# Solution: 2009-3 Intersecting family

Let $$\mathcal F$$ be a collection of subsets (of size r) of a finite set E such that $$X\cap Y\neq\emptyset$$ for all $$X, Y\in \mathcal F$$. Prove that there exists a subset S of E such that $$|S|\le (2r-1)\binom{2r-3}{r-1}$$ and $$X\cap Y\cap S\neq\emptyset$$ for all $$X,Y\in\mathcal F$$.

The best solution was submitted by Hyung Ryul Baik (백형렬), 수리과학과 2003학번. Congratulations!