## proves that...

Given a positive whole number n, $$\exists$$ 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 $$\cap$${m+1, m+2,..., m+k}|>=k/2

$$\forall$$ k = 1, 2, …, n.
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 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.

## proves that...

this is an olympic problem, by the way