A four-digit number $\overline{abcd}$, and a five-digit number $\overline{efghi}$, where $a,b, c, ..., i$ are from 1-9 and are distinct. We have
$\overline{abcd}*3=\overline{efghi}$.
What are $a, b, ..., i$?
What I have tried: I can deduce that $\overline{efghi}$ must be divisible by 9, but then the enumeration does not give the answer? Can this hold at all?
By exhaustive search there are two solutions:
$$5823\cdot 3 = 17469$$ $$5832\cdot 3 = 17496$$