Maths Olympiad Prep

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Number theory Difficulty 2.4 Junior Find the answer Netherlands

Farida makes a list of the integers between 11 and 10, ⁣00010,\!000 that are divisible by 77. For every number on the list she adds the digits of the number. What is the smallest number that occurs as an outcome?
A) 11 B) 22 C) 33 D) 44 E) 55

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is B, and the solution below works it through.

Solution

B) 22

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