Hat colour
Three men A, B and C are captured by cannibals. They are tied to stakes. A can see B and C. B can only see C. C can't see either A or B. They are then shown five hats. Three are black and two are white. The men are then blindfolded. A hat is put on each one's head, the remaining two hats are hidden away and then the blindfolds are removed. They are told that if one of them can call out the colour of his own hat, they can all go free. Otherwise they'll really be in hot water.
After a short time A calls out, "I don't know my hat colour". Soon B calls out, "I don't know my hat colour either". C thens called out the colour of his hat.
What colour is C's hat?
After a short time A calls out, "I don't know my hat colour". Soon B calls out, "I don't know my hat colour either". C thens called out the colour of his hat.
What colour is C's hat?
Labels: logic
posted by Chris at
2:36 PM
8 Comments:
black hat
So you're not going for purple!
Hat colour
Given:
5 hats, 3 black 2 white
A sees B+C
B sees C
C sees nothing
If A saw both hats were white he could deduce his is black. As he does not know, at least one of B or Cs hats are black.
Then B sees Cs hat. If it is white then Bs hat must be black as, at least one of B or Cs hats are black.
Since B can't deduce the answer, C deduces that his hat is black.
Answer:
C's hat is black
Unless the cannibals have a really sick sense of humour, in which case, the hat is purple.
Cam
Looks like the vote is for purple then.
But I'll settle on black.
Well done both.
I only have one question for that logic.
You said that
(sorry just copied and pasted to make easier)
"If A saw both hats were white he could deduce his is black. As he does not know, at least one of B or Cs hats are black.
(But what if both B and C's hats were black. That could be possible seeing as A's hat could then still be either black or white seeing as there are 3 Blacks hats and 2 Whites.)
Then B sees Cs hat. If it is white then Bs hat must be black as, at least one of B or Cs hats are black.
Since B can't deduce the answer, C deduces that his hat is black."
Can someone answer that for me?
Hi Alex. Consider all possible cases and the associated responses of A, B and C. The first three columns are the hat colours, the second three are what would have been called out and by who.
ABC ABC
BWW B--
BBW ?B-
WBW ?B-
BBB ??B
BWB ??B
WBB ??B
WWB ??B
Cases BWW, BBW and WBW are not possible because the problem states that neither A or B could say their hat colour. In all the other cases, C is wearing black.
Ok yea I understand in a way but still I have a question. In the case off BWW, A will know his hat color becuase he can see the two white hats. in the case of BBW you say ?B- but A does not know if his hat is W or B so how does B know that his is black when he can only see the white in front of him.. for all B knows is that A's hat is still either W or B. So he can not give a positive answer. with the case of BBB, A does not know if he is wearing W or B becuase he see's 2 Blacks hats. He could still be wearing a white one. and then B can only see one Black hat not knowing off of A's answer if he is wearing white. I just see no way this can be answered without a guess by them. just becuase there are 3 black hats. the only way one possible to actually know their hat color would be A, and that only if it is BWW
The only way that A can identify his hat colour is if both B and C are wearing W. As A says he can't tell, then both B and C know, using that info alone, that at least one of B or C is wearing a B hat. None of them know what colour A's hat is. If B sees that C is wearing a W hat, then B knows that he is wearing a B hat and would say so, But B can't say, so C's hat isn't W - so it must be B. C understands what has happened, and so knows that he is wearing a B hat. Neither B or C know what colour A or B's hat is.
Here's the table again, but I've modified it to make it clearer.
ABC ABC
BWW B--
?BW ?B-
??B ??B
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