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

Tags were heavily modified to better represent problems.

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Found problems: 3

2010 Contests, 3
Tags: combinatorics , set systems , projective plane
In an exam every question is solved by exactly four students, every pair of questions is solved by exactly one student, and none of the students solved all of the questions. Find the maximum possible number of questions in this exam.

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.

2010 Turkey Junior National Olympiad, 3
Tags: combinatorics , set systems , projective plane
In an exam every question is solved by exactly four students, every pair of questions is solved by exactly one student, and none of the students solved all of the questions. Find the maximum possible number of questions in this exam.