2025 AMC 8 Problem 15

Kei draws a 6-by-6 grid. He colors 13 of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically, forming pairs of overlapping unit squares. Let m and M equal the least and greatest possible number of gold-on-gold pairs, respectively. What is the value of m+M?

\textbf{(A)} 12 \qquad \textbf{(B)} 14 \qquad \textbf{(C)} 16 \qquad \textbf{(D)} 18 \qquad \textbf{(E)} 20

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