Desk Calendar Problem

So, I saw this on a colleague's desk. It got me thinking: "These are six-sided cubes. So, how can twelve digits split as a six and a six represent all thirty-one days of a month?"

It's a problem that makes use of trial and error, make a model and test and thinking logically. I made a sheet to introduce the problem:

The sheet, with differentiated support and my answer can be found here.

I wonder how many combinations of answer there are...