Multi-Digit Multiplication · Superchallenge problem

When you multiply $213 \times 3$ with the standard algorithm, you never have to carry: $3 \times 3 = 9$, $1 \times 3 = 3$, $2 \times 3 = 6$, so the answer is $639$. How many three-digit numbers can be multiplied by $3$ with no carrying at all (and give a three-digit answer)?