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## #1 2019-02-07 08:42:53

derek Deschler
Guest

### helpppp

i think i know the answer is white im just not sure how to explain it well enough to get a useful grade on it

## #2 2019-02-07 15:12:02

Grantingriver
Member
Registered: 2016-02-01
Posts: 115

### Re: helpppp

Hi Derek, it is straightforward for the final person to deduce the correct color of her hat. This can be proven as follows: For clarity let me call "the first person" from back (Dom) the first person and the next one "the second person" and so no. Since there are just three black hats so if the second, third and forth persons wearing them then the first person would be certain that his hat is white (remember that there are just three black hats and they know this fact). Therefore some of the hats on the other persons are black and some are while or all of them are white. The second person know the previous conditions from the answer of the first person, but if the two hats of the third and forth persons are black then he would be sure (from the information he had got from the first person and from his observation) that his hat is white, However, his uncertainty insured the third person and the forth person that not all of their hats are back. At this stage the third person would be sure that his hat most be white if the front person has black hat (since he know all the answers of the previous students) and the froth and final student "Amy" knew all of this information therefore she is certain that her hat is white.

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