AMC 8 1987 Problem 7

The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is $\text{(A)}\ 10 \text{(B)}\ 16 \text{(C)}\ 20 \text{(D)}\ 22 \text{(E)}\ 24$