ASU 001 All Russian MO 1961 8.1 curve intersecting 16 segments
Source:
June 17, 2019
combinatoricscombinatorial geometry
Problem Statement
Given a figure, containing segments. You should prove that there is no curve, that intersect 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]