, they can indeed tell that there are people with blue eyes, which is exactly what she says. But without the Guru saying it, the chain never starts.
If anyone knows the answer but is still stumped by why the guru's information actually counts as information despite it already being known by all the inhabitants of the island, you can think of it like this:
The guru is giving information to hypothetical people in the heads of hypothetical people in the heads of ... etc ..., who can look around and see that no one else has blue eyes. It turns out that these hypothetical people don't exist! But their nonexistence leads to their inaction in spite of the information the guru gives them, which tells the next level of hypothetical people that they have blue eyes. But these people don't exist either. One night at a time, the guru's information propagates up one level in the giant pyramid of people imagining other hypothetical people that see the previous level as brown-eyed, until finally it reaches the actual blue-eyed islanders.
(January 24th, 2013, 15:48)scooter Wrote: Here's a pretty simple one that I like (pretty likely some of you have heard it before):
You're in a dark room with 100 coins on a table, 12 are heads and the rest are tails, and the two faces are completely indistinguishable in the dark. How do you separate the coins into two piles so that the number of face up heads in each pile are equal?
(again, no dumb solutions like "turn the lights on")
Good one, must try that on some of my brighter students...
Take 12 coins from the main piln and form pile 2. Then flip those 12 coins.
In the main pile there are now 12 - n heads remaining (n being the number of heads you selected. n is random number [0-12])
Now in the 12 you selected there were n heads. You flip them, and get 12-n heads, which is equal to the main pile.
Say you took 10 tails and 2 heads, leaving 10 heads in main pile.
Flip those 12 and you get 10 heads and 2 tails.
About island puzzle
To find solution I reduced the problem to 5 islanders, 1 guru and 2 each with blue/brown eyes. Easy to imagine that the blue eyed girls will look at the other and think "If I have brown eyes then she is getting off tonight". So since noone gets off, both immediately deduces that they do not have brown eyes. Each person added adds one layer of deducion needed, and one day for things to work out. So 100 blues leave on day 100.
. I won't mention how long I spent on it...