MathDB
ASU 406 All Soviet Union MO 1985 no of painted parts by n straight lines

Source:

August 5, 2019
linescombinatorial geometrymaximum

Problem Statement

nn straight lines are drawn in a plane. They divide the plane onto several parts. Some of the parts are painted. Not a pair of painted parts has non-zero length common bound. Prove that the number of painted parts is not more than n2+n3\frac{n^2 + n}{3}.