Guessing hat colors

Question

Red or Black
There are 3 children sitting on three chairs. The children can only look forward and all wear one hat. The hats are either black or red. They are a total of 5 hats, 3 are colored red and 2 are colored black. The child on chair A says: "I don't know what color of the hat I have." Then the child on chair B says: "Also, I don't know the color of my hat." Then the child on chair C says: "In that case, I know the color of my hat."
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 +---+    +---+    +---+
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   A        B        C

The question is: What color of hat does the child on chair C have and why?
Bonus question: Do we also know the color of the hat of the child on chair A and the color of the hat on chair B?

Joe Z. · Accepted Answer

If A doesn't know the colour of his hat, then at least one of B and C must be wearing a red hat, because if they were both wearing black, then A would know immediately that he was wearing a red one.

B knows this as well. But if C were wearing a black hat, then B would know that she was wearing a red one because of that. So since B doesn't know, C must be wearing a red hat.

C knows this as well. So C knows that his hat is red.

As for the bonus question, no, we cannot know what colour hat either A or B is wearing. All else we can deduce from the problem is that at least one of B and C is wearing a red hat, but C wearing a red hat fulfills that already, so B could be wearing either colour of hat. And in general, nobody can know what A's hat's colour is, since nobody can see it. So all four arrangements where C wears a red hat are possible.

SQB · Answer

With three children (Alice, Bob, and Carol), three red hats and two black hats, there are 7 different configurations possible (with knowable hats boxed):
$$begin{array}{cccl}
text{Alice} & text{Bob} & text{Carol} 
 hline
text{red}   & text{red}   & fbox{red}   & text{(1)} 
text{black} & text{red}   & fbox{red}   & text{(2)} 
text{red}   & text{black} & fbox{red}   & text{(3)} 
text{black} & text{black} & fbox{red}   & text{(4)} 
text{red}   & fbox{red}   & fbox{black} & text{(5)} 
text{black} & fbox{red}   & fbox{black} & text{(6)} 
fbox{red}   & fbox{black} & fbox{black} & text{(7)} 
end{array}$$
If Alice sees two black hats (7), she'll know the black hats have been exhausted and she is wearing a red one. Since Alice knows the colour of her hat, Bob and Carol will know that they are both wearing black hats, since this is the only configuration that allows Alice to know her hat's colour.
If Alice sees at least one red hat, she doesn't know the colour of her own hat and will state so. Now if Carol is wearing a black hat (5, 6), Bob will know the colour of his hat, since Alice has seen at least one red hat and Carol's hat isn't it, so his must be. When Carol hears that Bob knows the colour of his hat, she can deduce that her hat is black, or else Bob wouldn't have known.
If Carol is wearing a red hat (1, 2, 3, 4), Alice won't know the colour of hers and neither will Bob know the colour of his, because all he can see is that Carol is wearing a red hat, but he will not know whether Alice saw two red hats or just one.
As we can see, Carol will always know the colour of her hat, while Alice will almost never know.

Alternative table using the new Markdown table formatting. Knowable hats are in all caps.

Alice
Bob
Carol

red
red
RED
(1)

black
red
RED
(2)

red
black
RED
(3)

black
black
RED
(4)

red
RED
BLACK
(5)

black
RED
BLACK
(6)

RED
BLACK
BLACK
(7)

Ashik Bekal · Answer

The possibilities are :

RED   RED   RED   : A won't know for sure, B know either B or C or both have RED but isn't sure, but C is sure he has RED since both declined.
RED   BLACK BLACK : A knows for sure since rest have Black Hats. B knows too. So does C.
RED   RED   BLACK : A won't know for sure, B know either B or C or both have RED  hence is sure since it sees a BLACK Hat ahead
RED   BLACK RED   : A won't know for sure, B know either B or C or both have RED but isn't sure, but C is sure
BLACK BLACK RED   : A won't know for sure, B know either B or C or both have RED but isn't sure, but C is sure
BLACK RED   BLACK : A won't know for sure, B know either B or C or both have RED  hence is sure since it sees a BLACK Hat ahead
BLACK RED   RED   : A won't know for sure, B know either B or C or both have RED but isn't sure, but C is sure

Implies 1,4,5,7 are the possible cases/.

Nai · Answer

As A doesn't know which color his hat is, B & C's color are not the same. (means [B != Black] OR [C != Black]) 
If C's hat color [Black], according to A said, B would think his is [Red] definitely. 
But B said he doesn't know; C's hat color is not [Black].

So the color of hat the child on chair C have is RED.

To answer the Bonus question: 
If C is wearing Black, we might be able to find out B's hat color is not Black; RED. 
But as the above solution; C's color is RED, so A cannot know the answer if B is also wearing RED. With that case, B also cannot know which color he is wearing when C's color is RED and A color can be RED.
I think no one can answer this as no one can know hat color of A and B.

Guessing hat colors

Red or Black

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Alice	Bob	Carol
red	red	RED	(1)
black	red	RED	(2)
red	black	RED	(3)
black	black	RED	(4)
red	RED	BLACK	(5)
black	RED	BLACK	(6)
RED	BLACK	BLACK	(7)