Problem

Source: 2021 Dürer Math Competition Regional E+5 https://artofproblemsolving.com/community/c2773609_2021_

Tags: combinatorial geometry, combinatorics, lines, planes, 3D geometry, geometry



There are $n$ distinct lines in three-dimensional space such that no two lines are parallel and no three lines meet at one point. What is the maximal possible number of planes determined by these $n$ lines? We say that a plane is determined if it contains at least two of the lines.