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UKMT Grey Kangaroo, 2024

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Johan has a large number of identical cubes. He has made the structure on the right by taking a single cube and then sticking another cube to each face. He wants to make an extended structure in the same way so that each face of the structure on the right will have a cube stuck to it. How many extra cubes will he need to complete his extended structure?

(A) $10$ (B) $12$ (C) $14$ (D) $16$ (E) $18$

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