# FMC: a Complete Tutorial

#### FJT97

##### Member
Wow.

Very nice work!
I definitly gonna learn from this!

#### porkynator

##### Member
Mistake under 'think outside the box' section.
You must have made this tutorial earlier but it would be unfair to Vincent Shew if you don't add his name with Sébastien Auroux in Intro. Please do the same.
Thanks, it's going to be fixed as soon as I upload the new version.

Overall, a very nice document.

I think one of the glaring omissions in the document is the technique of making use of symmetries and inverses in algs, where applicable. Well, I know this issue (and even cyclic shifts) is talked about briefly on page 21, but I think being aware of when you can use mirrors and inverses, or apply algs from another angle is so fundamental for FMC, that it should have its own section.

For example, an OLL case that is solved by:

R U R' U' R' F R F'

can also be solved by the mirror alg:

R' U' R U R B' R' B

This gives two possibilities for a PLL skip instead of one. (Or at least two chances of cancelling out the previous move, saving at least 2 moves.)

The double-sune OLL case has 8 possibilities. The standard alg won't change corner permutation, but all 8 3-cycles of the 4 edge pieces (preserving orientation) can be accomplished, simply from using the standard alg or its inverse, its mirror or its mirror's inverse; and applying from appropriate angles.

An A-perm can be replaced by an inverse mirror, again with the possibility of getting a better cancellation.
Thanks for this, I think I will add a section.
I actually use this in solves, but didn't think about it while making this tutorial.

Pure piece-swapping algs (standard J-perm and T-perm, for example) are always self-inverse, so you can always apply the inverse in place of the "normal" alg(s) that you know. This gives you another chance to get good cancellations when using these algs for insertions (or even linear finishes).
It's quickly mentioned under the "Other Insertions: 2 Corners and 2 Edges" subsection. Maybe I should make a longer explanation.

One other thing, in talking about corner 3-cycles, I'm not sure that it was mentioned that the same 3-cycle can often have two different 8-move commutator solutions. A good cancellation could be missed if only one of them is considered.
I have put this in a note in the first example for insertions. I didn't say "often" but, just pointed out it was possible in this case. I thought this would be enough, since I am not explaining commutators anyway, but just linking another tutorial for them.

It doesn't look to me that there is any mention of corner/edge pair 3-cycles.
There is, under "Block Commutators" Also, I've linked Ryan Heise's page about them multiple times and repeatedly advised taking a look at it... I hope this is enough.

There are some CFOP-related techniques not mentioned, though perhaps not very mainstream by experts as they tend to avoid CFOP generally. There is the technique of solving skewed corner/edge "pairs." There is also a rather obscure technique of using slot-swapping "PLLs." (Have you ever wished you could do an "N-perm" in 5 moves?)

All in all, I would say it's probably far from "complete," but at least a good solid introduction to most of the standard techniques.
This is interesting, but I don't know if it can be really useful in FMC. After all, an N perm is just a 2c2e swap, I think the best way to deal with it is trying to insert an algorithm. Same for other PLLs (like R, V, ...).

This looks very nice! I can't think of anything obvious that's missing (although Bruce's examples of symmetries are useful), and it looks great for solvers of any skill level.

Have you considered making this a website, e.g. a page (or multiple pages) at fmcsolves.cubing.net?
In particular, being able to link to specific sections would be useful. I think this could also benefit from continual updates, which is usually more appropriate for a website than a PDF. (Although you can still provide a PDF, like we do for the Regulations.)
I have considered it, but when I was done translating I just wanted to publish this tutorial as soon as I could
anyway, it would be nice to have some tool automatically converting from ODT (or PDF) to a web-based something (the first that comes to my mind is this). Do you (anyone) know one?
Also the opposite would be cool, so that I just need to update the HTML page and a new PDF version is created automatically (otherwise I need to update the ODT and make a new PDF everytime).

To anyone saying "great", "good job" and other kind words: Thanks
To anyone saying "thanks": you are welcome

#### guusrs

##### Member
Hi Sebastiano,

Good tutorial end very complete.
Compliments!

Gus

#### brian724080

##### Member
Wow, that must have taken you a lot of time, good work!

#### FJT97

##### Member
Typo in: 2. How to proceed during a solve:
Here I will described some basic techniques used in FMC solves.

#### stoic

##### Premium Member
Really awesome document.
Thanks for posting.

#### RageCuber

##### Member
I only know CFOP so I understood very little of this
but I think I can learn some by oct, thats when FMC 2014 is (in the u.s)

#### porkynator

##### Member
Thanks again everybody

Fixed the reported typos, added a nice table of contents (now you can click on the page number to get there).
Haven't added the new section about "how to use algorithms" yet.

#### Keroma12

##### Member
Footnote 1: I think you want to say "consisting of"
Roux: not sure what you are trying to say with "will make in some way complete it"
just before blockbuilding: "and other tutorials"
few lines down: missing a space between "... FMC.It ..."
just after footnote 24: "and"
edge commutators: [M' U2] is missing a comma
footnote 35: this isn't english?
footnote 51: is cut awkwardly across two pages
in cycle theory: "the posts I've linked"
footnote 64: "more in brackets" should be move
section 4: "Trying for one hour"

Thanks again

#### Cubenovice

##### Forever Slow
Nice tutorial.

I feel honoured that you included a link to my Human Thistlethwaite FMC thread

I have just added some examples, including my 27 HTM PB for this method, to the thread.

Some other stuff:
Under the "Get Lucky" title you could expand a bit more.

As an example:
In FMC you often work towards a F2-1
When you are there it is a good moment to try your luck:
Insert the last pair in several different ways: you may get lucky and end up with just a three cycle or 2C2E swap left.
You can also finish F2L in the shortest way and try some of the 6-7 move OLL's

You need to hunt a little for luck

Last edited:

#### cuBerBruce

##### Member
It's quickly mentioned under the "Other Insertions: 2 Corners and 2 Edges" subsection. Maybe I should make a longer explanation.
Not really. You said that inverses and cyclic shifts (of a 2C,2E swap alg) would would also solve a 2C,2E swap case, but did not mention that inverses of a 2C,2E swap alg will solve the exact same case. This will also be true for corner double swaps and for edge double swaps, as long as there are no "misoriented swaps" involved. (A cyclic shift, of course, will not generally solve the exact same case.)

There is, under "Block Commutators" Also, I've linked Ryan Heise's page about them multiple times and repeatedly advised taking a look at it... I hope this is enough.
Yep, I missed it. You are right.

This is interesting, but I don't know if it can be really useful in FMC. After all, an N perm is just a 2c2e swap, I think the best way to deal with it is trying to insert an algorithm. Same for other PLLs (like R, V, ...).
Well, insertions are more time-consuming than simply using a memorized alg, and also not generally useful for linear FMC. I see it as another thinking-outside-the-box technique that one can consider, perhaps particularly for a linear solve or a last-minute attempt to avoid a DNF. Anyway, the idea is to end up with a shorter "PLL" alg than you would have had if you solved every F2L pair into the correct slots. In some cases you might be able to avoid an extra AUF during F2L by inserting a pair into the wrong (diagonally opposite) slot. One obvious downside is that the "skip" case is no longer a skip.

I just did a God's algorithm analysis for the 288 PLL+AUF cases. I got an average of 11.497 moves for slot-swapping PLLs, whereas for normal PLLs it is 11.642. So the overall advantage of slot-swapping PLLs is very small, and is worse in terms of best case (5 vs. 0) and also worst case (16 vs. 15). I do agree that this is a very obscure technique and don't consider its omission a big deal.

- - - - -

Your response ignored the other much more common technique that I mentioned, that of using skewed CE pairs, as in using a sequence like D R U' R' D' to solve both a corner and an edge. While the D layer moves may seem somewhat costly, if the alternative is a 6- or 7-move sequence to solve a conventional pair, it's still a win (assuming the skewed pair is solved in 5).

This is in some way an extension of the keyhole idea, except you try to solve both a corner and an edge at once, instead of only one piece at a time. With keyhole, you're tending to spend about 4 moves to solve only 1 piece. A moves-per-solved-piece ratio of 4.0 is pretty bad. For a 30-move solution, you need a ratio of 1.5 overall. In your keyhole example, you get sort of locked into having to solve a single edge piece at a time anyway with the layer-minus-a-corner start.

#### Cubo largo

##### Member
Potrebbe sembrare eccessivo o ridondante farlo anche qua ma è fatto perchè sei più su questo forum che su quello italiano.
Volevo ringraziarti molto perchè finalmente questo lavoro mi ha dato una grossa spinta ed ha avviato un positivo processo che spero non si arresti più. Forse mancavo di coraggio o forza di iniziativa, forse avevo solo paura che rimanesse una cosa a metà come le molte altre che ho (quasi) fatto.
Mi viene da ripensare a quell'obbrobrio che feci a Monterotondo. Acqua passata. Spero di ricominciare in positivo
Vorrei romperti il meno possibile ma se posterò mie solve sul thread italiano risponderai o sarebbe meglio secondo te proporle su questo forum, anche per un discorso di maggior confronto?
Dimmi tu se potrebbe essere produttivo o se solo lasciata passare come la solve del primo che capita-->non la guardiamo e commentiamo l'ultima di Sebastiano.
Ti ringrazio anche in anticipo per la risposta. A presto,
Davide

*for non italian user: sorry but the message was too long and I can't translate it in english, it's too complicate for me, not only long.

#### porkynator

##### Member
Footnote 1: I think you want to say "consisting of"
Roux: not sure what you are trying to say with "will make in some way complete it"
just before blockbuilding: "and other tutorials"
few lines down: missing a space between "... FMC.It ..."
just after footnote 24: "and"
edge commutators: [M' U2] is missing a comma
footnote 35: this isn't english?
footnote 51: is cut awkwardly across two pages
in cycle theory: "the posts I've linked"
footnote 64: "more in brackets" should be move
section 4: "Trying for one hour"

Thanks again
Fixed

Nice tutorial.

I feel honoured that you included a link to my Human Thistlethwaite FMC thread

I have just added some examples, including my 27 HTM PB for this method, to the thread.

Some other stuff:
Under the "Get Lucky" title you could expand a bit more.

As an example:
In FMC you often work towards a F2-1
When you are there it is a good moment to try your luck:
Insert the last pair in several different ways: you may get lucky and end up with just a three cycle or 2C2E swap left.
You can also finish F2L in the shortest way and try some of the 6-7 move OLL's

You need to hunt a little for luck
Thanks, I will add some "Get Lucky!" example.

Not really. You said that inverses and cyclic shifts (of a 2C,2E swap alg) would would also solve a 2C,2E swap case, but did not mention that inverses of a 2C,2E swap alg will solve the exact same case. This will also be true for corner double swaps and for edge double swaps, as long as there are no "misoriented swaps" involved. (A cyclic shift, of course, will not generally solve the exact same case.)
Right, I should add a few lines.

Well, insertions are more time-consuming than simply using a memorized alg, and also not generally useful for linear FMC. I see it as another thinking-outside-the-box technique that one can consider, perhaps particularly for a linear solve or a last-minute attempt to avoid a DNF. Anyway, the idea is to end up with a shorter "PLL" alg than you would have had if you solved every F2L pair into the correct slots. In some cases you might be able to avoid an extra AUF during F2L by inserting a pair into the wrong (diagonally opposite) slot. One obvious downside is that the "skip" case is no longer a skip.

I just did a God's algorithm analysis for the 288 PLL+AUF cases. I got an average of 11.497 moves for slot-swapping PLLs, whereas for normal PLLs it is 11.642. So the overall advantage of slot-swapping PLLs is very small, and is worse in terms of best case (5 vs. 0) and also worst case (16 vs. 15). I do agree that this is a very obscure technique and don't consider its omission a big deal.
I may consider adding this; do you have any resource to link, besides your posts in this thread? I'd like to study this technique better before writing about it, and just googling "speedsolving slot swap pll" gives this page as first result.

Your response ignored the other much more common technique that I mentioned, that of using skewed CE pairs, as in using a sequence like D R U' R' D' to solve both a corner and an edge. While the D layer moves may seem somewhat costly, if the alternative is a 6- or 7-move sequence to solve a conventional pair, it's still a win (assuming the skewed pair is solved in 5).

This is in some way an extension of the keyhole idea, except you try to solve both a corner and an edge at once, instead of only one piece at a time. With keyhole, you're tending to spend about 4 moves to solve only 1 piece. A moves-per-solved-piece ratio of 4.0 is pretty bad. For a 30-move solution, you need a ratio of 1.5 overall. In your keyhole example, you get sort of locked into having to solve a single edge piece at a time anyway with the layer-minus-a-corner start.
I wasn't sure what you meant by "skewed" pairs, I thought you were referring to the slot-swapping PLL thing.
This is really something I should add. I've just realized I don't mention multislotting in any way, another thing I need to study more before writing about (or maybe I can just explain what it is and link some good resources).

Potrebbe sembrare eccessivo o ridondante farlo anche qua ma è fatto perchè sei più su questo forum che su quello italiano.
Volevo ringraziarti molto perchè finalmente questo lavoro mi ha dato una grossa spinta ed ha avviato un positivo processo che spero non si arresti più. Forse mancavo di coraggio o forza di iniziativa, forse avevo solo paura che rimanesse una cosa a metà come le molte altre che ho (quasi) fatto.
Mi viene da ripensare a quell'obbrobrio che feci a Monterotondo. Acqua passata. Spero di ricominciare in positivo
Vorrei romperti il meno possibile ma se posterò mie solve sul thread italiano risponderai o sarebbe meglio secondo te proporle su questo forum, anche per un discorso di maggior confronto?
Dimmi tu se potrebbe essere produttivo o se solo lasciata passare come la solve del primo che capita-->non la guardiamo e commentiamo l'ultima di Sebastiano.
Ti ringrazio anche in anticipo per la risposta. A presto,
Davide

*for non italian user: sorry but the message was too long and I can't translate it in english, it's too complicate for me, not only long.
Ci sono anche sul forum italiano, solo che scrivo poco
Ad ogni modo, se posti qualche solve sul forum italiano stai tranquillo che 10 minuti per guardarla e commentarla li trovo. Comunque, anche se le posti qui qualcuno probabilmente risponderà.

#### okayama

##### Member
I wasn't sure what you meant by "skewed" pairs, I thought you were referring to the slot-swapping PLL thing.
This is really something I should add. I've just realized I don't mention multislotting in any way, another thing I need to study more before writing about (or maybe I can just explain what it is and link some good resources).
Do the scramble D R U R' D'. Bruce sometimes calls the UFL-UF piece a "skewed c/e pair", or "skewed slot".
Maybe this is enough explanation for you.

#### porkynator

##### Member
Do the scramble D R U R' D'. Bruce sometimes calls the UFL-UF piece a "skewed c/e pair", or "skewed slot".
Maybe this is enough explanation for you.
Yes I understand (and sometimes use) this particular case, but there are many other algorithms that fall in the "multislotting" category, of which I don't know many (I think).

#### sneze2r

##### Member
This is best speedcubing tutorial i've ever seen, great job! Contains a lot of interesting techniques!

#### Methuselah96

##### Member
This is best speedcubing tutorial i've ever seen, great job! Contains a lot of interesting techniques!
It's not speedcubing...

#### CriticalCubing

##### Member
Awesome. Now I will also start doing FMC not until I am better at Skewb

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