I got this question on one of my Computer Science assignments. Hanson's actually asked me this question before. I thought it was kind of neat. You try and solve it now. Have fun!
Three logicians are each wearing a black hat or a white hat, but not all white. Nobody can see their own hat. However A can see the hats of B and C, and B can see the hats of A and C. C is blind. You go and ask them one by one in order A, B, C, whether they know the color of their own hat. A answers "No". B answers "No". Then C answers "Yes". Explain how this is possible.
Answer: Since A answered "no", not both of B and C have white hats (if they had, then A would had known his own hat was black, since not all hats are white). Now, if C's hat were white, then B (knowing that she and C can not both have white hats) would have known she had a black hat. Since B does not know, this must mean that C's hat is black.
10 comments:
My first answer before thinking about it is: Braille. She numbers the hats like in the Ray Charles movie.
Anyways after thinking about it:
If you have 3 hats and not all white, one must be black.
A and B can see therefore they must see a black hat without knowing their own colour.
Therefore, C must be wearing a black hat.
the answer i think is cause c is blind so all she sees is black so she thinks shes wearing a black hat
lol Steph wrote a detailed version of mine... I made mine simple and to the point so I could go back to studying -.-' stupid math and physics
WAIT! I can guess this.
Okay. Person A sees that person B is wearing white, and person C is wearing black. He doesn't know if he's wearing white or black.
Person B sees that person C is wearing black, and person A is wearing white. He can't tell either.
Person C, knowing that neither of the above could tell, knows that one of of both (B and C) and (A and C) is wearing black. (If either set were both white, that remaining person would know that he was black, since not all three could be white.) The common factor on both those sets is him. Thus, he is obviously wearing a black hat, and the other two are white.
Am I right? Close? I've never heard this question before, so I'm not sure, but I think that works.
Argh. I went and had a totally logical answer, but it turned out it was totally flawed instead. I don't know.
HeeHeee sweeeeeet
Definately didn't see your answer, Alex, before posting my own. :P I think yours actually makes more sense. I was having trouble explaining my thinking.
tell us! tell us!
the blind guys asked someone what colour his hat was.... thats my answer.
A must see at least one black hat, or she would know that her hat is black
since they are not all white. B also must see at least one black hat, and
further, that hat had to be on C, otherwise she would know that her
hat was black (since she knows A saw at least one black hat). So C knows
that her hat is black, without even seeing the others' hats.
(haha i see that i am a slow answerer)
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