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MathNet 2019-part-04 — 184 problems (EN–VI) Question 123

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 123

A positive integer is called sparkly if it has exactly 9 digits, and for any $n$ between $1$ and $9$ (inclusive), the $n^{\text{th}}$ digit is a positive multiple of $n$. How many positive integers are sparkly?