2023 Cayley Problem 11

Karim has 23 candies. He eats n candies and divides the remaining candies equally among his three children so that each child gets an integer number of candies. Which of the following is not a possible value of n?

\textbf{(A)}\ 2\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 9\quad \textbf{(D)}\ 11\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 Cayley contests here.