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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.. | Comment 11 of 20 |

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
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