Painted
Cube
You
have a 3 x 3 x 3 cube made from wooden cubes.
It
is painted on the outside.
Suddenly
you drop the cube and it falls apart. How many little cubes are painted
on:
0 faces?
1 face?
2 faces?
3 faces?
How
did you work it out?
Are
there any cubes with more than 3 faces painted? Why?
What
if you had a different sized cube to start with?
Or
even a cuboid?