Polyline and intersections [Czech-Polish-Slovak Match 2018]
Source: Czech-Polish-Slovak Match 2018, Problem 5
July 2, 2018
combinatoricsinequalities
Problem Statement
In a rectangle there is a polyline of length , which can have self-intersections. Show that there exists a line parallel to two sides of the rectangle, which intersects the other two sides in their interior points and intersects the polyline in fewer than points.Proposed by Josef Tkadlec, Czechia and Vojtech Bálint, Slovakia