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MathNet 2016-part-04 — 184 problems (EN–VI) Question 25

Math Olympiad Vault · MathNet 2016-part-04 — 184 problems (EN–VI)

Question 25

Let the natural number be $n=\overline{11 \ldots 1}+\overline{22 \ldots 2}+\ldots+\overline{88 \ldots 8}+\overline{99 \ldots 9}$, where each number of the form $\overline{a a \ldots a}$ has $2015$ digits equal to $a$. Determine how many digits $9$ the number $n$ contains.