406

Part of 1985 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

n

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

\frac{n^2 + n}{3}

linescombinatorial geometrymaximum