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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

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