33.58 Our common number system is the decimal system. If we change to the quaternary system, it becomes $1_{4}, 2_{4}$, $3_{4}, 10_{4}, 11_{4}, 12_{4}, 13_{4}, 20_{4}, 21_{4}, 22_{4}, 23_{4}, 30_{4}, \cdots$. Then the 20th number is
(A) $20_{4}$.
(B) $388_{4}$.
(C) $44_{4}$.
(D) $104_{4}$.
(E) $110_{4}$.
(7th American High School Mathematics Examination, 1955)
[Solution] Since $20=1 \cdot 4^{2}+1 \cdot 4^{1}+0 \cdot 4^{0}$, the 20th quaternary number is $110_{4}$. Therefore, the answer is $(E)$.