Riddle courtesy of William Wu’s riddle archive.

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 could he know?

Hint: Write down all permutations of hats and test them against the way each man answered.

assuming they hear each other’s answer, it’s pretty simple. the only way a could know what color his hat is was if b and c were both wearing white hats. therefore, b and c are either both wearing black hats or one white and one black. b responded that he didn’t know either, that means that c had to have been wearing a black hat. if c had been wearing a white had, b would have known that he was wearing a black one, because they both could not have had white hates.

:p

I also assumed that each man could hear the other answers and came up with the same answer as you.

I’ve posted a harder riddle in this same vein. That one took me a while.

but what if A was wearing a white hat, B was wearing a black and C was wearing a black. then A wouldn’t know because he saw one of each, B wouldn’t know because he see’s a black, and doesn’t know if he has a black or a white because both are possible… then also C wouldn’t know because no information was giving to him besides 2 i don’t knows.

There are 7 possible combinations. We know there is at least 1 black hat being worn.

A B C

1 w w b

2 w b w

3 b w w

4 w b b

5 b w b

6 b b w

7 b b b

If A sees two white hats, then he knows he is wearing a black hat since there are only 2 white hats. Since he answered “I don’t know”, this eliminates case 3.

The possibilities are now:

A B C

1 w w b

2 w b w

4 w b b

5 b w b

6 b b w

7 b b b

If B thinks about this, he knows it means A does not see two white hats. A either sees one white and one black, or two black hats.

If B looks at C and sees a white hat, he knows that he has a black hat. Since he also says “I don’t know”, this eliminates all the cases where C is wearing a white hat. This leaves us with:

A B C

1 w w b

4 w b b

5 b w b

7 b b b

If C thinks about it, he knows he is wearing a black hat.

A B C

-> facing this way

b w w

X w b

X b w

X b b

a can see the above cases

if B and C are wearing white hats A would have said yes. So option 1 is out.

now B can look at C and he knows A’s answer.

So he has to decide from the last three cases.

if b saw a white hat in front he would have been sure that he is wearing a black one.

But he said no. So C knows that he has to pick from cases 2 and 4. In both cases he wears a black hat.

So the answer is BLACK.