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The sum of the digits of the number given by the product $$ \frac{666.....666}{2021 digits}$$ X$$ \frac{999.....999}{2021 digits}$$ is
Correct Answer: 18189
Let $$n=2021$$. The first factor is $$\frac{2}{3}\left(10^n-1\right)$$ and the second is $$10^n-1$$. Their product has the digit pattern corresponding to $$666\ldots666\times999\ldots999$$, whose digit sum is $$9n$$. Thus the required digit sum is $$9\times2021=18189$$.
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