Review question

# How many integers less than $100$ have digits that add to $8$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5519

## Question

We define the digit sum of a non-negative integer to be the sum of its digits. For example, the digit sum of $123$ is $1+2+3=6$.

1. How many positive integers less than $100$ have digit sum equal to $8$?

Let $n$ be a positive integer with $n<10$.

1. How many positive integers less than $100$ have digit sum equal to $n$?

2. How many positive integers less than $1000$ have digit sum equal to $n$?

3. How many positive integers between $500$ and $999$ have digit sum equal to $8$?

4. How many positive integers less than $1000$ have digit sum equal to $8$, and one digit at least $5$?

5. What is the total of the digit sums of the integers from $0$ to $999$ inclusive?