SEAMO 2027 - Paper F - SET 06 - Self-study Question 25

A three-digit number $\overline{abc}$ has no zero digit; its digits need not be distinct. If $\overline{abc}$, $\overline{bca}$ and $\overline{cab}$ are all divisible by 7, find the sum of all possible numbers $\overline{abc}$.