3. Carla builds a cube by gluing together 1000 small identical cubes (with 10 cubes along each edge). She then paints all the faces of the cube she has built red. How many of the initial small cubes will have exactly two red faces?
(A) 60
(B) 120
(C) 104
(D) 90
(E) 96
(3) The correct answer is $(E)$.

The cubes that will have two faces painted red correspond precisely to the cubes that lie on the edges of the larger cube, but not at the vertices. On each edge, excluding the vertices, there are 8 cubes, and the total number of edges of a cube is 12: such cubes will thus be $8 \cdot 12=96$.

Question proposed by Carmelo di Stefano.