2026 AMC 8 Problem 15

Elijah has a large collection of identical wooden cubes which are plain on 4 faces and shaded on 2 faces that share an edge. He glues some cubes together face-to-face. The figure below shows 2 cubes being glued together, leaving 3 shaded faces visible. What is the fewest number of cubes that he could glue together to ensure that no shaded faces are visible, no matter how he rotates the figure?

\textbf{(A)} 4 \qquad \textbf{(B)} 6 \qquad \textbf{(C)} 8 \qquad \textbf{(D)} 9 \qquad \textbf{(E)} 27

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