Question

A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then
cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger sizes.
Also no faces of any of the bigger cubes is painted blue.
How many cubes do not have any of their faces painted yellow ?

Answer 1

There are 36 cubes, 32 of which are of the same size and 4 others are of bigger size. Clearly, each
side of bigger cubes is twice as large as that of smaller cubes. Also, since no face of any of the larger cubes
is painted blue, so, each one of the larger cubes has one face painted red, one face painted black and all
other faces unpainted.

So, The number of cubes having at least one of the faces painted yellow is 20.