1956 AHSME Problem 31

In our number system the base is ten. If the base were changed to four you would count as follows: 1,2,3,10,11,12,13,20,21,22,23,30,\ldots The twentieth number would be:

\textbf{(A)}\ 20 \qquad\textbf{(B)}\ 38 \qquad\textbf{(C)}\ 44 \qquad\textbf{(D)}\ 104 \qquad\textbf{(E)}\ 110

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.