# 5cyles

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#### fp4316

##### Guest
Is there any documentation regarding 5cycles? IIRC there was a doc long ago but I can't locate it. I think it would be interesting to learn a few cases.

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#### fp4316

##### Guest
Thanks Cale, do you know if anyone uses these practically in solves?

#### Cale S

##### Member
Thanks Cale, do you know if anyone uses these practically in solves?
I read somewhere that Ville Seppänen used one in a solve once

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#### fp4316

##### Guest
I read somewhere that Ville Seppänen used one in a solve once
LOL, I guess I'm going to learn a few and see if I can use them.

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#### Daniel Lin

##### Guest
all MU 5-cycles with UF buffer:

found from a post by Oleg

6 movers are fun to learn:
M' U M U' and variations
r U r' R U' R' and variations

also this: (R2 U' R2 F2)2
yay thankyou
Time to upgrade to 5-style! lol

how many total cases are there for edges counting non MU cases? and corners?

and also, is there an intuitive way to understand these? I guess some of them are two comms canceled into each other, but for most of them it looks like you have to memorize them

#### Cale S

##### Member
yay thankyou
Time to upgrade to 5-style! lol

how many total cases are there for edges counting non MU cases? and corners?

and also, is there an intuitive way to understand these? I guess some of them are two comms canceled into each other, but for most of them it looks like you have to memorize them
not all groups of 4 targets are 5-cycles, but for the ones that are:
first target can be any of 22, second can then be 20, then 18 and 16, so 126,720 I guess

then for corners it's 21*18*15*12 = 68,040

#### CyanSandwich

##### Member
Would any of them be worth learning? 4 movers are obviously awesome, but the chances of a given 5-cycle coming up in a solve are 1 in 126,720-ish.

I guess you could learn all the M'UMU' variations. With 1 move setups, I think that leaves you with a 1 in 6336 chance of it coming up in a solve.

Corners have almost half the cases, but still, it seems like any 5-cycle is too rare to be used effectively (you're waiting 10,000 solves for one you know to come up, then pause for 3 seconds recognizing it)

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#### Daniel Lin

##### Guest
not all groups of 4 targets are 5-cycles, but for the ones that are:
first target can be any of 22, second can then be 20, then 18 and 16, so 126,720 I guess

then for corners it's 21*18*15*12 = 68,040
oh yeah should've knew that. But for big cube centers it's 23*22*21*20*19, right?

If people used full 5style I think execution would be significantly faster.

#### tseitsei

##### Member
Would any of them be worth learning? 4 movers are obviously awesome, but the chances of a given 5-cycle coming up in a solve are 1 in 126,720-ish.

I guess you could learn all the M'UMU' variations. With 1 move setups, I think that leaves you with a 1 in 6336 chance of it coming up in a solve.

Corners have almost half the cases, but still, it seems like any 5-cycle is too rare to be used effectively (you're waiting 10,000 solves for one you know to come up, then pause for 3 seconds recognizing it)
THIS! it will no way ever be practical in any BLD solving...

#### Cale S

##### Member
oh yeah should've knew that. But for big cube centers it's 23*22*21*20*19, right?

If people used full 5style I think execution would be significantly faster.
For big cube centers you don't have two adjacent targets on the same face
and if you do the targets on each face in alphabetical order it would also reduce the cases by a lot

an upper limit if you assume no U layer targets would be 20*16*15*15 = 72,000

5-style centers might actually work because of highly reduced cases and super easy setups (you could learn like 1 alg for every order of faces and do face turns for really easy setup moves)

#### CyanSandwich

##### Member
Yeah 5-style centers actually sound pretty practical when you put it like that.

I wouldn't know how to create algs for it, but it'd be cool if someone could (or if there already are).

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#### Daniel Lin

##### Guest
(you could learn like 1 alg for every order of faces and do face turns for really easy setup moves)
brilliant idea. Let's call it Cale's bigbld center method. CBCM
but you can't do one alg for every order of faces because targets on the same face could be diagonal or adjacent

Is this faster than 3style though? not sure but probably. If someone gens algs I'll learn it.

Also, would 4 cycles work?
I mean for 3x3 you could do algs that do a 2 swap of edges (like UB and UL) and a 4 cycles of corners(like UBL>UBR>FDR>BDL) Not sure if this would be good. Also, this would require you to memorize in sets of 3 letters (which might be more efficient).
And then for cycle breaks like (UBR>FUR>UBR) you could do something like R U R2 F R F' R U' R' F' U F ( i learned that from Jay)

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#### JanW

##### Member
Also, would 4 cycles work?
I mean for 3x3 you could do algs that do a 2 swap of edges (like UB and UL) and a 4 cycles of corners(like UBL>UBR>FDR>BDL) Not sure if this would be good. Also, this would require you to memorize in sets of 3 letters (which might be more efficient).
And then for cycle breaks like (UBR>FUR>UBR) you could do something like R U R2 F R F' R U' R' F' U F ( i learned that from Jay)
I noticed there's a lot of short corner 4 cycles. Mainly I've been thinking about them as means to solve last cycle + parity.

I use UF and UFR as buffers, swap UF and UR when I have parity. I actually memorized that if my last corner cycle is UFR->UBR->LUB, then parity shooting to LUF, I can solve last cycle and parity with U+Sune. Not that this has ever happened in a solve. With one setup move this could be expanded to a lot more cases, with 2 setup moves it could cover a ton of cases. And then there's the opposite, AS+U', and a lot of other 8-9 move algs that can do similar stuff. Though I haven't made any serious efforts to learn to use stuff like this. Have to focus on the basics first.

It also occured to me that one could solve parity in the middle of corners, making it a lot more likely that you get a chance to use a 4-cycle. Let's say I have UFR->UBR->LUB and the next cycle starts by shooting to LUF, at any point in a memo with parity, I could solve parity right then with U+Sune. Of course, this would change the memo after this if you want to keep remembering your cycles as pairs, so probably not worth it for those of you who are very fast already.

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#### Daniel Lin

##### Guest
It also occured to me that one could solve parity in the middle of corners, making it a lot more likely that you get a chance to use a 4-cycle
Nope i don't think so, it only works sometimes, if the piece goes back to the correct sticker on the buffer
If it's a "twisted cycle" then it wouldn't work

good point though. There are a couple good cases but it's a lot of work to learn them all

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#### JanW

##### Member
Nope i don't think so, it only works sometimes, if the piece goes back to the correct sticker on the buffer
If it's a "twisted cycle" then it wouldn't work
Not sure what you mean with twisted cycle...

I think it should always work. Your corner memo is a series of targets that you solve in a specific order. In 3-style you solve them two at a time and a single target at the end if you have parity. A 4-cycle would solve 3 targets and swap 2 edges (fix parity). Let's say your corner memo is ABCDEFG. What's the difference if you solve the corner targets as AB - CD - EF - G or AB - CDE - FG?

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#### Daniel Lin

##### Guest
Not sure what you mean with twisted cycle...

I think it should always work. Your corner memo is a series of targets that you solve in a specific order. In 3-style you solve them two at a time and a single target at the end if you have parity. A 4-cycle would solve 3 targets and swap 2 edges (fix parity). Let's say your corner memo is ABCDEFG. What's the difference if you solve the corner targets as AB - CD - EF - G or AB - CDE - FG?
Oh yeah you're right it still works. I was just confusing something else with this

what I meant by twisted cycle is something like DF>FL>BR>BL, when BL goes back to FD.

I guess 4style might actually work, since it gives you more flexibility during memo. And its less cases than 5style so probably easier to learn. Is there someone who knows how to gen algs?

#### JanW

##### Member
I think it could work as well, at least to semi-frequently solve parity with a 4-cycle. Solving all corners 4style would take a lot of algs.

The cool thing is that you can also influence how often you get these with cycle breaks. Let's say I want to use U+Sune, then I need the consecutive targets UBR->LUB->LUF somewhere during the solve. If the first target in a 3-cycle is UBR and then there's a cycle break (not too rare), I can select LUF as the next target, then there's at least 4/15 chance that the next target can be set up to form a 4 cycle with a D-face move + L' (LDF, FDR, RDB, BDL). Another case: first target is RDB, then a cycle break. If the sticker in UBR is blue (my left face), I pick that next and can set up the 4-cycle with L-face move+B. Or, if I have a cycle UBR to anywhere on the L face, then a cycle break, I can pick the next target clockwise from the second target on the L face for a 1 move setup, assuming that corner isn't solved yet.

So if you learn a handful of 4-cycle algs, which cases they can cover with easy 1-2 move setups, and the optimal cycle breaks to maximize occurrence, you should be able to use one quite frequently in solves.

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#### abunickabhi

##### Member
For big cube centers you don't have two adjacent targets on the same face
and if you do the targets on each face in alphabetical order it would also reduce the cases by a lot

an upper limit if you assume no U layer targets would be 20*16*15*15 = 72,000

5-style centers might actually work because of highly reduced cases and super easy setups (you could learn like 1 alg for every order of faces and do face turns for really easy setup moves)
We can even reduce the number with nicer setups. For setups, I am trying to use the concept of shapes to make recognition easier. Doc

x-center 5cycle

I hope to use it in my solves soon after some practise.