When 27 cubes are assembled, one of the cubes fills the center, leaving 26 cubes visible on the outside. How many "corner" cubes are there (with 3 sides visible), how many are "edge" cubes (with 2 sides visible) and how many are "center" cubes (with 1 side visible)?

 

Correct Answer

8 corner, 12 edge, 6 center

The "corner" cubes are marked in orange, "edge" cubes are marked in blue, and "center" cubes are marked in magenta in the visualization above.

Each of the smaller cubes in the 3 by 3 by 3 configuration that is touching a vertex of the larger cube has 3 sides visible; there are 8 vertices of the larger cube, so there are 8 corner cubes.

Each of the 6 sides of the larger cube has 4 "edge" cubes as marked where 2 sides are visible.

Each of the 6 sides of the larger cube has 1 "center" cube in the middle with only 1 side visible.