A Tale Of My Hat!

Casework (3 cases): If you see two black hats, your hat is obviously white.

If you see one black and one white hat, the person wearing a white hat would know his hat color if yours was black. Since he didn't guess anything, your hat must be white.

If you see two white hats and your hat was black, then the people with white hats would both see one black and one white hat. They would think that since nobody answered immediately, they must be wearing a white hat themselves which would cause the other white hat person to not be able to guess their own hat. This would let both of them to be able to guess their hat color, which contradicts the premise saying that the others can't deduce the color of their hats. Therefore, your hat color must be white.

Let the three people be A, B and me . B is unable to determine the colour of his own hat. This means that both I and C cannot wear a black hat, otherwise he would've known that he was wearing a white hat. Similarly C is unable to determine the colour of his hat. This means that both I and B cannot wear a black hat. However B also knows that C is unwilling to say anything about his own hat. This means that B knows that he and I are not both wearing a black hat. This means that were I wearing a black hat, B would have come to know that he is wearing a white hat. But he is unable to determine anything. So I am wearing a white hat. Yippee!!

Let's do it using Binary values

Let '0' represent the white hat and '1' represent the black hat.

So, now we have three heads, three zeros for white caps and two 1's for black caps. Hence the possible combinations can be written as:

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

Now consider the first case: Here I can see that two people are wearing white hats so I could have dawned the remaining white hat or one of the two black hats, I am not sure. Similarly, prove this for other cases.

Except the "Case 6": Here I can see that the two logicians are wearing the black hats so all the black hats are consumed and hence I could only be wearing white hat. Hence the answer is white hat as deduced from case 6.

me 2nd 3rd

b b w Straight forward case where 3 can guess that his hat color is white. b w b Straight forward case where 2 can guess that his hat color is white. b w w Tricky one. A person who sees one black and one white can deduce that his hat color is white if the other person is silent. So all the scenarios where the person wearing black is eliminated since none of the others are able to guess their hat color. So my hat color is white. w w w w b b w b w w w b

Assume for the sake of contradiction that you are wearing a black hat. Then, we need only consider two cases:

1. Exactly one of the other two people is wearing a black hat. Let's call him $B_1$ , and we'll call the other guy $W_1$ , since he's wearing a white hat. Then, $W_1$ will see two black hats–one on $B_1$ and one on you. Since there are only two black hats, $W_1$ realizes he must have a white hat, and he guesses correctly.

2. Both of the other two people are wearing white hats. Let's call them $W_1$ and $W_2$ . When $W_1$ doesn't say anything immediately, $W_2$ realizes that he must not be wearing a black hat (if he were wearing a black hat, $W_1$ would have guessed "white" immediately), and he guesses correctly. Of course, $W_1$ could use the same logic to guess the color of his own hat. Either way, someone's going to guess correctly.

Since there are only two black hats, you may now triumphantly shout out "White!" and win the challenge.

it takes only a bit of common sense to deduce that............ one can only deduce what color is he wearing when he sees two other black hats and realizes that there were only 2 black hats and hence the color of his hat must be white then! surely the other two see a black and a white hat and are left guessing as to which color should they say!

let the three ppl be X,Y,Z ( i m Z ) .... if will be using the same order in the rest of solution. for example : ( W,W,B) means that X and Y are wearing White hats , and I am wearing Black hat

case 1 : ( B,B,W)

I can clearly say that I am wearing Black hat

case 2 : ( B,W,B) or ( W,B,B)

in this case, at least either one of X and Y will be able to tell the color of his own hat

case 3: (W,W,B)

at first , X and Y will not be able to guess the color of their own hats. Then , X will deduce that his own hat's color must be white because otherwise Y could have easily found out his own hat's color

case 4 : ( W,B,W) // same reasoning for ( B,W,W)

in this case , X will come to know that his own hat is white because if X was wearing a Black hat , then Z could have easily guessed his own color

case 5: ( W,W,W)

since neither X nor Y was able to give any answer, this case must be different than all the case listed above, which means that all the three are wearing White hats

It is one of the traditional puzzle: http://en.wikipedia.org/wiki/Prisoners and hats_puzzle

lets say "me" is wearing black...then there are only 2 possible cases. person A is wearing black and person S is wearing white, or both wearing white. If one is wearing black, other one will yell. If both are wearing white, "A" will think if I was wearing black, "S" would have yelled and so I am wearing white and thus both "A" and "S" will yell they are wearing white. Hence "me" cant be wearing black and is wearing white. And as "A" and "S" think like "me", and neither "A" or "S" yells means neither of them are wearing white. (as "me" sees 2 blacks and "A" and "S" see 1 black and 1 white and thats why "me" yells and not "A" or "S"). So as soon as "me" yells white, "A" and "B" will yell black.

Well thats what I think how it should end up.

1) white/total =3/5

2) black/total = 2/5

1 > 2... so, white.. This the way i think. coz, there is no other way to know the color before before placing the hat on your head. you can deduce the color by judging the colors of other two hats only when you are in that situation. but, in this story or problem there are no info about which might be the other two hats.. so, i think using mathematics is the only way to find out the ans here, because here you have to just click on an answer.!

It says "you see the others can't deduce the color of their hat or are unwilling to guess... " .. So , I thought that i would have been wearing A white hat and i saw that the other 2 are wearing the white hat . The third person would have been in the same situation in which I was . So , I was sure that I was wearing a white hat .

it is said that you can deduce the colour of your hat.this means that the other two people are wearing black hats in which case you are wearing a white hat(given there are 2 black hats,3 white hats and 3 people).