Given a figure, containing 16 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] combinatoricscombinatorial geometry