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: 3 Hats  ( 6366 )
« : May 14, 2007, 02:06:41 PM From Shrinidhi»

3 Hats

There are 3 black hats and 2 white hats in a box. Three men (we will call them A, B, & C) each reach into the box and place one of the hats on his own head. They cannot see what color hat they have chosen. The men are situated in a way that A can see the hats on B & C's heads, B can only see the hat on C's head and C cannot see any hats. When A is asked if he knows the color of the hat he is wearing, he says no. When B is asked if he knows the color of the hat he is wearing he says no. When C is asked if he knows the color of the hat he is wearing he says yes and he is correct. What color hat and how can this be?

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« #1 : May 25, 2007, 11:52:51 PM From spazinvader»

Since A cannot answer the question,we can assume that there will not be white hats for both B and C.If so,then he would have answered it as yes.
Hence the possibility comes as (1 black,1 white) and (2 blacks).
Then by B,he cannot also answer the question.If this is the case then the possibility is C wearing black or white.
But if the hat of C is white then B could have judged that his should be black. Because this is the reason for which A cannot answer(1 white,1 black).

So the hat suits the head of C is black in either cases and so C can judge that.
« #2 : June 10, 2007, 12:24:29 AM From Shishir»

ans is white hat
reasoning: if possible let C wears black hat then 3 cases arises viz.
               1. w b; 2. b w; 3.w w
   1. in this case A sees 2 black hats & he could have guess his hat's color
   2. in this case B sees 2 black hats & he could have guess his hat's color
   3. in this case A's reply is no. So now B could have thought that had he wore a black hat A could have easily guessed his.......... hence he should have been definately be wearing a white hat 
« #3 : June 16, 2007, 10:13:38 PM From spazinvader»

How A could guess if there are two black hats on B & C?
There are totally 3 black hats and so his hat could be either black or white right?
« #4 : June 18, 2007, 10:04:58 AM From PSM»

guys the answer is black hat...........
now because doesn't answers the question means the possibility that B n C r wearing only white hat is cacelled.....this u know...
now three possibilities r their......(B,C) = (b,b) or (b,w) or (w,b)
now if u see if B would have seen that C is wearing white one then he would have answered that he is wearing black......right?
now because he cant answer it means C is wearing Black only right...
spazinvader u wee right earlier....
@shishir A is the only person who can see the other two hats .......B can see only one hat of C....and c cant see any hat....i think u leaved this fact......
« #5 : June 24, 2007, 01:58:48 PM From Varunendra»

A doesnt know wht hes wearin in three situations

1. B is black
   c is black

2. B is black
   c is white

3. B is white
   C is black

when B says he doesnt know what he's wearin the reasonin
behind it can be that A is wearin white then B will be
sure of which coloured hat he's wearin i.e black

But since he said that he dont know which coloured hat
he's wearin there is a possibility tht is in either
situation 1 or 3 which implies in both of them that C
is wearin black
« #6 : December 30, 2009, 04:23:35 PM From Joe»

Well i think the reason behind this is quite simple...
Lets start with the assumption that A knew what color hat he had (Black being the only possibility for this to be true). Now also assume that since A said a yes, B now knows that his hat color is White. Also since B has said that he knew the color of his hat , C now knows that his hat color is White. Now if we though of this reverse, if A and B didn't know the color, then the only alternate choice of color for C to choose was Black. Thus C said Yes and the color was black.

I hope i made sence  :P
« #7 : December 30, 2009, 04:40:04 PM From Nishan»

Ok i've got the right answer for this.

Person    P1    P2    P3    P4    P5    P6    P7
C             b      b      w     w     b       b      w
B             b      b       b     b     w      w      w
A             b      w      b     w     b      w       b

There are 7 probabilities. Only P7 probability is the one in which A, B and C would have said Yes.
Observe P3 and P4. If C where White, B would have for sure known that he had a black Hat
Observe P1, P2, P5 and P6. In all these possibilities of C being Black, B could have been Black or White (Hence he said No).
So the answer is Black. Cause the only possible color that C's Hat could have been was Black since both B and A don't know their hat colors.

TC people

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