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

## Suggestion

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

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

How many numbers have a digit sum equal to $1$? How many numbers have a digit sum equal to $2$? To $3$?

Can we spot a pattern emerging? Could we try arranging our results into a table?

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

Can we use our findings from (ii) to help us? Try picking $8$ again - can we see a pattern?

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

We know that the hundreds digit must be greater than or equal to $5$. What does that tell us about the digits in the tens and units columns?

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

Maybe we can use our answer to (iv) to help us here?

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

How many times does each digit appear in each position?