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2019/20 AHSMC Part 1 Problem 3

Problem 3 of 16

The sum of the digits of a positive integer nn is 20192019. The smallest number of digits nn can have is

Answer choices

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Solution

Since 9⋅224<2019<9⋅225, 9 \cdot 224 < 2019 < 9 \cdot 225, 224224 digits are too few. 225225 digits are possible, indeed, 224224 nines and a three will lead to a sum of 224⋅9+3=2016+3=2019. 224 \cdot 9 + 3 = 2016 + 3 = 2019. The answer is (D).

University of Alberta