TITLE: A closed path is made up of 11 line segments. Can one line, not containing a vertex of the path, intersect each of its segments?
QUESTION [5 upvotes]: This  problem is taken from the book Mathematical Circles by Dmitri Fomin, et al., translated by Mark Saul and published by the American Mathematical Society. Can anyone describe what the question actually means?

REPLY [4 votes]: Alas, I didn't read the question too well.  The OP was not asking for a proof, but a proof is here in the hidden portion.

 The answer is no.  Suppose contrary that a line $L$ exists with the required property.  This line cuts the plane into two open half plane.  Note that two consecutive vertices cannot belong in the same half plane.  Do you see a contradiction now?