Message #3356

From: joelkarlsson97@gmail.com
Subject: Re: About the number of permutations of MC4D calculating
Date: Sun, 08 May 2016 05:50:02 -0700

I believe that the factors should be arranged like this: B: 6^31 * 12^15*4 * 16!
S: 6^32/2 * 12^16/3 * 16!/2

Like Pham pointed out, the middle factors (regarding orientation of corner pieces) are matching.

The first factor is probably, as Pham said, about the orientation of central edge pieces (since it’s a group of 32 pieces). David V has already proven that Smith is correct here since the orientation of the last of those pieces is limited by 1/2 (see: https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/2136 https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/2136)

The third is indeed about corner permutation. It seems like Balandraud missed to account for the parity of the permutations of corner pieces and that Smith is correct in this regard as well.

To conclude, Balandraud seems to have missed that the last central edge piece (3C piece) can have three different orientations and that the parity of permutations of corner pieces always are even. Thus, I suggest that Melinda changes the count at Superliminal to the value provided by Smith Wolfram|Alpha: Computational Knowledge Engine http://www.wolframalpha.com/input/?i=(16!%2F2)+*+(24!*32!%2F2)+*+64!%2F2+*+(96!%2F24%5E24)%5E2+*+64!%2F(8!)%5E8+*+96!%2F(12!)%5E8+*+48!%2F(6!)%5E8+*+12%5E16%2F3+*+6%5E32%2F2+*+3%5E64%2F3+*+2%5E24%2F2+*+(2%5E96%2F2)%5E2)