2025 AMC 10B Problem 21

Each of the 9 squares in a 3 \times 3 grid is to be colored red, blue, or yellow in such a way that each red square shares an edge with at least one blue square, each blue square shares an edge with at least one yellow square, and each yellow square shares an edge with at least one red square. Colorings that can be obtained from one another by rotations and/or reflections are to be considered the same. How many different colorings are possible?

\textbf{(A)} 3 \qquad \textbf{(B)} 9 \qquad \textbf{(C)} 12 \qquad \textbf{(D)} 18 \qquad \textbf{(E)} 27

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