Teachers' Hair

We're told the first person to speak has black hair. According to his statement, he is not Mr Black; nor is he Mr White, who responds to him; so he must be Mr Redhead, the history teacher.

Because I was laying in bed, had no paper, pencil only my tired mind. I thought about this problem in a pure "numerous" way without recognizing the names and colours.

So I started by thinking about *1,2,3 *as digits and all their combinations so that each number isn't on its "name position".

There where only 2 solutions: 231 and 312 .

After this I interpreted each digit with the teachers hair colours and the index with their names .

I just used the order of the names given in the beginning of the text (white, black, red).

So I could write the solutions as followed:

Sol. 1: (=231)

• Mr. White - black hair
• Mr. Black - red hair
• Mr. Redhead - white hair

OR

Sol. 2: (=312)

• Mr. White - red hair
• Mr. Black - white hair
• Mr. Redhead - black hair

After being given the information, that Mr. White and the black haired person are not the same one, solution 2 has to be true : Mr. Redhead, the history teacher, has black hair.

Maybe my solution is too complicated, seeing the other ones, but I like it solving problems in an abstract/ mathematical way and learning new concepts throughout the process. Maybe it helps someone ;)

The black-haired teacher who first spoke can either be Mr. White or Mr. Redhead. Since Mr. White answered him, he could not be Mr. White. So he must be Mr. Redhead, the history teacher, and he has black hair.

We start with the clue "nobodys name gives away the color of their hair" eliminating Mr White + white hair, Mr Black + black hair and Mr Red + red hair.
Next, we take the clue "said the black haired person, Mr White replied". Since those cannot be the same person we eliminate Mr White + black hair.
That forces Mr White to have red hair, which in turn forces Mr Black to have white hair.
This leads us to our answer, the history teacher Mr Red has black hair.

As nobody had a name that matched their hair color, Mr. Redhead couldn't be a redhead as in hair color, so he had either black or white hair color, but since we can assume that Mr. White wasn't a redhead the only possible option for him(as in Mr. White) is having black hair leaving white hair the only possible option for the history teacher, Mr. Redhead.

another thing to note is that mr black said. one of us has white hair. implying that either mr black or mr white has white hair. since it cannot be mr white then mr black must have white hair. and therefore mr redhead must have black hair

Thank you.