$35 \cdot 1$ A regular triangle is completely painted black. Each transformation involves dividing the black triangle into four congruent smaller triangles, and painting the middle small triangle white (as shown in the figure). After five transformations, what fraction of the original triangle is still black?
(A) $\frac{1}{1024}$.
(B) $\frac{15}{64}$.
(C) $\frac{243}{1024}$.
(D) $\frac{1}{4}$.
(E) $\frac{81}{256}$.
(7th American Junior High School Mathematics Examination, 1991)
[Solution] After the first "transformation", the black part occupies $\frac{3}{4}$ of the whole;
After the second "transformation", $\frac{1}{4}$ of each small black triangle is painted white, so the remaining black part occupies $\frac{3}{4} \cdot \frac{3}{4}=\left(\frac{3}{4}\right)^{2}$ of the entire triangle;
After the fifth "transformation", the remaining black part occupies $\left(\frac{3}{4}\right)^{5}=\frac{243}{1024}$ of the entire triangle. Therefore, the answer is $(C)$.