This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2001 239 Open Mathematical Olympiad, 6
Tags: combinatorics , projective plane , block designs , line
On the plane 1000 lines are drawn, among which there are no parallel lines. From any seven of these lines, some three pass through one point. But no more than 500 lines pass through each point. Prove that there are three points such that each line contains at least of of them.

2000 239 Open Mathematical Olympiad, 8
Tags: combinatorics , block designs
Given a set of 102 elements. Is it possible to choose 102 17-element subsets so that the intersection of any two subsets contains no more than 3 elements?