LOGIC/RED HERRING QUESTION! HELP!!! (this is extra credit)?

Question

20 students were brought into a class room. the teacher made them stand in a circle and placed a black or white hat randomly on everyones head. the students could not see their own hat but could see everyone elses. they could not talk or they all would fail. they could not signal in any way. in a clockqise ritation, the students were told to say what color hat was on their head.

these students were smart though. they talked it over beforehand and figured out how to get everyone to pass and get their hat color right without depending on luck or chance.

HOW DID THEY DO IT????

Answer 1

the classroom had mirrored walls.

Answer 2

EDIT: I think they should stand facing a black hat and facing forward if between white hats. If at least one person were facing you, you'd have a black hat. If two people were not facing you, you'd have a white hat. But would need to base off of one specific person and go out from them. That should also be the first person to make a selection.

Answer 3

If they couldn't talk can they still read lips?

Answer 4

Each person paired up with someone, so now you have 10 pairs.  When standing in the circle they would take a position directly across from their partner.  If partner A had a white hat, partner B would look to A's left, if a black hat, he would look to A's right.

Answer 5

The seem to have known how many hats of each color there were before hand.  If there are 20 hats (10 black, 10 white, for example) and you know what 19 of them are... you can figure out what your own hat is.

Answer 6

They decided beforehand to move so that every other person had a black or white hat. No one would have to signal, you would just have to make sure that there both people around you had black hats (or white hats) meaning that you had a white hat. (or black hat) This is assuming that there are an equal number of black and white hats.