Question 58
A certain number of open segments are placed in the plane, none of them parallel to the $x$ or $y$ axes. These segments are pairwise disjoint. Thanima starts moving from $(0,0)$ parallel to the $x$-axis. Each time she meets a wall, she turns by 90 degrees and keeps moving without crossing the wall.
Prove that it is impossible for Thanima to visit both sides of every wall.
Prove that it is impossible for Thanima to visit both sides of every wall.