Logic puzzle

[her209]

Three mathematicians are applying for a job. There are 5 hats, 3 white, 2 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 they have 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. 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?

NOTE: I don't know the answer to this one.

 

[AgaBoogaBoo]

he looked up!

 

[her209]

Here is the possible combinations of hat (assume person 1 is on the left)
WWW
WWB
WBW
WBB
BWW
BWB
BBW

 

[AgaBoogaBoo]

he asks the guy behind him what he sees

 

[AgaBoogaBoo]

a-ha!

I figured it out, let's see if you guys can, I'll tell you if you're right or not

 

[esun]

EDIT SOLUTION / SPOILER





This is what I came up with:

W W W
W B B
B B W *
B W B *
W W B
B W W *
W B W

The ones with asterisks are cases where either person 2 or person 3 know their color hat (see below), so the other cases are the only ones in which neither of them would answer hence person 1 must have a white hat.

For B B W, person 3 knows he must be white since there are only two black hats. For B W W and B W B, person three doesn't respond because he doesn't know, but person two knows that since person 3 doens't respond, there must be either white white or some combo of black and white for persons 1 and 2, and since he sees a black he knows he must be white (if he sees white, he could be either white or black).

 

[dafatha00]

The first guy has a white hat on and he knows it.

I'll break it down by possible combinations in which the each letter represents the color of each guy.

BBW
The third guy would automatically know he had white so that's not it.

BWB
The second guy would know he has a white hat on because he knows the third guy would've said something if the second guy had a black hat on. The third guy doesn't know what he has so the second guy does know. That's not it either

BWW
The above explanation applies to this one as well.


WBB, WBW, WWB, and WWW are the only combinations left

The first guy knew that the these are the only ones that can apply so he knows he has a white hat.

 

[PowerEngineer]

If the third mathematician in line saw two black hats in front of him, then he would know his hat was white. Since he doesn't say anything, he must either see two white hats or one black and one white. If the second mathematicain sees a black hat, then he knows his own hat must be white. Since he says nothing, the first mathematician knows his hat must be white. (I think)

 

[her209]

You guys are quick tonight

 

He has a white hat on.

He knew by process of elimination. For, given the assumptions that all were mathematicians and intelligent, if the third person couldn't give an immediate answer, it meant that neither of the other two in front of her had black hats. Hence, the first person and the second person reasoned that they had either 2 white hats or 1 person had a white hat and the other a black hat. However, if the first person had a black hat, then the second person would have immediately known that he had a white hat on. Therefore, if the second person could not provide an immediate answer either, then the first person could safely conclude that he had a white hat on.

Edit: Oops! I got the colors mixed up.

 

[her209]

Originally posted by: DearQT
He has a black hat on.

He knew by process of elimination. For, given the assumptions that all were mathematicians and intelligent, if the third person couldn't give an immediate answer, it meant that neither of the other two in front of her had white hats. Hence, the first person and and the second person reasoned that they had either 2 black hats or 1 person had a white hat and the other a black hat. However, if the first person had a white hat, then the second person would have immediately known that he had a black hat on. Therefore, if the second person could not provide an immediate answer either, then the first person could safely conclude that he had a black hat on.

Re-read the riddle.

 

Originally posted by: her209
Re-read the riddle.

Oops! I got the colors mixed up. I thought the riddle said 3 black hats and 2 white hats.

 

[DrPizza]

You said the mathematicians were intelligent (which goes without saying)
How do you know the guy in the back wasn't thinking: "heh heh... I see 2 black hats, therefore I have a white hat.... but if I keep my mouth shut, the guy in front is going to be killed. Man, I hate that dude."

You guys above didn't think of that... did you. That's cause *I'm* a mathematician... we're pretty smart, but, that goes without saying.)

 

Originally posted by: DrPizza

You said the mathematicians were intelligent (which goes without saying)
How do you know the guy in the back wasn't thinking: "heh heh... I see 2 black hats, therefore I have a white hat.... but if I keep my mouth shut, the guy in front is going to be killed. Man, I hate that dude."

You guys above didn't think of that... did you. That's cause *I'm* a mathematician... we're pretty smart, but, that goes without saying.)

No, that isn't called intelligence. That is called malice (evilness) and connivance. Don't mix up the two concepts.

Edit: Now, here's a better other reason that the third person may have kept her mouth shut--in spite of knowing the answer: She was not interested in the job. (Maybe she changed her mind about the job.)

 

[her209]

Originally posted by: DrPizza

You said the mathematicians were intelligent (which goes without saying)
How do you know the guy in the back wasn't thinking: "heh heh... I see 2 black hats, therefore I have a white hat.... but if I keep my mouth shut, the guy in front is going to be killed. Man, I hate that dude."

But in that case where the front two have black hats, the 2nd guy would speak up and be killed.