Pre-Algebra · Superchallenge problem

For each whole number $k$ from $1$ to $36$, the fraction $\dfrac{k}{37}$ is a repeating decimal $0.\overline{abc}$ with a three-digit repeating block (for example $\dfrac1{37}=0.\overline{027}$). For how many of these $36$ fractions is $a+b+c=18$?