1. Andrea glues 27 ordinary 6-sided dice together to form a large cube. The dice are oriented so that the sums of the values readable on each face of the cube are, in some order, 14, 22, 30, 38, 46, 54. What is the sum of all the faces of the dice that, having been glued together, are no longer readable?
(A) 189
(B) 204
(C) 261
(D) 333
(E) 363
1. The answer is $\mathbf{( E )}$. The sum of the values on the faces of a die is $1+2+3+4+5+6=21$. The sum on all faces, visible and not, is therefore $27 \cdot 21=567$. To obtain the sum on the hidden faces, we can subtract from this number the sum of the numbers written on those visible: the answer is therefore $567-(14+22+30+38+46+54)=567-204=363$.