Last week my old son had a nice challenge problem in his weekend math program:

An 8x8x8 cube is painted black out the outside and then chopped into 1x1x1 cubes. How many of the 1x1x1 cubes have paint on 0, 1, 2, 3, 4, 5, and 6 faces?

This problem was even accessible to my younger son, in fact, we started the project to by discussing that problem:

So, for today’s project I thought it would be interesting to try out a similar problem in 4 dimensions.

It turned out to be far more confusing to the boys that I was expecting. So, whoops, I guess. I’ll go through this project again with them, but using a very different approach. But, for now, here are the 4 long discussions we had about how to attack this problem.

Mostly this post is a reminder to me that not everything goes as well as you’d hoped it would: