posted by John .
Determine the largest positive integer N, such that given any N-gon (not necessarily convex), there exists a line (infinitely extended in both directions) that contains exactly 1 edge of the N-gon.
The figure in blue is an example of a 20-gon that doesn't satisfy the conditions of the challenge. The dotted lines indicate why there is no line which contains exactly 1 edge of the 20-gon This shows that N\neq 20. It does not imply that N > 20 or N < 20 .