Sven wrote:I think the speedcubing numbers are way too large, I have more confidence in the Wikipedia numbers. The speedcubing approach sees a 3x3x3 cube (for instance) as consisting of 27 pieces that can be moved. But in reality there is one "invisible" piece in the middle that is irrelevant, and furthermore the six central pieces always remain fixed relative to each other (from a viewer's perspective) so their movements are irrelevant as well. And as a third point, I think that there are many cases where two different move sequences lead to identical states of the cube for the viewer. Finally, the speedcubing approach also considers different orientations of each single piece which is irrelevant to the viewer (you can turn a red square by 90, 180, 270 degrees and it still looks the same) so it should also be irrelevant to permutation calculations.
As I said in my previous post, if you feed n = {2, 3, 4, 5, 6, 7, 8} into that equation, it gives the same exact results than in Wikipedia:
You are right, I initially misunderstood that part of your previous post regarding Wikipedia numbers.
Sven wrote:Another question is, do n x n x n Rubik's cubes actually exist with even n? If so, how many "fixed" central pieces do they have (0 or 24)? If they only exist in mathematical theory then why should they be relevant for us?
According to the first paragraph of each article, these cubes do exist and have not fixed facets. YouTube searches might return videos of people solving 2x2x2 cubes, 4x4x4 cubes and so on.
Thanks for the links, very interesting indeed!
Sven Schüle (engine author: Jumbo, KnockOut, Surprise)