17. Find the sum of the digits of the product
$$
(\underbrace{111111111 \ldots 111}_{20071^{\prime} s}) \times 2007
$$
17. Ans: 18063.
Since there is no carry, this is simply $9 \times 2007$. Or observe it is actually
$$
222 \underbrace{99999999 \text { 9...999 }}_{2004} 777 .
$$