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?
person D will declare that he has white first.
- D will say- if C, D, E all have black then F should know that he has white, but F has not answered yet. this means either me(D) or E has white.
if i(D) had black then E would have known that if E had black then F would have answered first. since F has not answered till now, it means that E must have white if i (D)have black. since E has not answered yet, it means that i(D) have white. hence, E would answer first.