1999 Cayley Problem 14

In an election for class president, 61 votes are cast by students who are voting to choose one of four candidates. Each student must vote for only one candidate. The candidate with the highest number of votes is the winner. The smallest number of votes the winner can receive is

\textbf{(A)}\ 15\quad \textbf{(B)}\ 16\quad \textbf{(C)}\ 21\quad \textbf{(D)}\ 30\quad \textbf{(E)}\ 31

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.