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in Guess / Riddles / Quizzes by (329k points)

There are 3 black hats and 2 white hats in a box. Three men (we will call them Tom, Bob, and Bill) 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 Tom can see the hats on Bob and Bill's heads, Bob can only see the hat on Bill's head and Bill cannot see any hats. When Tom is asked if he knows the color of the hat he is wearing, he says no. When Bob is asked if he knows the color of the hat he is wearing he says no. When Bill 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? There is no play on words and there are no tricks.




6 Answers

0 votes
by (511k points)

The man in front knew he was wearing a black hat because he knew the first man did not see two white hats and he knew that the second man did not see one white hat because if he saw a white hat, the second man would have known that his hat was black from hearing the first man's statement.

0 votes
by
Bill has a black hat
0 votes
by
Tom didn't know because Bob and Bill were NOT both wearing white hats. If they were, Tom would know that he was wearing a black hat because there are only two white hats. Since Tom didn't know, that means to Bob and Bill:

1) both wear black hats

2) Bob wears a white hat and Bill wears a black hat

3) Bob wears a black hat and Bill wears a white hat.

But Bob also doesn't know what color hat he's wearing, but if Bill was wearing a white hat, he would know he was wearing a black hat, or if Bill was wearing a black hat, Bob would be wearing a white hat.

So Bill knows he's wearing a black hat!
+1 vote
by (91.9k points)
The man in front knew he was wearing a black hat because he knew the first man did not see two white hats and he knew that the second man did not see one white hat because if he saw a white hat, the second man would have known that his hat was black from hearing the first man's statement.
+1 vote
by (448k points)
Bill has three black hats. Tom and Bob have the two white hats
+1 vote
by (45.5k points)
You have really cool questions!



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