2002 AMC 10A Problem 18

A 3 \times 3 \times 3 cube is formed by gluing together 27 standard cubical dice. (On a standard die, the sum of the numbers on any pair of opposite faces is 7.) The smallest possible sum of all the numbers showing on the surface of the 3 \times 3 \times 3 cube is

\text{(A)}\ 60 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 84 \qquad \text{(D)}\ 90 \qquad \text{(E)} 96

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