Cube

Imagine a Rubik's cube, but one without any of the internal mechanics that make it turn - so, one made up of 27 smaller cubes.

Question: How many cubes have zero, one, two or three painted sides?

The answers are 1, 6, 12 and 8 respectively.

Now imagine a similar cube, but rather than being made up of 3 smaller cubes on each side, it is made up of n smaller cubes on each side. Now how many cubes have zero, one, two or three painted sides?

Answers:

0 - (n-2)^3

1 - 6(n-2)^2

2 - 12(n-2)

3 - 8

Answers all worked out by Jake in a self-inspired work extension at school.

Now there's someone who is ready for the challenges of grammar school!

*Dad glows a little bit with pride*