2024 Fermat Problem 4

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?

\textbf{(A)}\ 11\quad \textbf{(B)}\ 7\quad \textbf{(C)}\ 17\quad \textbf{(D)}\ 20\quad \textbf{(E)}\ 14

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.