{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A)}\\ 200\\qquad \\textbf{(B)}\\ 2n\\qquad \\textbf{(C)}\\ 300\\qquad \\textbf{(D)}\\ 400\\qquad \\textbf{(E)}\\ 4n$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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?

\\textbf{(A)}\\ 200\\qquad \\textbf{(B)}\\ 2n\\qquad \\textbf{(C)}\\ 300\\qquad \\textbf{(D)}\\ 400\\qquad \\textbf{(E)}\\ 4n

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12B_p21", "prev": "/problem/09_amc12B_p19"}}