Imam Alam
Member
- Joined
- Apr 2, 2019
- Messages
- 12
bismillaahir raHmaanir raHeem
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What This Post is About
Just sharing a bunch of simple methods and variants for solving the 3x3x3 cube in fun, novel and elegant ways.
I guess this is more of a concept idea post than a new method post.
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Methods Overview
This is my collection of "mini-methods" that have only "mini-algs", along with other cubing concepts.
Feel free to add more methods or method variants to this list!
The methods outlined here would have the following properties:
- solving as fast as possible is not the goal, nor winning competitions (rather the goal of using these methods would be pure fun/enjoyment, or a better understanding of the cube, or both)
- methods that require some intuitiveness are preferred (simplified versions of the popular methods are also welcome)
- have significantly different step(s) compared to more popular methods, and preferably do not end with LL (last layer) algorithms
- diverse solving styles, fun new methods to try out (elegant, aesthetically pleasing solutions are a bonus)
- relatively few (<10) algs, learning new algs with every new method is not desired (shorter and ergonomic algs are a bonus)
- relatively low (<70) move count STM/HTM
That's what I am aiming for.
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Algorithms Overview
The algs should be easy to understand and easy to implement, i.e. it should be a nice alg set.
Hence shorter and simpler algorithms are preferred.
The algorithms included here would have the following properties:
- the alg set is short (<10 algs for one complete method)
- each alg is short (3 ~ 6 moves HTM and STM)
- the algs should be easy to understand and recall (the user of the method should know exactly what the algs do to which pieces)
- additionally, the algs should be ergonomic if possible (preferably 2-gen)
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Methods List
The mini-methods that I am sharing may be put into the following groups:
[2-Generator Methods]
Method 1. Wu
Method 2. ZZ
Method 3. Petrus
[Edges First Methods]
Method 4. Heise
Method 5. Keyhole
Method 6. Coffer
[Corners First Methods]
Method 7. Sandwich
Method 8. Columns
Method 9. Roux
[Orient First Methods]
Method 10. Thistlethwaite
Method 11. Morozov OF
Method 12. Morozov CF
[Permute First Methods]
Method 13. Benek CF
Method 14. Benek PF
Method 15. Benek 2GR
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Algorithms List
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Methods Comparison
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Yup, that's my first post in this forum!
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subHaanakallaahumma wa biHamdika ashhadu an laa ilaaha illaa anta astaghfiruka wa atoobu ilaika
Code:
Gilles Roux said:
Hey Ryan, you could be much faster.
You know what's the problem with you?
You think too much, you'll never be a speedcuber!
... P.S.: I've got the same problem...
([email protected])
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What This Post is About
Just sharing a bunch of simple methods and variants for solving the 3x3x3 cube in fun, novel and elegant ways.
I guess this is more of a concept idea post than a new method post.
The main goal is to solve the cube with more understanding, and rely less on rote memorization.
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Methods Overview
This is my collection of "mini-methods" that have only "mini-algs", along with other cubing concepts.
Feel free to add more methods or method variants to this list!
a mini-method is a stand-alone (complete) method that solves the entire 3x3x3 cube. It is not just a sub-step. I am calling it "mini" because it is based on a simple idea, and it is possible to boil it down to one or two core concepts.
a mini-alg (or a trigger) is a very short sequence of moves that is so easy to understand and implement that you may even choose to call it "intuitive".
I don't believe that any method or variant can ever be 100% intuitive, just more intuitive or less intuitive (that, too, varies person to person).
I am simply focusing on the ones that are more intuitive for me.
I am simply focusing on the ones that are more intuitive for me.
I don't claim any credit for any of these methods.
Just trying to share and discuss methods invented by others.
My contribution (hopefully) is the way these methods are organized and modified to fulfill the requirements described below.
Just trying to share and discuss methods invented by others.
My contribution (hopefully) is the way these methods are organized and modified to fulfill the requirements described below.
The methods outlined here would have the following properties:
- solving as fast as possible is not the goal, nor winning competitions (rather the goal of using these methods would be pure fun/enjoyment, or a better understanding of the cube, or both)
No, I am not against speedsolving and competitions (both have their places in cubing), just looking for ways to expand the horizon, and to try out new things.
- methods that require some intuitiveness are preferred (simplified versions of the popular methods are also welcome)
No, I am not against memorization and algorithms (both have their places in cubing).
In fact, the more you practice intuitively the more it becomes memorized/algorithmic, and vice versa.
We still use algorithms as beginners, in one form or another, but we keep on trying to understand how those algorithms actually work.
In fact, the more you practice intuitively the more it becomes memorized/algorithmic, and vice versa.
We still use algorithms as beginners, in one form or another, but we keep on trying to understand how those algorithms actually work.
- have significantly different step(s) compared to more popular methods, and preferably do not end with LL (last layer) algorithms
Well, I am not against popular methods either.
It is just that popular methods are usually optimized for speedsolving, and here we are focusing more on other factors, such as fun, novelty, challenge, and elegance.
It is just that popular methods are usually optimized for speedsolving, and here we are focusing more on other factors, such as fun, novelty, challenge, and elegance.
- diverse solving styles, fun new methods to try out (elegant, aesthetically pleasing solutions are a bonus)
Concepts are preferred over memorized algorithm sets.
Examples: freedom of movement, symmetry, parity and twist constraints, group theory.
In practice: block building, commutators, generator reduction (domino, 2-gen), EO and CP etc.
Examples: freedom of movement, symmetry, parity and twist constraints, group theory.
In practice: block building, commutators, generator reduction (domino, 2-gen), EO and CP etc.
- relatively few (<10) algs, learning new algs with every new method is not desired (shorter and ergonomic algs are a bonus)
No, I am not against methods with large alg sets.
I just find a smaller alg set to be easier to digest, easier to understand thoroughly in less time, and easier to recall.
I just find a smaller alg set to be easier to digest, easier to understand thoroughly in less time, and easier to recall.
- relatively low (<70) move count STM/HTM
Here we are expressing move count in STM (Slice Turn Metric) and HTM (Half Turn Metric), i.e. these methods should not require more than 70 slice turns (and half turns) on average to solve the cube.
That's what I am aiming for.
Feel free to add to my list, your methods don't need to fulfill all of the above conditions, so if you think that you know of a method that goes with the general spirit, just go for it!
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Algorithms Overview
The algs should be easy to understand and easy to implement, i.e. it should be a nice alg set.
Hence shorter and simpler algorithms are preferred.
For the 15 mini-methods and variants I am sharing here, I propose an alg set of 9 triggers or mini-algs (yes, you read that correctly: 9 short algs for 15 methods combined!).
The algorithms included here would have the following properties:
- the alg set is short (<10 algs for one complete method)
I am using 9 algs for 15 methods, none of these methods require more than 8 algs, and there are one or two methods that virtually require 0 algs.
- each alg is short (3 ~ 6 moves HTM and STM)
The 9 triggers I am using have an average length of 4.89 moves HTM (4.11 moves STM), none of them is longer than 6 moves HTM (and 6 moves STM).
- the algs should be easy to understand and recall (the user of the method should know exactly what the algs do to which pieces)
All of the 9 algs I am using can be considered as nice (usually symmetric), so they are even shorter, and easier to understand.
- additionally, the algs should be ergonomic if possible (preferably 2-gen)
All of the 9 algs I am using are 2-gen.
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Methods List
From here onward "methods" stands for "methods and variants".
The mini-methods that I am sharing may be put into the following groups:
When I describe a method with the name of the inventor of that method, I do that only generally, sometimes only taking a method partially and simplifying the rest.
For example, when I describe a method as "Roux" I don't claim that this is exactly how Gilles Roux had proposed it.
So please take the method names with a grain of salt.
For example, when I describe a method as "Roux" I don't claim that this is exactly how Gilles Roux had proposed it.
So please take the method names with a grain of salt.
[2-Generator Methods]
Method 1. Wu
- 1x1x3: EO (trigger 1 / trigger 2) then CP (trigger 8 / 2GR / others), or CP (trigger 8 / 2GR / others) then EO (trigger 2)
- 2x2x3 (blockbuild)
- 3x3x3: make 4 corner-edge pairs (2-gen blockbuild) while doing CO L6C (triggers 1 and 7 / trigger 1 + mirror / corner 3-cycle / sune), then EP (trigger 6), then permute last 2 layers (trigger 9)
- 2x2x3 (blockbuild)
- 3x3x3: make 4 corner-edge pairs (2-gen blockbuild) while doing CO L6C (triggers 1 and 7 / trigger 1 + mirror / corner 3-cycle / sune), then EP (trigger 6), then permute last 2 layers (trigger 9)
Method 2. ZZ
- EOline (trigger 1 / trigger 2)
- F2L (blockbuild), optional CO L4C
- L4C (trigger 1 + mirror / corner 3-cycle + sune), or CP L4C if CO L4C already done (trigger 1 + mirror / corner 3-cycle)
- EP L4E (triggers 3, 4 and 5 / trigger 1 + mirror + inverse / sune + mirror)
- F2L (blockbuild), optional CO L4C
- L4C (trigger 1 + mirror / corner 3-cycle + sune), or CP L4C if CO L4C already done (trigger 1 + mirror / corner 3-cycle)
- EP L4E (triggers 3, 4 and 5 / trigger 1 + mirror + inverse / sune + mirror)
Method 3. Petrus
- 2x2x3 (blockbuild)
- EP L7E (trigger 1 + mirror using F turns)
- F2L (blockbuild), optional CO L4C
- L4C (trigger 1 + mirror / corner 3-cycle + sune), or CP L4C if CO L4C already done (trigger 1 + mirror / corner 3-cycle)
- EP L4E (trigger 1 + mirror + inverse / sune + mirror)
- EP L7E (trigger 1 + mirror using F turns)
- F2L (blockbuild), optional CO L4C
- L4C (trigger 1 + mirror / corner 3-cycle + sune), or CP L4C if CO L4C already done (trigger 1 + mirror / corner 3-cycle)
- EP L4E (trigger 1 + mirror + inverse / sune + mirror)
[Edges First Methods]
Method 4. Heise
- F2L-1 (blockbuild, then EO) (w/ or w/o pseudo blocks)
- L5E EP (w/ or w/o EC pairs)
- L5C or L3C (corner 3-cycle)
- L5E EP (w/ or w/o EC pairs)
- L5C or L3C (corner 3-cycle)
Method 5. Keyhole
- F2L-1
- EO L5E (trigger 1 + mirror)
- EP L5E (trigger 1 + mirror)
- L5C (trigger 1 + mirror + inverse / corner 3-cycle)
- EO L5E (trigger 1 + mirror)
- EP L5E (trigger 1 + mirror)
- L5C (trigger 1 + mirror + inverse / corner 3-cycle)
Method 6. Coffer
- F2L-1
- EP L5E (trigger 1 as R U2 R')
- EO L5E (trigger 1 as R U2 R')
- L5C (trigger 1 as R U2 R' + mirror / trigger 1 / corner 3-cycle)
- EP L5E (trigger 1 as R U2 R')
- EO L5E (trigger 1 as R U2 R')
- L5C (trigger 1 as R U2 R' + mirror / trigger 1 / corner 3-cycle)
[Corners First Methods]
Method 7. Sandwich
- 8C (trigger 1 + mirror / corner 3-cycle)
- E slice and S slice
- EP L4E (triggers 3 and 4)
- EO L4E (edge flip commutator)
- E slice and S slice
- EP L4E (triggers 3 and 4)
- EO L4E (edge flip commutator)
Method 8. Columns
- 8C (trigger 1 + mirror / corner 3-cycle)
- E slice and DL+DR as 3 pairs or LMCF style E2L (trigger 5)
- EO L6E (trigger 2)
- EP L6E as 3 pairs (triggers 3 and 4)
- E slice and DL+DR as 3 pairs or LMCF style E2L (trigger 5)
- EO L6E (trigger 2)
- EP L6E as 3 pairs (triggers 3 and 4)
Method 9. Roux
- FB and SB (blockbuild)
- LLC (corner 3-cycle)
- EO L6E (trigger 2)
- EP L6E (triggers 3 and 4)
- LLC (corner 3-cycle)
- EO L6E (trigger 2)
- EP L6E (triggers 3 and 4)
[Orient First Methods]
Method 10. Thistlethwaite
- EO and separate E slice edges (trigger 1 / trigger 2)
- CO (triggers 1 and 7 / trigger 1 only)
- CP (trigger 8)
- EP (triggers 3, 4 and 6)
- CO (triggers 1 and 7 / trigger 1 only)
- CP (trigger 8)
- EP (triggers 3, 4 and 6)
Method 11. Morozov OF
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EO L8E (trigger 2)
- CP (trigger 8)
- EP (triggers 3, 4 and 6)
- separate E slice edges (trigger 5) and EO L8E (trigger 2)
- CP (trigger 8)
- EP (triggers 3, 4 and 6)
Method 12. Morozov CF
- CO (triggers 1 and 7 / trigger 1 only)
- CP (trigger 8)
- separate E slice edges (trigger 5) and EO L8E (trigger 2)
- EP (triggers 3, 4 and 6)
- CP (trigger 8)
- separate E slice edges (trigger 5) and EO L8E (trigger 2)
- EP (triggers 3, 4 and 6)
[Permute First Methods]
Method 13. Benek CF
- CP (trigger 8 / 2GR / others)
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EO L8E (trigger 2)
- EP (triggers 3, 4 and 6)
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EO L8E (trigger 2)
- EP (triggers 3, 4 and 6)
Method 14. Benek PF
- CP (trigger 8 / 2GR / others)
- EO (trigger 2)
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EP (triggers 3, 4 and 6)
- EO (trigger 2)
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EP (triggers 3, 4 and 6)
Method 15. Benek 2GR
- EO (trigger 1 / trigger 2)
- CP (trigger 8 / 2GR / others)
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EP (triggers 3, 4 and 6)
- CP (trigger 8 / 2GR / others)
- CO (triggers 1 and 7 / trigger 1 only)
- separate E slice edges (trigger 5) and EP (triggers 3, 4 and 6)
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Algorithms List
The mini-algs (triggers) for the above methods are:
Trigger 1. R U* R' (U*) = [R: U] or [R, U]
Trigger 2. M' U M* = [M': U]
Trigger 3. U2 M2 U2 (M2) = [U2: M2] or [U2, M2]
Trigger 4. M' U2 M (U2) = [M': U2] or [M', U2]
Trigger 5. U M2 U* = [U: M2]
Trigger 6. R2 U2 R2 U2 R2 U2 = [R2 U2 R2, z' y2]
Trigger 7. (U) R2 U2 R* = [U R2, z' y2]
Trigger 8. R2 U R2 U' R2 = [R2 U: R2]
Trigger 9. R U R2 U' R' = [R U: R2]
I don't claim to have generated any of these algs.
I have simply collected, compared and selected the algs to come up with a relatively nice alg set.
I have simply collected, compared and selected the algs to come up with a relatively nice alg set.
Trigger 1. R U* R' (U*) = [R: U] or [R, U]
length: 3 or 4 HTM, 3 or 4 STM
application: this is the only alg required for method 5 (keyhole), it is also the only alg required for method 6 (coffer) as R U2 R', and it is useful for CO in methods 10 ~ 15 (OF and PF methods)
application: this is the only alg required for method 5 (keyhole), it is also the only alg required for method 6 (coffer) as R U2 R', and it is useful for CO in methods 10 ~ 15 (OF and PF methods)
Trigger 2. M' U M* = [M': U]
length: 5 HTM, 3 STM
application: EO alg in methods 7 ~ 15 (CF, OF and PF methods)
application: EO alg in methods 7 ~ 15 (CF, OF and PF methods)
Trigger 3. U2 M2 U2 (M2) = [U2: M2] or [U2, M2]
length: 4 or 6 HTM, 3 or 4 STM
application: EP alg in methods 7 ~ 15 (CF, OF and PF methods)
application: EP alg in methods 7 ~ 15 (CF, OF and PF methods)
Trigger 4. M' U2 M (U2) = [M': U2] or [M', U2]
length: 5 or 6 HTM, 3 or 4 STM
application: EP alg in methods 7 ~ 15 (CF, OF and PF methods)
application: EP alg in methods 7 ~ 15 (CF, OF and PF methods)
Instead of using 90 degree M slice turns, we can use R2 U2 R2 F2 R2 U2 R2 F2 = [[R2: U2], F2] (8 HTM, 8 STM), thus making the EP finish in methods 7 ~ 12 (OF and PF methods) purely with 180 degree turns.
In these methods we progressively reduce the cube to be solvable with 180 degree turns, so I find this alternative alg pretty elegant.
Although not a 2-gen alg, it is still quite ergonomic and short, and has some symmetry.
In these methods we progressively reduce the cube to be solvable with 180 degree turns, so I find this alternative alg pretty elegant.
Although not a 2-gen alg, it is still quite ergonomic and short, and has some symmetry.
Trigger 5. U M2 U* = [U: M2]
length: 4 HTM, 3 STM
may also be applied as R E2 R*
application: EP alg (M slice or E slice) in methods 7 ~ 15 (CF, OF and PF methods)
may also be applied as R E2 R*
application: EP alg (M slice or E slice) in methods 7 ~ 15 (CF, OF and PF methods)
Trigger 6. R2 U2 R2 U2 R2 U2 = [R2 U2 R2, z' y2]
length: 6 HTM, 6 STM
application: EP alg in methods 10 ~ 15 (OF and PF methods)
application: EP alg in methods 10 ~ 15 (OF and PF methods)
Trigger 7. (U) R2 U2 R* = [U R2, z' y2]
length: 3 HTM, 3 STM
application: CO alg in methods 10 ~ 15 (OF and PF methods)
source: Morozov method
application: CO alg in methods 10 ~ 15 (OF and PF methods)
source: Morozov method
Trigger 8. R2 U R2 U' R2 = [R2 U: R2]
length: 5 HTM, 5 STM
application: CP alg in methods 10 ~ 15 (OF and PF methods)
source: Morozov method
application: CP alg in methods 10 ~ 15 (OF and PF methods)
source: Morozov method
Trigger 9. R U R2 U' R' = [R U: R2]
length: 5 HTM, 5 STM
application: this is the permutation alg for method 1 (Wu), and this is the main alg for that method
application: this is the permutation alg for method 1 (Wu), and this is the main alg for that method
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Methods Comparison
Code:
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type | steps | #EO | features | redux
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| Wu EO CP BB BB | 12 | BB OF PF | RU
2G | ZZ EO BB CS EP | 12 | BB OF | RU
| Petrus BB EO CS EP | 7 | BB | RU
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| Heise BB EO EP CS | 5 | BB |
EF | Keyhole EO EP CS | 5 | |
| Coffer EP EO CS | 5 | |
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| Sandwich CS EP EO | 0 | CF | MU
CF | Columns CS EO EP | 6 | CF | MU
| Roux BB CS EO EP | 6 | BB CF | MU
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| Thistlethwaite EO CO CP EP | 8 | CF OF | G1+G2+G3
OF | Morozov OF CO EO CP EP | 8 | CF OF | MU G1+G2+G3 RU
| Morozov CF CO CP EO EP | 8 | CF OF | MU G1+G2+G3
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| Benek CF CP CO EO EP | 8/11 | CF OF PF | G1+G2+G3 RU
PF | Benek PF CP EO CO EP | 8/11 | CF OF PF | G1+G2+G3 RU
| Benek 2GR EO CP CO EP | 11/12 | CF OF PF | G1+G2+G3 RU
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- Generally speaking, the earlier methods in the list (methods 1 ~ 6) have more of a blockbuilding/edges first/face turns/direct solve style, and later methods (methods 7 ~ 15) have more of a corners first/columns first/slice turns/reduction style
- Earlier methods in the list (methods 1 ~ 9) solve the corners relatively directly, later methods (methods 10 ~ 15) solve corners more indirectly.
- Number of edges to be oriented during the EO stage gradually decreases and then increases again as we progress through the list.
- For methods 7~ 9 and 10 ~ 15, each method builds upon the previous ones, hence they get more and more complex as we progress through the list.
- Generally speaking, methods 10 ~ 15 first reduce the cube to <F2, B2, R, L, U, D>, then to <F2, B2, R2, L2, U, D>, and then to <F2, B2, R2, L2, U2, D2>, before finally solving it with 180 degree turns only.
- Will add more methods to the list, that is when I find them.
- Earlier methods in the list (methods 1 ~ 9) solve the corners relatively directly, later methods (methods 10 ~ 15) solve corners more indirectly.
- Number of edges to be oriented during the EO stage gradually decreases and then increases again as we progress through the list.
- For methods 7~ 9 and 10 ~ 15, each method builds upon the previous ones, hence they get more and more complex as we progress through the list.
- Generally speaking, methods 10 ~ 15 first reduce the cube to <F2, B2, R, L, U, D>, then to <F2, B2, R2, L2, U, D>, and then to <F2, B2, R2, L2, U2, D2>, before finally solving it with 180 degree turns only.
- Will add more methods to the list, that is when I find them.
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Yup, that's my first post in this forum!
(Been lurking around for a long time...)
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Code:
Tony Fisher said:
Intuitive means you are fully aware of every move you are making and understand what each turn is doing.
(http://twistypuzzles.com/~sandy/forum/viewtopic.php?f=8&t=27543)
subHaanakallaahumma wa biHamdika ashhadu an laa ilaaha illaa anta astaghfiruka wa atoobu ilaika
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