Problem #PRU-34991

Problems Methods Extremal principle Extremal principle (other) Pigeonhole principle Pigeonhole principle (other) Combinatorics Systems of points and line segments Systems of points, lines, and line segments
 13–15  4.0

Problem

On a line, there are 50 segments. Prove that either it is possible to find some 8 segments all of which have a shared intersection, or there can be found 8 segments, no two of which intersect.