How many 3 digit positive integers a, b,c are there who’s nonzero digits a,b,c satisfy 0.abcabc…(repeating) =1/3(0.a…+0.b…+0.c…)

Question

The three dots indicate repitition

Answer 1

Recall:

0.aa... = a / 9

0.bb... = b / 9

0.cc... = c / 9

and

0.abcabc... = abc / 999