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Problem 311

Number theory Difficulty 2.4 Find the answer Junior Mathematical Olympiad · Netherlands

Farida makes a list of the integers between $1$ and $10,\!000$ that are divisible by $7$ . For every number on the list she adds the digits of the number. What is the smallest number that occurs as an outcome?
A) $1$ B) $2$ C) $3$ D) $4$ E) $5$

This was a multiple-choice question, but the options didn't survive into the source we have, so there is nothing here to pick from. Work it on paper and mark yourself against the solution below.

Official solution

B) $2$

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