My God..... It's full of stars
There are 4 men, Zaux, Wizard of Oz, Cam and Rajesh Lal, all buried up to their necks in the ground. They cannot move so can only look forward. Between Zaux and the Wizard of Oz is a brick wall which cannot be seen through. They all know that between them they are wearing 4 hats, 2 x black and 2 x white, but they do not know what colour they are wearing. In order to avoid being shot one of them must call out to the executioner the colour of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out.
There are no outside influences nor other ways of communicating. They cannot move and are buried in a straight line. So Zaux and the Wizard of Oz can only see their respective sides of the wall, Cam can see the Wizard of Oz, and Rajesh Lal can see the Wizard of Oz and Cam.
After 1 minute, one of them calls out.
Question: Which one of them calls out?
Question: Why is he 100% certain of the colour of his hat?
- Karl Sharman
There are no outside influences nor other ways of communicating. They cannot move and are buried in a straight line. So Zaux and the Wizard of Oz can only see their respective sides of the wall, Cam can see the Wizard of Oz, and Rajesh Lal can see the Wizard of Oz and Cam.
After 1 minute, one of them calls out.
Question: Which one of them calls out?
Question: Why is he 100% certain of the colour of his hat?
- Karl Sharman
Labels: SharedPuzzle
posted by ToM at
10:46 AM
13 Comments:
This post has been removed by the author.
This post has been removed by the author.
I think the question got changed from when you first posted. I've deleted my other posts because my guessed arrangement was no longer correct.
So the arrangement that I think was intended is:
R->C->W->¦Z->
If C and W had the same coloured hats, R would have been able to call out immediately. As he didn't, C and W must have different coloured hats. C being smart, will realise that he has the "opposite" colour to W and so can call out.
The question is still set incorrectly, because Z cannot see the wall, but you say he can.
I agree with Chris.
Why did I have to be separated from the other guys ... I swear I used deodorant and took a bath less than a week ago ... heh heh.
Yep ... C gets the privilege of being the caller.
I'm a little upset that I can't see the wall ... unless I am either buried facing the wall, or the executioner breaks my neck and rotates my head ... OUCH!
Given:
-Raj can see Wiz's hat and my hat
-I can see Wiz's hat
-Zaux and Wiz see no hats
If both my hat and Wiz's hat are the same, Raj should know that the only 2 remaining hats are of opposite color, one of which he is wearing, and should call out the opposite of Wiz's hat.
I then assume that Raj isn't suicidal or trying to get everybody killed, and additionally assume that Raj, being a bright fellow, would be able to quickly deduce his own hat color if both Wiz and my hat were the same color.
I thus deduce that my hat color must be different from Wiz's. Usually I would play it safe, and wait for 8 minutes, just in case Raj is having a slow day, and to perversely enjoy watching everyone sweat, while the clock forecasting the groups impending doom was ticking down. However, this day I am in a big hurry and shout out the color opposite from Wiz's hat after only 1 minute.
I then rush off to my appointment, without taking time to perform an exiting bow. All in a days work.....
Cam
For the survivors of this cruel experiment...
The "seating" arrangement was as follows - R->C->W->¦<-Z, and in my defence, I did say they were facing forward, not necessarily in the same direction.... Although I shall re-word the question to ensure Zaux faces the wall next time!
The answer:-
Cam calls out that he is wearing a black hat. He is 100% certain of the colour of his hat because, after a while, he comes to the realization that he must answer.
This is because Rajesh Lal can't answer, and neither can Zaux or the Wizard of Oz.
Rajesh Lal can see Cam and the Wizard of Oz, but can't determine his own hat colour. The Wizard of Oz can't see anyone and also can't determine his own hat colour. Zaux is in the same situation as the Wizard of Oz, where he can't see anyone and can't determine his own hat colour.
Since Zaux, the Wizard of Oz, and Rajesh Lal are silent, that leaves Cam. Cam knows he is wearing a black hat because if Rajesh Lal saw that both the Wizard of Oz and Cam were wearing white hats, then he would have answered. But since Rajesh Lal is silent, Cam knows that he must be wearing a black hat as he can see that the Wizard of Oz is wearing a white hat.
Hi Zaux. There isn't nough information to say what the actual hat colours are
Chris ...? I didn't post this one. Hope I'm wearing a cool hat!
Hmmm ... seems I'm always facing forward ... unless my positioning is in relation to another object.
Sorry Zaux, I've just gotten used to you being the poster.
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