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Proves that

  1. Dec 10, 2007 #1
    Given a positive whole number n, [tex]\exists[/tex] N with the following property: if A is a subgroup of {1,2,...,N} with at least N/2 elements, then there is a positive whole number m<= N - n such that

    |A [tex]\cap[/tex]{m+1, m+2,..., m+k}|>=k/2

    [tex]\forall[/tex] k = 1, 2, …, n.
    Last edited: Dec 10, 2007
  2. jcsd
  3. Dec 10, 2007 #2


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    Just look at the top half and the bottom half.
  4. Dec 10, 2007 #3
    Hi, I'll be glad if you put your solution here. I already saw a proof, but I don't know if it's correct.
  5. Dec 10, 2007 #4
    this is an olympic problem, by the way
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