## Counting Nines

#### Problem

If you wrote all of the numbers from one to one-hundred on a piece of paper, 1, 2, 3, 4, ..., 99, 100. How many number nines would you write in total?

#### Solution

Let us consider the first and second digit.

Changing the first digit, | ?9 | 10 numbers (i.e. 09, 19, 29, ... , 99) | |

Changing the second digit, | 9? | 10 numbers (i.e. 90, 91, 92, ... , 99) |

Making a total of 20 number nines being written.

If all the digits on the piece of paper were added together, what would be the total?

Problem ID: 100 (Feb 2003) Difficulty: 1 Star