This is a follow-up question of Is there an equation for permutations with different numbers of element available?
For a regular permutation, the number of possible configurations for a 2 * 2 * 2 cube(not considering symmetries) would be (4*6)!=24! . However, since for every colour only 4 blocks are available the case would be a lot more complex. So my questions are:
- What is the number of possible configurations of a 2 * 2 * 2 Rubik's cube(without considering symmetry)?
- Is there a way to generalise this process, so that we could apply the same procedure to similar cases, for example a 3 * 3 * 3 Rubik's cube?
- What is the number of possible configurations of a 2 * 2 * 2 Rubik's cube if symmetry is to be considered(might be related to group theory...)?
This page https://www.therubikzone.com/number-of-combinations/ has the number of permutations up to a 10x10, although if you wanted even more you can calculate it via the formula found here: https://oeis.org/A075152
This is going to be way less than just rearranging any of the "stickers" on the cube, as most of these are not a valid rubiks cube permutation.