2017 Gauss 8 Problem 21

The number of dots on opposite faces of a regular die add to 7. Four regular dice are arranged as shown. Which of the following could be the sum of the number of dots hidden between the dice?

\textbf{(A)}\ 22\quad \textbf{(B)}\ 26\quad \textbf{(C)}\ 24\quad \textbf{(D)}\ 21\quad \textbf{(E)}\ 23

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 Gauss contests here.