# Problem #1461

 1461 How many positive integers less than $1000$ are $6$ times the sum of their digits? $\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 12$ This problem is copyrighted by the American Mathematics Competitions.
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