## Task 3 - 110613

Four faces of a wooden cube with an edge length of $3 \mathrm{~cm}$ are painted red, the other two remain unpainted. Afterwards, the cube is cut into exactly 27 smaller cubes, each with an edge length of $1 \mathrm{~cm}$. Determine the number of these small cubes that have

no red-painted face, exactly one red-painted face, exactly two red-painted faces, exactly three red-painted faces!

Distinguish the following cases:

a) The unpainted faces do not share an edge.

b) The unpainted faces share an edge.

It is sufficient to provide the numbers without justification.
a) Exactly 3 small cubes have no red-painted surface.

Exactly 12 small cubes have exactly one red-painted surface.

Exactly 12 small cubes have exactly two red-painted surfaces.

None of the cubes have three red-painted surfaces.

b) The numbers in this case, in the above order, are: $4 ; 12 ; 9 ; 2$.