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 can guess first, considering a considerable amount of time frames to each logicians.
Firstly - F can guess his color, if he sees same color(b/w) on heads of C,D and E. but he cant. so the hat colors on the heads of C,D and E are in 2:1 ratio.
Secondly - Now E can guess his color, if he sees same color on both C and D's heads. But he cant. So the hat colors on the heads of C and D are 1:1 ratio.
Finally - So If D sees Black hat on C, he was sure his hat was White and Viceversa.
Thus D guesses his hat color is White.
I think this explanation is enough.