Hedge Fund Jobs Interview Question: Hats and a Blind Man

Interviews for hedge fund jobs … We don’t want you to get blind sided by this question. It’s a good one.

Q: Inside of a dark closet are five hats: three blue and two red. Three smart men go into the closet, and each selects a hat in the dark and places it unseen upon his head. Each man knows both that the closet contains three blue hats and two red and that the other two men have the same knowledge.

Once outside the closet, no man can see his own hat. The first man looks at the other two, thinks, and says, “I cannot tell what color my hat is.” The second man hears this, looks at the other two and says, “I too cannot tell the color of my hat.” The third man is blind. The blind man says, “Well, I know what color my hat is!”

What color is the blind man’s hat and how do you know?

A: If the first man saw the other two both wearing red hats, he would know his own hat was blue. Since he says he does not know its color, the second and third both know that between them, they are wearing both blue, or else one red and one blue.

Therefore if the second man could see a red hat on the first or third, he would know his own hat was blue. So, when the second announces that he cannot determine his own hat color, he effectively tells the third that his hat is blue.

Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews

Bookmark and Share


pd April 16, 2008 at 10:38 pm

what if the first man sees blue on second and red on third.

And the second sees blue on first and red on third.

paul rinfret May 29, 2008 at 7:49 pm

if man #1 has a blue hat, #2 has a blue hat and the blind man is wearing a red hat please explain how the blind man would know he is wearing red.

Caddie November 5, 2009 at 3:11 pm

in this game there are three scenarios:

1)first guy see’s blue on both second guy and blind guy;
2)first guy see’s blue on second guy and red on blind guy;
3)first guy see’s red on second guy and blue on blind guy.

keep in mind second guy and blind guy both know that either a) they are both wearing blue or b) between the two one is wearing blue and the other is wearing red.

in scenario #2, the second guy looking at blind guy would be able to deduce that he’s wearing a blue cap since he sees a red cap on the blind and knows that he must be wearing a blue cap. since the second guy also does not know what color hat he’s wearing the blind guy knows this cannot be scenario #2. So he correctly guesses he’s wearing a BLUE cap. Either scenario one or two is acceptable.

Comments on this entry are closed.

Previous post:

Next post:

Real Time Web Analytics