No curve intersecting each segment only once
Source: 1961 All-Soviet Union Olympiad
August 4, 2015
combinatoricsgraph theory
Problem Statement
Consider the figure below, composed of 16 segments. Prove that there is no curve intersecting each segment exactly once. (The curve may be not closed, may intersect itself, but it is not allowed to touch the segments or to pass through the vertices.)
[asy]
draw((0,0)--(6,0)--(6,3)--(0,3)--(0,0));
draw((0,3/2)--(6,3/2));
draw((2,0)--(2,3/2));
draw((4,0)--(4,3/2));
draw((3,3/2)--(3,3));
[/asy]