https://mathenchant.wordpress.com/2019/01/16/the-magic-of-nine/

After you read this essay, you’ll be able to compute the answer to questions like “What’s the remainder when you divide 123456789 by 9?” or “What’s the sum of the digits when you multiply 123456789 by 9?” without setting pencil to paper, purely through the power of your mind. But before I explain that, I’d better address the question many of you are asking: why would anyone *want* to learn how to do this sort of thing? (Short answers: to stay sane, to balance their checkbook, and/or to become fame-ish.)

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