$35 \cdot 49$ Divide a cube with an edge length of $3 \mathrm{~cm}$ into $n$ smaller cubes of different volumes. If the edge lengths of the smaller cubes are whole centimeters, then $n$ is
(A) 4 .
(B) 8 .
(C) 12 .
(D) 16 .
(E) 20 .
(7th American Junior High School Mathematics Examination, 1991)
[Solution] The volume of a cube with a side length of $3 \mathrm{~cm}$ is $27 \mathrm{~cm}^{3}$. It can only be divided into one cube with an edge length of $2 \mathrm{~cm}$, whose volume is $8 \mathrm{~cm}^{3}$.

Thus, the remaining $19 \mathrm{~cm}^{3}$ can only be divided into cubes with an edge length of $1 \mathrm{~cm}$, totaling 19 pieces. Therefore, it can be divided into a total of 20 small cubes that are not all the same.
Hence, the answer is $(E)$.