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.

AND:
OR:
NO:

Found problems: 1

1981 Czech and Slovak Olympiad III A, 2
Tags: combinatorial geometry , closed , segment , geometry
Let $n$ be a positive integer. Consider $n^2+1$ (closed, i.e. including endpoints) segments on a single line. Show that at least one of the following statements holds: a) there are $n+1$ segments with non-empty intersection, b) there are $n+1$ segments among which two of them are disjoint.