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Problem 746

AMC 12 late, AIME early

Number theory Difficulty 4.0 Find the answer BMO Round 1 · United Kingdom · 2023

A road has houses numbered from $1$ to $n$ , where $n$ is a three-digit number. Exactly $\frac{1}{k}$ of the numbers start with the digit $2$ , where $k$ is a positive integer. Find the possible values of $n$ .

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