# of 2G L6C corner permutations

[shadowslice e]

So, I have 2 real questions here:
1) what is the number of possible 2 gen permutations for the last 6 corners ignoring orientation and edges? (I believe that CP can always be solved in 4 moves from this step)
2) how would you go about calculating this number?

Thanks

 

[ch_ts]

120
http://www.jaapsch.net/puzzles/pgl25.htm

 

[Robert-Y]

6 choices for any corner position, 5 for the next one, 4 for the next one and this leaves no more choices therefore I think it's 6*5*4=120 cases.

 

[Christopher Mowla]

At math.stackexchange, I wrote a post about the order of the <U,R> subgroup for which I wrote independently of any previous works. Quite a few people liked it, so if you cannot understand Jaap's page, check it out.

Specifically, Lemma 5 is the one which answers your question (the answer is 120 as the previous posters have said), but Lemma 4 and its corollary are what we use to conclude with Lemma 5. So read from Lemma 4 to the end of Lemma 5.

 

[rokicki]

At math.stackexchange, I wrote a post about the order of the <U,R> subgroup

In that post you use diameter at least twice where you mean order.