Problem #PRU-32135

Problems Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.) Discrete Mathematics Combinatorics Systems of points and line segments Systems of points and line segments (other)
 12–14  3.0

Problem

101 points are marked on a plane; not all of the points lie on the same straight line. A red pencil is used to draw a straight line passing through each possible pair of points. Prove that there will always be a marked point on the plane through which at least 11 red lines pass.