# math puzzle: 4 digit number times 3

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?

$$5823\cdot 3 = 17469$$ $$5832\cdot 3 = 17496$$