In a certain area there are n villages linked by a network of roads
in such a way that exactly three roads meet in each village,
and none of the roads meet between villages. Prove that if
someone starts in one village and moves round this road system
alternately turning right and left whenever he comes to a village,
then he will eventually return to the village he started from.
i can see that this is the case when n is even but im not sure why?