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Black and white hats (Posted on 2006-06-15) Difficulty: 3 of 5
Six logicians stand one behind the other facing an opaque wall such that 2 are on one side and 4 are on the other. None of the logicians can turn around or see beyond the wall.

Each wears a black or white hat as shown below; "|" represents the wall, capital letters are used to identify the logicians, and "b" and "w" refer to black and white respectively.

b   w   |   b   w   b   w 
A   B   |   C   D   E   F 
Each knows the location of the others and the quantity of each colour of hat. Who will be first to declare having which colour?

No Solution Yet Submitted by Sir Percivale    
Rating: 3.8889 (9 votes)

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Solution Solution | Comment 14 of 20 |

Here is my solution:

D will come to know after a few minutes that he is wearing a White hat. Reasoning is:

A B do not have enough information to come up with an answer.

F can give an answer only if C D E have the same colours of hat. Now, F has not given an answer which means that C D E have different colours.

If C and D were both wearing the same colour, E would know that his own hat was different otherwise F would have answered as per logic above. Due to this E does not answer.

D therefore knows that C and his own hat is different and hence he can say he is wearing White.

  Posted by RA on 2006-07-09 09:05:05
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