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?
D - Will be able to guess it as white.
Here is the reasoning: Let's start by reading F's mind. If F had seen C,D,E = b,b,b then F would have easily guessed as w, but he couldn't, because he sees something different. Now to the next person E; if he had seen C,D = b,b then it is easy for him to say that his color is w, because F would have guessed if it was bbb. But, E couldn't guess either because he sees something different b,w instead of bb. Next to the third person in the queue D. If D had b, then E would see b,b and would have guessed it as w as per previous line. Hence, D would be able to deduce that his is w. :-)
Posted by Partha
on 2006-06-20 02:12:02