20. A cube has a side length of $n$ units (where $n$ is an integer greater than 2). The entire surface of the cube is painted black, and then the cube is cut into $n^3$ smaller cubes, each with a side length of 1 unit, using planes parallel to the faces of the original cube. If the number of smaller cubes that have exactly one face painted black is equal to the number of smaller cubes that have no faces painted, what is $n$?
(A) 5 ;
(B) 6 ;
(C) 7 ;
(D) 8 ;
(E) None of the above.
20. The small cubes with no faces painted can only come from the interior of the cube, totaling $(n-2)^{3}$; the small cubes with one face painted come from the sides of the original cube, but not on the boundaries of these sides, totaling $6(n-2)^{2}$; thus $(n-2)^{3}=6(n-2)^{2}$. Since $n>2$, we can cancel $(n-2)^{2}$ from both sides, yielding $n-2=6$, or $n=8$. (D) True.