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2001 OIM Problems/Problem 3

Revision as of 03:12, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>S</math> be a set of <math>n</math> elements and <math>S_1, S_2, \cdots , S_k</math> subsets of <math>S</math> (<math>k \ge 2</math>), such that each...")
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Problem

Let $S$ be a set of $n$ elements and $S_1, S_2, \cdots , S_k$ subsets of $S$ ($k \ge 2$), such that each of them has at least $r$ elements. Show that $i$ and $j$ exist, with $1 \le i < j \le k such that the number of common elements of$S_i$and$S_j$ is greater than or equal to

\[r-\frac{nk}{4(k-1)}\]


~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

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