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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.)
Better solution with E | Comment 13 of 20 |
Ok, if they all reason quickly, then E can answer before D does. A is looking at a white, therefore he has to realize C D E have to be either Bl W Bl or W Bl W. (BlBlW would give E the answer, and so would WWBl, B B B would give F the answer) <- all in A's mind, but E realizes that A could be looking at black OR white, and these realizations would still be made. So E concludes that CDE have to be BlWBl or WBlW. E then sees white infront of him, and knows hes Bl.
  Posted by john on 2006-07-08 18:19:46
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