Four men in hats

Here's a fantastic puzzle that I found here (no peeking).**

Imagine four men buried up to their necks in the ground, as shown in the illustration. Between A and B is a solid brick wall. The men can only look forward, so A and B can see only the brick wall, C can see only B, and D can see both B and C.

The men know that among them are four hats: two black and two white. None of the men knows the colour of the hat on his own head.

To avoid being shot (I l-o-o-ove puzzles that include that phrase), any one of the men must correctly call out the colour of his own hat. If he gets it wrong, all four men will be shot. The men are not allowed to talk to each other and have 10 minutes to think.

After one minute, one of them calls out the correct colour of his own hat, thereby saving them all. I'd like to think that what happens next is that they are immediately dug up, relieved of their triangular hats, and taken to a Radiohead concert as a reward.

Questions for you:
1. Who calls out?
2. How does he know?

** I pinched the illustration from that site too.


Darren said...

C cannot see D.
Does C know that D is behind him facing in the same direction and therefore can see both B and C?

if so, then C calls out black.
He knows B is white.
He knows D can see B and C.
If C had white, D would see two white hats and easily be able to conclude his own hat was black, and thus call out.
After a minute, he has not done so.
Ergo C must have black.

fiona-h said...


Mark Hanington said...

C calls out the answer.

If his hat were the same colors as B's, D would have known right away what color his own hat was and called it out. Because he did not do so, C knows that his hat cannot be the same color as B's.

No sure what took him 10 minutes, though.

Molly said...

C has to assume that D isn't just too stupid to figure out that if the two people he sees have one color hat, then he must be wearing the other color.

Anonymous said...

C calls out that he is wearing a black hat. Why is he 100% certain of the colour of his hat ?

After a while, C comes to the realization that he must answer.

This is because D can't answer, and neither can A or B.

D can see C and B, but can't determine his own hat colour. B can't see anyone and also can't determine his own hat colour. A is in the same situation as B, where he can't see anyone and can't determine his own hat colour.

Since A, B, and D are silent, that leaves C. C knows he is wearing a black hat because if D saw that both B and C were wearing white hats, then he would have answered. But since D is silent, C knows that he must be wearing a black hat as he can see that B is wearing a white hat.