I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
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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?
Black. A and B got the two white hats.
ReplyDeleteVery good, Dee! That's right.
ReplyDeleteHere'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! :-)
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.
ReplyDeleteThat'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.
ReplyDeleteWhat if A sees B wearing a black hat and A wearing a white hat? Wouldnt he still say he doesnt know?
DeleteWhat 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?
Delete