Originally posted by piderman
Um, we have here a 20x20x20 cube, but only the sides have cubes. Furthermore, the corners are always corners etc. So you have 6! possibilities for the corners, (12*18)! possibilities for the edges and (6*18*18)! possibilities for the rest of the cubes. That's a total of 6!*12!*(18!)^3. Then allow for mirroring, same coloring(!) etc. You calculate, TM37! (I don't have a calculator nearby )
The 20X20X20 cube is a lot trickier than the standard cube. one reason it is tougher to solve is that, unlike odd number cubes (for example 7X7X7 or 3X3X3), there are no immobile center tiles on each face. if you want to see some facts on the 20 cube, including the number of possible combinations, you can go to
the actual number of combinations is about 1400 orders of magnitude more than your estimate! it is truly a mind boggling number. i have really no concept of just how big the number is -- i don't think many people do.