Problem

Source: 2000 Estonia National Olympiad Final Round grade 10 p5

Tags: lines, combinatorial geometry, combinatorics



At a given plane with $2,000$ lines, all those with an odd number of different points of intersection with intersecting lines. a) Can there be an odd number of red lines if in the plane given there are no parallel lines? b) Can there be an odd number of red lines if none of any 3 given lines intersect at one point?