Question 67
A group of people of different height decided to dance the Hungarian traditional dance at the opening ceremony of MEMO 2013 in Veszprém. We say that a person is *average* if he is taller than one of her neighbours and shorter than the other. (People stand in a circle and every person has exactly two neighbours.)
If the number of people is $N$ ($N \ge 3$), determine all possible numbers of average people. (Belarus 2012)
If the number of people is $N$ ($N \ge 3$), determine all possible numbers of average people. (Belarus 2012)