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Number theory Difficulty 1.1 Junior Find the answer Canada

Shuxin begins with $10$ red
candies, $7$ yellow candies, and
$3$ blue candies. After eating some
of the candies, there are equal numbers of red, yellow, and blue candies
remaining. What is the smallest possible number of candies that Shuxin
ate?

Pick one

Solution

For there to be equal numbers of each colour of candy, there must
be at most $3$ red candies and at
most $3$ yellow candies, since there
are $3$ blue candies to start.

Thus, Shuxin ate at least $7$ red
candies and at least $4$ yellow
candies.

This means that Shuxin ate at least $7 + 4 =
11$ candies.

We note that if Shuxin eats $7$ red
candies, $4$ yellow candies, and
$0$ blue candies, there will indeed
be equal numbers of each colour.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.