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 Black and white hats (Posted on 2006-06-15)
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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 Is it logical to stand and face a wall? Solution | Comment 1 of 20

If F saw all the same color then F could make the first call.
Since E does not hear F declare a color, then E needs only see two of the same color to make the call.
Since D does not hear E declare a color, then D's hat must be different from C's.

D makes the call of white after waiting for E and F.

Edited on June 15, 2006, 12:52 pm
 Posted by Leming on 2006-06-15 12:46:50

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