# Solution: 2009-11 Circles and lines

Does there exist a set of circles on the plane such that every line intersects at least one but at most 100 of them?

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

Here is his Solution of Problem 2009-11.

There were 2 other incorrect solutions submitted.

Reference: L. Yang, J. Zhang, and W. Zhang, On number of circles intersected by a line, J. Combin. Theory Ser. A, 98 (2002), pp. 395–405.

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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 $$X,Y\in\mathcal F$$.