Question 164
Fix an integer $n \ge 6$ and consider $n$ coplanar lines, no two parallel and no three concurrent. These lines split the plane into unbounded polygonal regions and polygons with pairwise disjoint interiors. Two polygons are *non-adjacent* if they do not share a side. Show that there are at least $\frac{1}{12}(n-3)(n-2)$ pairwise non-adjacent polygons with the same number of sides each.
Cristian Șăvescu
Cristian Șăvescu