Professor Merle White of the Mathematics department ,Profess

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Professor Merle White of the Mathematics department ,Professor Leslie Black of Philosophy,and Jean Brown who worked in the university's office,were lunching together.
"Isn't it remarkable,"observed the lady,"that our last names are Black,Brown and White and one of us has black hair,one brown hair,and one white.""It is indeed,"replied the person with black hair,"and have you noticed that not one of us has hair that matches his or her name?"
"By golly,you're right!"exclaimed Professor White.
If the lady's hair isn't brown,what is the color of Professor Black's hair?

lady's hair isn't brown
lady's hair isn't black since the person with black hair replies to the lady
so lady's hair is white
Also Professor White's hair is not black since he replies to the person with black hair
so Professor White's hair must be brown
and Jean Brown's hair must be black
and Professor Black's hair must be white

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