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Australian AMC 2020 - Senior Question 24

AMC AUSTRALIA · Australian AMC 2020 - Senior

Question 24

Alex writes down the value of the following sum, where the final term is the number consisting of 2020 consecutive nines:
$$9+99+999+9999+\cdots+\underbrace{99\ldots9}_{2019\text{ nines}}+\underbrace{99\ldots9}_{2020\text{ nines}}$$
How many times does the digit 1 appear in the answer?
  1. 0
  2. 2016
  3. 2018
  4. 2020
  5. 2021