# Solving the whole cube intuitively



## badmephisto (Aug 6, 2009)

I started to think a little about how the cube could be solved entirely intuitively, and what the best way to go about doing it is. By saying intuitively I mean that every single move is directed in itself for a specific goal... So commutators for example are not strictly intuitive under this definition.

I can get pretty far but run into trouble near the end naturally when you have less degrees of freedom

cross, f2l except for one slot,
then do petrus orient of all edges, 
and then you can solve all 5 edges purely intuitively only using RU. (the 4 edges in LL and the edge in the F2L slot you didnt solve)

Then you are left with 5 unsolved corners... and I use commutators to finish that off, by solving 2 corners at a time. But thats the part that I am trying to see if its possible to eliminate... somehow..? I dont even know if it possible...

Did someone come by some other way? of maybe orienting the corners or positioning them, without using any black-box algorithms? 
or did someone try some other strategy entirely?
How far is it possible to get before having to use black-box algs/commutators?


----------



## brunson (Aug 6, 2009)

Did you see the posts on 8355? That's about the most intuitive method I've seen.


----------



## Cride5 (Aug 6, 2009)

If you're going for completely intuitive, I think completing the corners is probably the hardest bit. If you start with corners its inevitably going to make your life a bit easier but whether they can be done _completely_ intuitively is really the question. I think the initial steps of Guimond (ie orienting two opposite layers) could be done intuitively by an experienced cuber, and I remember the final permutation of corners (PBL) can also be done intuitively if you really have a go at it. I remember doing this when trying to work out how to solve the Square-1.

If you leave the end game (the hardest bit) to edges only it'll probably be easier to brute force. Have a go at CF Roux intuitively and see how far you get. The advantage of Roux is that it handles orientation of the final 6 edges early enough that it can be done without too much trouble. The final edge permutation only has three cases, and is not to hard to work out 

EDIT: Just had a go and managed to complete it using zero algs and zero commutators, but its possible that having experience in the methods makes them easier to do intuitively.

EDIT2: Just to provide extra motivation ... the very first solve by Erno Rubik himself had to be intuitive and was done corners-first


----------



## joey (Aug 6, 2009)

I don't get why commutators don't fit under 'intuitive'


----------



## Am1n- (Aug 6, 2009)

Heise method is intuitively for most of the time, only the tree last corners are commutator-based (and sometimes some pair-cycles)

mvg


----------



## eragg0 (Aug 6, 2009)

Maybe corners can be permuted by using RDR-commutator (and oriented also usong beginners way)
(R' D' R) U (R' D R) U (R' D' R) U2 (R' D R) << 3-cycle
And E-perm is made using same principle


----------



## calekewbs (Aug 6, 2009)

eragg0 said:


> Maybe corners can be permuted by using RDR-commutator (and oriented also usong beginners way)
> (R' D' R) U (R' D R) U (R' D' R) U2 (R' D R) << 3-cycle
> And E-perm is made using same principle



Yeah I was thinking the same thing. just do intuitive F2L for the last edge pair then rotate the edges with R' D' R D then permute edges by pulling one out ( M D' M' ) turn where you want it on the UF edge slot then put it in ( M D M' ) do this till all the edges are solved always switching between D and D'. Same idea for the corners. pull it out, put it in. (that's what whe said) lol


----------



## rjohnson_8ball (Aug 6, 2009)

I like this topic. I have heard of a couple people who say they solved the cube intuitively -- I assume they meant without commutators. I've wondered.


----------



## ErikJ (Aug 6, 2009)

I think I averaged like 23 seconds a while ago for solving without algorithms. I didn't even allow myself to use A, U and a few other permutations even though they are commutators. It's been a while.


----------



## bwatkins (Aug 6, 2009)

I have a friend at my college who solves the cube completely intuitively, it seems crazy to me and my way of thinking but i still think its kinda cool. First he places in all 8 corners oriented correctly. This obtains an "X" on all 6 sides. Second he solves the remaining 12 edges in no particular order until they are all done. It is completely brute-force way of solving as nothing is done inefficiently, but its way cool. He completes the V-7's 3x3x3 reduction with no problem, then simply asks someone to solve it from there as the method is quite the mind boggler. Any way just thought id share.


----------



## Pseudoprogrammer (Aug 6, 2009)

My calculus teacher is very intelligent (PhD) and was in high school during the original cube craze, and can intuitively solve it (she never learned a method, but she does have a 'system' as she calls it, but it's basically a set of goals you achieve for each step). But her system mostly amounts to corners first, solve top and bottom edges, solve center slice. She uses a weird alg for flipping the final edges if they are flipped in the middle layer she says she discovered by fiddling for a few hours (It's by far not the most efficient, about 20 moves long for that one 'alg'). Still pretty neat though.


----------



## vgbjason (Aug 6, 2009)

bwatkins said:


> I have a friend at my college who solves the cube completely intuitively, it seems crazy to me and my way of thinking but i still think its kinda cool. First he places in all 8 corners oriented correctly. This obtains an "X" on all 6 sides. Second he solves the remaining 12 edges in no particular order until they are all done..



That sounds like pochman method (BLD) to me


----------



## DavidWoner (Aug 6, 2009)

badmephisto said:


> By saying intuitively I mean that every single move is directed in itself for a specific goal... So commutators for example are not strictly intuitive under this definition.



I'm afraid I don't quite understand what you mean. Do commutators not have a goal? Please clarify this.



vgbjason said:


> That sounds like pochman method (BLD) to me



Then you should get your hearing checked.


----------



## cmhardw (Aug 7, 2009)

I also have to ask you to clarify your definition of intuitive. For a corner commutator I can describe the logic and reasoning behind every single turn I do.

Are you saying that every turn must be toward the goal of solving the cube as a whole, whereas the 8 turns of a commutator are focused on first destroying, then restoring the cube (while also affecting a small number of other pieces)?

Perhaps you mean to say: "How can the cube be solved without using any strictly 'destroy and restore' concepts?" Or am I not correctly understanding your intention?

The reason I ask, is that if I wanted to solve a cube "completely intuitively" I would visually trace the cycles and determine if the cube has parity. If it does I would correct this by doing a quarter turn, if not then I would begin solving. For the solving I would use only commutators.

This method is very inefficient, but I would understand the logic and reasoning behind every turn I used. A much better approach would be your method exactly as described, and use commutators to solve the last 5 corners. Again, this could be done while completely understanding the purpose and reasoning behind every turn you execute.

Chris


----------



## blah (Aug 7, 2009)

bwatkins said:


> First he places in all 8 corners oriented correctly. This obtains an "X" on all 6 sides.


That was brief.


----------



## bwatkins (Aug 7, 2009)

would you prefer a long drawn out explanation?...There is no exact routine, that's literally how its done, i tried it a few times. No specific algs, just "how do i place this piece there? its totally a long drawn out process of excessive symmetric moves.


----------



## blah (Aug 7, 2009)

bwatkins said:


> would you prefer a long drawn out explanation?...There is no exact routine, that's literally how its done, i tried it a few times. No specific algs, just "how do i place this piece there? its totally a long drawn out process of excessive symmetric moves.


How would you do something like twisting only two corners?


----------



## deadalnix (Aug 7, 2009)

blah said:


> How would you do something like twisting only two corners?



It's a thing I have found by myself when I was a beginer. But I was using a commutator (without knowing it was a commutator, I discover it later).

Commutator are for most of them very intuitive. I don't see how to solve corner without commutators . . .


----------



## spdcbr (Aug 7, 2009)

Okay, this is off topic, but what's...

A Premuim member?

and a Supermoderator?


----------



## bwatkins (Aug 7, 2009)

blah said:


> bwatkins said:
> 
> 
> > would you prefer a long drawn out explanation?...There is no exact routine, that's literally how its done, i tried it a few times. No specific algs, just "how do i place this piece there? its totally a long drawn out process of excessive symmetric moves.
> ...



I know exactly what you mean, i run into this when solving this way, and i guess you use a commutator, but if this is your main method and thats all you know, i guess it counts as intuitively, seeing as how many many mistakes occur along the way.


----------



## mrCage (Aug 8, 2009)

Twisting 2 corners can be done with 2 so-called sunes like so:

R' D' R D' R' D2 R - L D L' D L D2 L' (2 mirrored sunes)

or commutator style like so:

R D R' F D F' - U - F D' F' R D' R' - U' (for instance)

Yet another 2-twist:

(R' D2 R B' U2 B)*2

"Final example":
(L B' D2 B L' - U2)*2 (yet another commutator).

See how the 2 last ones are essentially the same algorithm!!

One can do a 4-twist by a slight variation of the "final example" like so:

L B' D2 L' B2 D B' - U2 - B D' B2 L D2 B L' - U2 D)

Understanding commutators is not exactly intuitive, but with some practice and experience they become intuitive  In the sense that making up new ones can be done easily using basic principles. (Check 2nd algorithm above!)

Bonus corner 3-twist:

(R' D' R L - z)*4


----------



## badmephisto (Aug 9, 2009)

you're right. I phrased the question wrong by putting in those terms, and I was just hoping that people would try to avoid commutators, but obviously I could have seen it coming that people would instead just attack my assumption that commutators are not intuitive 

well to be perfectly honest I want to be able to teach this completely intuitive method to people, in the end. And explaining how commutators work is extremely hard. If I were to explain to a really smart person (albeit a beginner) about how you can use commutators to solve 2 corners at a time, I would almost surely fail, miserably. 

So, I was looking for a method that a very bright beginner can pick up, and i didnt want it to involve the idea of commutators because they are too hard to explain. And I dont mean just the idea... but more of the idea of how to use them, effectively, in a directed fashion to your immediate advantage.

(Of course... Now im just waiting for someone to swoop in and tell me that is not so...)


EDIT: 
I would consider the R' D2 R thing and M D2 M' thing as an intuitive way to finish up PLL step. So the problem then becomes just how to orient the corners.
And I never tried the corner first approach, I should play around with that.


----------



## cmhardw (Aug 10, 2009)

badmephisto said:


> So, I was looking for a method that a very bright beginner can pick up, and i didnt want it to involve the idea of commutators because they are too hard to explain.



Completely agree, 100%. Teaching commutators and how they work is extremely difficult, and every time I have tried I succeed in only frustrating the learner to the point of not wanting to cube.

I do, however, still teach commutators. I have only drastically changed my approach to how I teach them.

For cycling corners I teach the same commutator method that Joël van Noort teaches on his site. The actual 3 cycle, in full notation, is:
R' D2 R U R' D2 R U R' D2 R U2 R' D2 R

As a commutator this is: [R' D2 R U : R' D2 R, U] 

or

S = Setup Move = R' D2 R U
A = R' D2 R
B = U

and the algorithm is: S A B A' B' S'

Although this is a commutator, and a complicated one at that, I teach it as follows:

R' D2 R I call the "baseball move". In a visual sense it is like someone is throwing a low sidearm throw. The R' is the dropping of the arm, the D2 turn "throws" the corner at DRF to DLB. Then the R is the motion of the arm coming back up. The U turns I call "pinwheel" turns. I tell students that it is like one of those pinwheels on a plastic stick. You blow into the pinwheel and it spins, like a windmill. The U layer turns are like that.

So a student remembers the algorithm
(R' D2 R U) (R' D2 R) (U) (R' D2 R) (U') (U' R' D2 R)

like this:

(baseball move) (pinwheel the next corner around) (baseball move) (pinwheel the next corner around) (baseball move) (pinwheel the original corner around) (baseball move).

They are doing commutators, and complicated ones at that, but don't even realize it!

------------

I also teach twisting corners as commutators.

R' D2 R F D2 F' U F D2 F' R' D2 R U' is a commutator I teach. In notation it is written:
[R' D2 R F D2 F', U]

I also teach this as baseball moves and pinwheels. The R' D2 R I call "the right baseball glove move" and F D2 F' I call "the front baseball glove move"

Students remember:
(R' D2 R F D2 F') (U) (F D2 F' R' D2 R) (U')

as

(right baseball glove move) (front baseball glove move) (pinwheel the next twisted corner over) (front baseball glove move) (right baseball glove move) (pinwheel the corner back to its original spot)

Easy as pie. Trust me, if 6 and 7 year old kids can learn this, then any adult can. The failing is not in the learner but in the teacher. I don't mean this as an insult to you, but rather to get your attention. I have learned so much in terms of how to teach cubing through my *many* failures in teaching kids how to cube. I have tried teaching commutators as commutators, and just like you said it was a *miserable* failure. Just find a way to present the topic to the student that makes more sense to the student. You'd be surprised how complicated of a thing they can learn by doing this. Don't ever teach them the term "commutator" or talk about As and Bs and (A')s and (B')s, just phrase it in a very visual sense.

Again, I'm not trying to come across as insulting, I am just relaying things I have learned by teaching cubing to young kids. The failure of the student to learn is really in not teaching it a good way to learn *for that particular student*. If you can find a good method *for that student* then they will comprehend it just as well as you do, they might only think of the concept in *completely* different terms than you do.

Hope this helps, and yes I am an ally to what you are doing, even though it might not sound like it!

Chris

--*******EDIT*******--
To preempt the question of how to twist 3 corners, here is how I teach kids to do this:

(R' D2 R F D2 F') (R' D2 R F D2 F') U (F D2 F' R' D2 R) U (F D2 F' R' D2 R) U2

As a commutator, this is the best I can come up with as to how to represent how that algorithm works:
Let
A = R' D2 R F D2 F'
B = U

The commutator is actually not a single commutator, but rather a cyclic shift of the concatentation of a commutator with a conjugated commutator. Here is what I mean by that.

Using the above definitions of A and B we will call the "conjugated commutator": (A'A') A B A' B' (AA)
The "commutator" we will call: (A'A') B' (AA) B

The concatenation of the two will do the commutator first, followed by the conjugated commutator. This concatenation is:
(A'A') B' . (AA) B (A'A') A B A' B' (AA)

The cyclic shift starts at the period and wraps around after reaching the end. This makes the algorithm become:
(AA) B (A'A') A B A' B' (AA) (A'A') B'

Including the cancellations this becomes: A A B A' B A' B' B' which is the structure of the above alg that twists 3 corners.

---

Anyway, the way I teach kids to do this is to cycle the first corner "the wrong way" the very first time. This means they do R' D2 R F D2 F' to twist the corner in the opposite direction that they should. After this, they will cycle all corners the "correct" way. They finish the first corner with R' D2 R F D2 F', which is now the correct way to twist the corner. Then they "pinwheel" the next corner over, and continue similar to above.

In the student's mind they are doing:
(Read the first corner incorrectly the first time around) (Read the first corner correctly the second time around) (pinwheel the next twisted corner over) (twist the next corner correctly) (pinwheel the next corner over) (twist the final corner correctly) (bring the U layer back into the original start position)

In actuality I have them skip the last U turn, as the corners all show the correct sticker on top, which makes this step already completed by that point.

[/ridiculously long post]


----------



## fanwuq (Aug 10, 2009)

Very insightful post Chris!
I think the corners are the hardest to solve intuitively. For edges, solving middle layer than using M2 is pretty easy. I've taught one beginner to solve edges that way and it's not too hard to learn.


----------



## Am1n- (Aug 10, 2009)

Maybe you can use something like the human thistlewaite, there, you orient the edges first, make a cross on D and U (while you tread oposite colours as the same), then you insert the corners on D and U while preserving orientation. This can all be done easily without any algs. Then permute the corners, this has 1 alg, but a very simple one, so you could teach this as intuitive. Next you permute the edges, wich is also is intuitive.

some tutorials you can find here:
writen: http://www.ryanheise.com/cube/human_thistlethwaite_algorithm.html
youtube: http://www.youtube.com/watch?v=xw5luzfkO48 

most of this can be done intuitive, but its quite hard in the beginning.
hope this helps

mvg


----------



## badmephisto (Aug 10, 2009)

Thank you chris. Naturally, I did not take any offense, and I appreciate your insight. It is certainly a good strategy to relate new concepts to the old ones already acquired, in general. The trouble with that of course is that that way is not intuitive at all-- It's just a memory trick. My aim here is to try to find a way to solve the cube that a bright beginner could easily pick up, given enough fiddling-around time. ie no memory work at all. I think we can agree that for that purpose then, commutators are not exactly applicable.


----------



## cmhardw (Aug 10, 2009)

badmephisto said:


> My aim here is to try to find a way to solve the cube that a bright beginner could easily pick up, given enough fiddling-around time. ie no memory work at all. I think we can agree that for that purpose then, commutators are not exactly applicable.



Yes I can see that commutators would not be immediately considered intuitive by a beginner, and would start out as a memory trick - understanding would have to come later.

All that comes to mind right now is Am1n-'s suggestion of human thistlewaite. Explain the concept of "reduction" to a simpler sub-group of the cube as making the cube a "simpler puzzle" and just continue from there. I'm not sure if block building techniques work because of the LL. Also, if the method has to start out intuitive with no memory work whatsoever then commutators would have to be explained in the pure sense, which would most often result in frustrating the learner to the point of not learning :-(

I'd also vote for human thistlewaite, or some other form of reducing the cube to simpler sub-groups. That is if we're restricting the beginner to 100% intuitive with no memory work.

Also, I think some memory followed by understanding is ok for a beginner. To explain an entire solution to the point of 100% understanding might delay the learner from learning at the pace they want to. Remember that most beginners just "want to solve the damn thing". So to explain to them in a pure sense why every single turn they use works might take longer than using a mix of intuition and memory. If you use the right kind of memory tricks they will, hopefully, come to understand how those parts of the solve work later.

Just an idea. Perhaps we're asking the wrong question. Why should we teach beginners methods that are 100% intuitive right from the start? If there is a very simple way to do this, then of course that approach makes sense. But it seems we are down to the very theoretical options like Human Thistlewaite to accomplish this restriction.

Chris


----------

