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Algebra Difficulty 3.8 AMC 10/12 Find the answer Slovenia

The value of the expression $10^{2016} - 10^{15}$ is a positive integer. Determine the sum of its digits.

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Solution

The positive integer which represents the value of the expression $10^{2016} - 10^{15}$ has 2016 digits. The last 15 of them are 0 and the rest are equal to 9. The sum of the digits is therefore $(2016 - 15) \cdot 9 = 18\,009$ .

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