## Thursday, September 01, 2005

### Three hats on three men... what could be simpler?

There are 3 black hats and 2 white hats in a box. Three men (we will call them A, B, & C) each reach into the box and place one of the hats on his own head. They cannot see what color hat they have chosen. The men are situated in a way that A can see the hats on B & C's heads, B can only see the hat on C's head and C cannot see any hats. A is asked first if he knows the color of the hat he is wearing, he says no. Then B is asked if he knows the color of the hat he is wearing he says no. Then C is asked if he knows the color of the hat he is wearing he says yes and he is correct. What color hat and how can this be?

1. Black. A and B got the two white hats.

2. Very good, Dee! That's right.

Here's the full explanation:
The key to this problem is the number of white hats (2).
So, if B & C were wearing white hats, A would know he was wearing black. Since A doesn't know what hat he's wearing, we can conclude that B & C aren't wearing white and white, respectively. So, if B saw C wearing a white hat, he could definitely say he was wearing a black hat, but he says he does not know. Therefore C is wearing a black hat and he knows it.

Of course, you have to assume the three are logical enough to figure this out, too! :-)

3. this does not make sence because if all the men drew a black hat then none of them would know what color hat they were wearing. so it doesnt work out. why do we have to assume that B and C where wearing a black white combo. if they both drew black then A still wouldnt know what he had.

4. That's the tricky part of the problem; if B and C were both wearing black, then (a) A still couldn't determine...A eliminates one possibility-B and C white-... (b) now it stands WBB or WWB BBB BWB WBW and BBW one possibility has been eliminated (c) if B sees a white hat on C he can determine WBW or BBW and know, or WWB or WBB or BBB...in either case C must wear black and in BBB C still wears black.

1. What if A sees B wearing a black hat and A wearing a white hat? Wouldnt he still say he doesnt know?

2. What if A sees B wearing a white hat and C wearing a black hat? Wouldnt he still say I dont know and C could guess wrong?

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