PCMS (pairs, CLL, M and S slices) is an advanced method for speedsolving using columns first, designed by Kenneth Gustavsson in late 2008. The method compromises between easy look ahead and low move count (slice metric), and the result is 'decent' for both parts. The first two steps of PCMS leave the cube in a very similar state to the first two steps of Roux method.
Starting the solve
As most cubers I start from the same side/colour most times but if there is one (or more) pair compleated in the opposite colour from the scramble, then I use that side. When doing so I only solve columns opposite. These are bi-directional so you just need to turn the cube up-side-down before the slices are solved and you can go in your normal colour from there.
Inspection, this is the key to success, practice inspection to be able to predict the turns for solving 2-3 pairs and you will have good times.
Looking for the pieces for the pairs while going is the slowest part of this method so it really pays to be good at predicting the turns. Use what you got, in some scrambles two corners are solved next to each other, pair the edges on the opposite side and then put the corners there using D2 (or use a solver to find algs to put them in directly from some easy to set up to positions).
If you cannot see a easy pair from start, then, to not wander over the puzzle in random, use exclusion; There are nine permutations for the edge that all needs three moves to be solved, the rest of the positions are two or possibly even one move to solve. If the corner is oriented in D as in the the image below, and the edge is sitting in one of the darker positions, (assuming it is not solved), then it is a bad pair. All these positions are near the corner so you can see it pretty easily and then exclude that corner and pick another one.
The bad pairs.
The rest of the positions you will soon learn to recognise, three of them are just a D (or u) move to pair up and then the last group that needs two moves are eleven diffrent ones. Beeing able to quickly find the first pair leaves enough inspection time to find at least one more, possibly even two.
The move count is dependendant on how well the first step is solved, if you add some extra look ahead and pair up more than one pair before you start to place them you can get as low as 10 turns for all four pairs at times. Going like so it is even possible to solve in under 45 moves on average but not while speeding, the number of moves is not that important, the gripping while solving the pairs is the part where you can gain speed in this step, rather place a pair using U Rw U R' than (y') R' U R, that to avoid cube orientations. If you are speeding 15-17 turns is not uncommon, rather normal.
Pairing up is done a bit diffrent from what is used in Fridrich F2L, first find a pair, preferably one where the corner is unoriented in the U-layer and the edge is in the D-layer. If the edge is not there, then one in the U-layer is a second choise because it is easy to place in D using a single slice move. Orient the cube so that the edge is in FD or BD position, move the corner to position using a U move and then the pair is built using the M-slice. For the pairs where the corner or the edge is in bad position you have to do some setup turns to fix that, or simply use the CFOP alg for the same pair.
L2 B F U2 F' L2 B' D F' U2 R D2 L F2 L' D' B2 F U2
- p1; pieces are good, just do M2 to pair up and (z) to place.
- p2; because only one pair is solved here we can do the next from bottom and up, like this: U L2 to pair and R' U (x) to place it.
- p3; nice corner, edge in U-layer so setup that one first using (y) M' then U M2 to pair up and U2 B' to place it (temporarly move the B-side to U before the B turn).
- p4; both pieces in position so: (y) U2 M2 to pair up and U R' U2 R to place.
16 moves not counting puzzle rotations, pretty normal.
At bottom of this page you can find some more examples.
CMSLL is pretty much the same as CLL for 2x2x2 (or CF) but in some cases you need to use double layer turns to preserve the pairs, for example R U' R' U' F' U F becomes R U' Rw' U' F' U F. In cases where that does not work any alg optimal for CMLL will do fine but with the advantage that you don't have to AUF the case so it fits with the empty M-slice, here the S-slice is equally good to use.
Algs and all cases you can find at the CxLL pages.
If we continue from the example for the pairs, then this case is Sune :P
- (y2) R U R' U R U2 R'
Try to look for edges to solve in the next comming step while executing the CLL alg. Advanced it is possible to solve some from inserting slice moves in the CLL, like if it is Sune: R U R' U (M) R U2 R'
The first part of the second half of the solve is all intuitive, you pair one first layer edge with it's centre and then place it into position. After some parctice this is really easy, no thinking required. It is possible to create more advanced methods than this and use algs for some parts but that is not a good idea, it would only kill the easiness and speed for this part of the solve.
(Continued from above)
- p1; U' M' to pair (y) M' to place.
- p2; paired! M' U2 M to place.
- p3; paired again, (y') U2 M' to place.
Note that you may solve the third pair before the second using only one move, that would save one U2 but add two puzzle rotations ((y') p2 (y) p3 (y') L5EO). I usally solve the edge opposite to the first as the second one just to save on rotations, I think that it is faster on average, aspecially if you look for that edge while solving the first one. If it is stuck in D then try to find one edge that goes to the side in U instead. Then the same thing applys; solve the edge opposite to the second as the third to save on rotations.
L5E: (dunno what name I used at first but it will be L5E from here, that to stick to cubing vocabulary standards =)
(Continued from above)
- L5EO; U' M' U' M U M' U' M to orient and place FD edge.
- L5EP; U-PLL
See L5E for description and algs.
You only need five algs for orientation but it is a good idea to add as many as possible that also solves the FD edge, this has two reasons, first is that EPLL is faster to recognise than the full L5E permutations (the 5-cycles are particulary slow), the second reason is that EPLL skips 1:12 times, for five oriented edges that number is 1:60.
Note; after I wrote this article I have compleated L5EOP, wich is the method I mostly use and also did in the examples of this page.
If you don't like L5E or already know ELL it is possible to end the solve by also putting down the last D-layer edge in the same manner as the other three and then end in ELL. But I do not recommend it, because the slow recognition of ELL L5E is faster on average, you may save a few moves but not many...
But as an extension to PCMS ELL is the first thing to think of because sometimes you skip the last edge while solving the third one and in some cases it was already skiped from start and you did not see that, so you end up having a ELL. You can still solve all ELL's using L5E and in some cases even optimal but there are good cases in ELL that you would miss.
The first half of this method, columns is much harder to master than the slice part, that can be learned fairly easy. Learning CLL, if you don't know it before can take some time, the algs are not that bad but the recognition part is. That also applys for solving the pairs in the start, look ahead is harder than in CFOP because there are more places to look for the edges (D layer).
So the first parts are where you need to put you efforts if you like to use this method for speedsolving, expect a good bit of struggling before it starts to get fluid. The second part on the other hand is where the fun is, aspecially if you are good at MU algs, most algs here are short and finding the cases is quick, sometimes it is hard to keep ut to the rapid phase, it just went solved and you don't know how :D
L D2 L' D2 L F2 D2 B2 U L' F' L' R F D2 R2 U2 B2 L
Inspection: One pair (orange/blue) is doable using a single M' but we like to find some more to do before we start. If we think we solve that first pair and also reorient using (z'), then the orange/green is in fine position, it needs a U' and a M to be paired and is then easily placed. Now inspection time is running out so we are pleased with that...
- p1; M' (z') as planned.
- p2; U' M as planned, then U2 L' U (x') to place.
- p3; then we find a red/green corner in front of the eye and the edge is right under it so U' M' to pair up and Rw U R' to place.
- p4; this last pair is looking bad but is not that hard, first orient the cube (y) and then R U' M2 to pair up and U R' to place.
16 STM again, as said, it's the normal.
CLL is mirror diagonal Sune, I'm using the usual Sune + inserts for this one, a COLL actually.
- L' U' L U' (R U') L' (U R') U2 L inserts in parentesis.
- p1; M' to pair and then reorient before placement (y) U2 M'
- p2; the opposite to the first is stuck in D so next will be orange; (y) U M' U' M.
- p3; bad, but; (y') M' (y') M' U M (y) M the last turn will go back up again in orientation but trying to see that while going does not work well.
Last five edges:
- L5EO; M' U M U2 M' U' M orients edges and permutes the FD edge.
- L5EP; H-PLL
R2 U' B2 F2 L2 B2 R' D2 B R' D F D' U2 B' U' R' B2 L2
Inspection: No solved pairs and no one move pairs in the D colour so let's look if there is any in the opposite colour and yes, the red/blue one is one turn. Orient the puzzle so it comes to solving position for that pair (x' y') and quickly look if there is one more... red/green will do, it is two moves to pair up:
- p1; D as planned.
- p2; B' M2 as planned, (temp tilt the B-side to U) then U2 R' U (x) to place.
- p3; fine, already paired and easy to place; U' L.
- p4; corner oriented in U, I use an alg for this one but first I need to set up the edge, AUF and orient the puzzle; M' U2 (y') -- L' U2 L2 F' L' F ... Yeha, I'm lefty.
16 STM, a little luck and a long pair in the end made it an average solve, expect the last pair to use more turns than the rest, often it is not easier to solve here than in normal F2L.
- (y) R' U L U' R U' L' U' L U' L' ... lefty alg again =)
Now, because I solved in the opposite colour from start I AUF and turn the puzzle up-side-down before I start the second half of the solve; U' (x2)
- p1; orange in front, centre in back so; U2 M U (y) M
- p2; skipped!.
- p3; (y') M U' M' easy =)
Last five edges:
- L5EO; U M' U M the finest case.
- L5EP; Z-PLL
That one was pretty nice, easy cases in the end, as it often is using this method.