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*