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Start - end by turning left and right alternatively, why?

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 29, 2012 #2
    i assume this only works if the number of villages is even. Let i=1,2,... then when we have 2i villages we have 3i roads. I can see that when you go alternatively left and right you end up at the start point, im just not sure why/ cant prove it.
     
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