2025 AMC 8 Problem 21

The Konigsberg School has assigned grades 1 through 7 to pods A through G, one grade per pod. Some of the pods are connected by walkways, as shown in the figure below. The school noticed that each pair of connected pods has been assigned grades differing by 2 or more grade levels. (For example, grades 1 and 2 will not be in pods directly connected by a walkway.) What is the sum of the grade levels assigned to pods C, E, and F?

\textbf{(A)} 12 \qquad \textbf{(B)} 13 \qquad \textbf{(C)} 14 \qquad \textbf{(D)} 15 \qquad \textbf{(E)} 16

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.