The Painted Cube, Revisited

I'm a big fan of the "Painted Cubes" problem (although to be honest, I don't think I have ever actually used it with kids...). I feel like most math-y people have seen the problem at some point: If you build an n x n x n cube out of unit cubes and paint all the faces, how many of the unit cubes will have one face painted? 2 faces? 3? 0?

This problem from NRICH Maths is a a cool extension. I love the use of the word "some"--it's so interesting how that word both increases access and makes the problem so much harder. I haven't actually done any work on the problem yet, but it just makes me want to play!