There are 3 black hats and 2 white hats in a box.?

Question

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?

Answer 1

Black. This only works if you assume that the three men are intelligent, and that each one knows not only that there are three black hats, and two white hats, but that the other two guys are also intelligent.

When A looks at B and C, he doesn't know the colour of his hat. This can only happen if at least one of the hats is black, because if both were white, A would know that there are no more white hats and thus he was wearing a black hat.

Since A did not know, B knows that there is at least one black hat on the heads of himself (B) and C, but he doesn't know the colour of his hat. This can only happen if C has a black hat on, because if C had a white hat on, knowing that either himself or C had a black hat on, would allow B to know that he had a black hat on. Since he doesn't know this, C must have a black hat on.

C listened to the first two people, made the same logical deductions that I just made, and knew that he was wearing a black hat.

OMG, someone actually copied my answer and used it for her own. Are you that sad and in need of 10 points?

Answer 2

Black. This only works if you assume that the three men are intelligent, and that each one knows not only that there are three black hats, and two white hats, but that the other two guys are also intelligent.

When A looks at B and C, he doesn't know the colour of his hat. This can only happen if at least one of the hats is black, because if both were white, A would know that there are no more white hats and thus he was wearing a black hat.

Since A did not know, B knows that there is at least one black hat on the heads of himself (B) and C, but he doesn't know the colour of his hat. This can only happen if C has a black hat on, because if C had a white hat on, knowing that either himself or C had a black hat on, would allow B to know that he had a black hat on. Since he doesn't know this, C must have a black hat on.

C listened to the first two people, made the same logical deductions that I just made, and knew that he was wearing a black hat.

Answer 3

C is wearing a black hat.

Because:
A did not know what color of hat he was wearing so B and C had to either be wearing 1 black and 1 white or 2 black hats.
B knew that and still did not know what he was wearing because he saw a black hat.

Answer 4

C is wearing a black hat.

B and C either have both black, or one black and one white. If they were both white, then A would know that his hat was black.

Hearing A say no, B looks at C's hat. If C's hat was white, then B would know that his hat was black. But, since he doesn't know, then that means that C's hat is black (meaning B's is either white or black)

Answer 5

why do they might desire to be adult adult males =P jk properly, if B and C have been the two wearing white hats, then A might immediately be attentive to that his is black... in spite of the indisputable fact that, he would not be attentive to, so the two B and C the two have black hats or one black and one white. a minimum of one is black. B might desire to no longer easily say the two one because of the fact he can no longer see 2 hats. yet, if he had seen C wearing a white hat, he might have common that his became in all likelihood black. He pronounced no, so C knew the two A and B had white hats on, eliminatiing the opportunity of him getting one. Black hat. Or, he might have purely taken a random wager and picked the colour he became greater probable to get =P Now the question is, are they wearing something different than hats? If no longer, are they warm? =D jkjk PEACE OUT

Answer 6

BLACK. coz A can see B&C's hat and B can see C's hat
so when A is asked if he knows the color of his hat he said NO it means one of the two hats should be black(may be both are black) bcoz if both are white then the color of A's hat is black sure.
then B is asked if he knows the color of his hat he said NO it means C's hat is black.

Answer 7

black because
1) if A doesn't know his color B or C or both have to be wearing black. If B and C both had on white, he would know he wore black.
2) If B knows this and sees white on C then he would know he was wearing black, but he doesn't know, so he must see black on C

Answer 8

it took some tyme ta work out...But...C is wearin a blacc hat.

Method:

If B and C were both wearing Whyte hats, it would have been obvious to A that he was wearing a blacc hat....But they weren't..so, A didn't know what hat he was wearing..

So then B looked over to C.
if C was wearing a whyte hat, then B would know within himself that he was wearing a blacc hat...Because...if he was wearin a whyte hat too..A would have known that he was wearin a blacc hat and he didnt...
If B and C were wearing a blacc n whyte hat each...It would have made sense as to why A didn't know what he was wearing...BUT..in the question it states that B doesnt know what he is wearing either..meanin...if he sees C wearin a whyte hat, he would definetly know that he is wearin a blacc one...BUT because he saw C wearing a Blacc hat...it was impossible for him to know what hat he was wearin...

Havin heard all of this..C correctly came to the conclusion that he was wearing a blacc hat.

Answer 9

I have brown tresses and I have Blonde highlights. Maybe you should try lighter blonde, this might look better than brown, brownish just looks kind of trashy.

Answer 10

This is a nice old problem. One of my favorites from 5th grade. (Stumped the principal with it!) The answer is of course black as Eulercrosser described.