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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
the problem | Comment 8 of 20 |

The problem with any solution to this puzzle is that there is no integral time frame in which declarations are to be made. How much time must go by for D to decide that E had enough time to figure out that F hadn't answered in time?

Unlike the puzzle about cheating husbands on on island, where the interval was one day, or other puzzles, where each character is asked in turn whether they can identify hat color, this puzzle has no set time frame.  Even if the logicians are perfect, there is no specification as to what a "perfect" length of time is to make a deduction.

  Posted by Charlie on 2006-06-18 13:29:50
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