Three mathematicians are applying for a job. There are five hats, three white, two black. They’re lined up, and a hat is placed on each. The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. The first person to correctly figure out what color hat he has gets the job; you guess wrong and you are killed. Assume these are INTELLIGENT mathematicians, and that they will do the logically correct thing at each stage — if something can be deduced, they will figure it out. A

Question

anonymous · Answer

i posted this one here a long time ago lol

anonymous · Answer

lol but let me finish-

After a long pause,the first person, who cannot see any hats, says he knows the color of his hat. What is the color, and how does he know?

anonymous · Answer

If the person at the back saw two black hats, he would immediately know that he wore a white hat. He does not, so the two front hats are either black and white, or both white. The second person would know this fact! If they saw a black hat in front of them, then they would know that their hat is white. Since they do not, the hat at the front must be white. The guy at the front realises all this, and knows that his hat is white.

anonymous · Answer

got the first part about the 3rd person seeing two black hats- confused from that part on :)

anonymous · Answer

w b w
b w w
w w b
w w w
b b w
b w b
w b b
o o o
L  L L
I know that those are my possibilities and wbb is out...
(the o's and L's are the mathematicians)

anonymous · Answer

The second mathematician knows that if his hat, and the first hat were both black, the third mathematician would shout out that he wore a white hat.

Therefore he knows that his hat and the hat in front are either black and white, or both white. If he saw a black hat, he would know that the hats are black and white, and that his hat is white. He does not shout it out though, so he must see a white hat.

The first mathematician can figure all of this out, so he knows his hat is white.

anonymous · Answer

OH got it! great job!