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?
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 20060709 09:05:05 