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27 dice make a 3x3x3 cube

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February 11, 2008
geometry3D geometry

Problem Statement

A 3×3×3 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 3×3×3 3 \times 3 \times 3 cube is (A) 60(B) 72(C) 84(D) 90(E) 96 \text{(A)}\ 60 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 84 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 96
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