How many three-digit positive integers \underline{a} \ \underline{b} \ \underline{c} are there whose nonzero digits a, b, and c satisfy
0 . \bar{a} \underline{b} \ \underline{c}=\dfrac{1}{3}(0 . \bar{a}+0 . \bar{b}+0 . \bar{c}) ?
(The bar indicates repetition, thus 0 . \underline{a} \ \underline{b} \ \underline{c} is the infinite repeating decimal 0 . \underline{a} \ \underline{b} \ \underline{c} \ \underline{a} \ \underline{b} \ \underline{c} \cdots )
Answer Choices
A. 9
B. 10
C. 11
D. 13
E. 14