Elijah has a large collection of identical wooden cubes which are white on 4 faces and gray 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 gray faces visible. What is the fewest number of cubes that he could glue together to ensure that no gray faces are visible, no matter how he rotates the figure?
(A)4(B)6(C)8(D)9(E)27
Using 1, 2, or 3 cubes is not possible. By considering all possible cases, you can quickly eliminate them.
(Since all choices are greater than 3, you may skip this part.)
Consider a rectangular prism 2×2×1.
We can rotate the unit cubes so that all gray faces are common faces touching each other; therefore, no gray face is visible.
