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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 with Explanation | Comment 12 of 20 |

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.

  Posted by Yosippavar on 2006-06-22 12:24:22
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