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