Question 20
A convex polyhedron $Q$ has vertices $V_1,$ $V_2,$ $\ldots,$ $V_n,$ and $100$ edges. The polyhedron is cut by planes $P_1,$ $P_2,$ $\ldots,$ $P_n$ in such a way that plane $P_k$ cuts only those edges that meet at vertex $V_k.$ In addition, no two planes intersect inside or on $Q.$ The cuts produce $n$ pyramids and a new polyhedron $R.$ How many edges does $R$ have?