## 4. Division with Remainder

Determine the sum of all natural numbers whose quotient when divided by 9 is less than the remainder.

Result: $\quad 960$
## Solution.

The remainder when dividing by 9 can be $0,1,2, \ldots, 8$, and the quotient must be less than the remainder. Let's list all the possibilities.

![](https://cdn.mathpix.com/cropped/2024_05_30_1fa462ef9f831ff2e2d1g-3.jpg?height=729&width=1566&top_left_y=145&top_left_x=255)

quotient

![](https://cdn.mathpix.com/cropped/2024_05_30_1fa462ef9f831ff2e2d1g-3.jpg?height=692&width=665&top_left_y=177&top_left_x=253)

The sum of all such numbers is

$36+98+141+165+170+156+123+71=960$.