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Need some hints

  1. Oct 14, 2005 #1
    i can solve question (a) but not (b)
    i totally dont know where to start, can anyone give me a some hints?
  2. jcsd
  3. Oct 14, 2005 #2
    Maybe by contradiction?
  4. Oct 15, 2005 #3
    Let's name the integers around the circle as
    a_1, a_2, ..., a_10 (they are the integers 1 through 10 in some order).

    Now let's go around the circle calculating partial sums
    s_1 = a_1 + a_2 + a_3
    s_2 = a_2 + a_3 + a_4
    s_8 = a_8 + a_9 + a_10
    s_9 = a_9 + a_10 + a_1
    s_10= a_10 + a_1 + a_2
    All possible triplets of integers in consecutive locations around the circle are represented here, as well as their sums.
    We can rephrase the question now:
    prove that there is at least one of those sums greater than or equal to 17.

    Does that help?
    Last edited: Oct 15, 2005
  5. Feb 14, 2007 #4

    i was hoping somebody could show me how to solve this problem....what proof would you use?
    Last edited: Feb 14, 2007
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