Question

A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

Answer 1

There was a general formula which I don't remember at this moment.

Answer 2

12

Answer 3

4 on two opposing faces + 2 on each adjacent face
4*2 + 2 * 2

Answer 4

Yes it will be \( 12, (3-2)\times 12 = 12 \)

Answer 5

Another way to think about it is there will be exactly one such cube along each edge and since a cube has \( 12 \) edges there will be exactly \( 12 \) such cubes.

Answer 6

As an exercise one could try solving exactly three,one and zero side colored too.