line a detaches line b, but b does not detach a, in a set of 2020 lines
Source: Ukrainian Geometry Olympiad 2020, VIII p5 , IX p4
April 27, 2020
combinatorial geometrycombinatorics
Problem Statement
The plane shows straight lines in general position, that is, there are none three intersecting at one point but no two parallel. Let's say, that the drawn line detaches the drawn line if all intersection points of line with the other drawn lines lie in one half plane wrt to line (given the most straightforward ). Prove that you can be guaranteed find two drawn lines and that detaches , but does not detach .