Consider a convex n-gon P (all interior angles strictly less than 180°).
A diagonal in P is a straight line segment connecting two of P's vertices which aren't neighbours.

What is the largest number of diagonals you can draw in P so that each of the drawn diagonals intersects at most two others (in the interior of P)?
Give a proof for your answer.

Il faut respecter la montagne -- c'est pourquoi les gypaètes sont là.