# # of 2G L6C corner permutations



## shadowslice e (Sep 17, 2015)

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


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## ch_ts (Sep 17, 2015)

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


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## Robert-Y (Sep 17, 2015)

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.


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## Christopher Mowla (Sep 18, 2015)

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*.


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## rokicki (Sep 19, 2015)

Christopher Mowla said:


> 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.


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