Given is a convex polygon
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
with
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
vertices. Triangle whose vertices lie on vertices of
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
is called good if all its sides are equal in length. Prove that there are at most
![\frac {2n}{3}](/media/m/1/e/2/1e25ffbacfb6d6c1ffba63541b9efba6.png)
good triangles.
Author: unknown author, Ukraine
%V0
Given is a convex polygon $P$ with $n$ vertices. Triangle whose vertices lie on vertices of $P$ is called good if all its sides are equal in length. Prove that there are at most $\frac {2n}{3}$ good triangles.
Author: unknown author, Ukraine