# Another four interesting cosets

These are the distributions of the optimal solution lengths for the cosets where the edges start at the given M-symmetric position, using the quarter turn metric. The first run took longer than the other three combined; not sure why. Only a handful of positions at length 24; none at 26 or higher. I'm currently running the coset where the edges begin in the known length-26 position. It's interesting to note that with the edges superflipped and reflected across the center, all solutions took either 18, 20, or 22 moves.
```edges at identity:
d      pos        M  M + inv
0        1        1        1
8      240        5        3
10      288        6        3
12     8764      197      113
14   116608     2475     1303
16  1075761    22536    11588
18  9978950   208393   105516
20 30348006   633616   320955
22  2561302    53756    27942
44089920   920985   467424
edges at pons asinorum:
d      pos        M  M + inv
12      130        6        6
14      464       16       14
16    81548     1712      892
18  1945598    40755    20782
20 33790110   705339   357035
22  8272070   173157    88695
44089920   920985   467424
edges at superflip:
d      pos        M  M + inv
14     2184       47       26
16    69880     1468      763
18  2125879    44430    22592
20 28197210   588540   297654
22 13694720   286495   146384
24       47        5        5
44089920   920985   467424
edges at superflipped pons asinorum:
d      pos        M  M + inv
18   164140     3442     1766
20 18013361   375910   189872
22 25912419   541633   275786
44089920   920985   467424
```

## Comment viewing options

### Same calculation differently?

Hi Tom,

Can you please share the code that produced the above tables? How much effort was it to produce such tables?

I would like to reproduce the same calculation so that the output is the number of positions at depths X,Y,Z,W where X is edges identity depth, Y is the edges PA depth, Z is the edges superflip depth and W is the superflip PA depth, something like:

X,Y,Z,W pos

0,12,14,18 N1
0,12,14,20 N2
0,12,14,22 N3
0,12,16,18 N4
0,12,16,20 N5
0,12,16,22 N6
:
:
:
22,22,24,22 Nn

of course the sum of Ni will be 44089920 and the list length will be :

9*6*6*3 = 972

The reason I want to do such a calculation is to see witch combination of depths is possible and what are the combinations that never occur... I am guessing for example that the combination 22,22,24,22 will never happen [Nn = 0]...

Thanks

### Nice work!!! Do you have ge

Nice work!!!
Do you have generator expressions for the 24q positions?