Don't really know where the best place to post this is, but I've been struggling with an assignment for a while and don't really know where to start

I need to write a short python program find the minimum number of moves to solve a 2x2x2 rubik's cube from any initial legal configuration, but don't necessarily need to find the actual steps to solve the cube.

For a maths subject, strong focus on set theory and graphs. Our task sheet is explicit in that we do not need to output the solution, and that the program should be very short, likely under 50 lines. This makes me think that simply implementing one of the many algorithms for solving a 2x2x2 cube isn't the goal here, and that there's a relatively simple solution for finding the optimal number of steps without needing to actually solve it.

Does anyone have any thoughts on where to start here? I've spent all day researching it and I'm not really making any progress