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MathNet 2018-part-01 — 181 problems (EN–VI) Question 153

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 153

a) Find the sum of the digits of $99 \cdot 33$.
b) Using $999999=10^{6}-1$, find the sum of the digits of $999999 \cdot 333333$.
c) Find the sum of the digits of $999\ldots999 \cdot 333\ldots333$, where each digit in the factors above appears 2018 times.