MathDB

There is a cube of

3 \times 3 \times 3

formed by the union of

27

cubes of

1 \times 1 \times 1

. Some cubes are removed in such a way that those that remain continue to form a solid made up of cubes that are united by at least one facing the rest of the solid. When a cube is removed, those that remain do so in the same place they were. What is the maximum number of cubes that can be removed so that the area of the resulting solid is equal to the area of the original cube?

Problem Statement