# Intuitive 3x3 Solution (no algs)



## Cride5 (Jul 21, 2010)

There has been some interest in 'no alg' solutions to the Rubik's cube lately, so I thought I would share this...

Related threads:
http://www.speedsolving.com/forum/showthread.php?t=22673
http://www.speedsolving.com/forum/showthread.php?t=14437


Preamble

The corners are generally recognised as being hardest to solve. It makes sense to solve them first, when there are least restrictions imposed. Erno Rubik himself actually used a corners first approach for the very first Rubik's cube solve!

The system proposed, breaks down the solve into many smaller sub-steps, each of which should be easy to follow and which require no 'algorithms' to solve. I wouldn't go as far as to say that a solver will understand exactly why the steps work, only that they will understand the sub-steps. In the same way, ZZ solvers may not understand 'why' the U-layer cross is solved after F2L, but will understand that it can be done by using only R, U and L during F2L.

Because it is a corners-first approach, this method can be used to solve either 2x2 or 3x3, and can equally be used with a reduction approach to solve larger dimension cubes.


Corners Phase / 2x2x2

In this phase ignore everything but the corners. When it says form a 'pair', it means a pair composed of corners. In addition, pairs in this first section need only have one adjoining sticker on each piece matching. Where the term 'opposite colours' is used, it means colours on opposite faces on the cube. U/D for example.

The term a '_pair of opposite colours_' means two corner pieces in which two stickers of opposite or the same colour are beside each other.



*3+2 on Opposite Sides*

Form a pair of opposite colours on any side, then hold that pair in DL.

Now using only R and U turns:

Form a pair of opposite colours on the top face, then position that pair in UL.

Use R turns to create a 3 of opposite colours on the D-face, while keeping only a pair on the U-face.

If it is not possible to create a 3 on the D-face without creating a 3 on the U-face, then twist the U layer, so that a different pair is preserved while doing the R-turns. It will now be possible to create a 3 on the D-face, with just a pair on the U-face.

If it is not possible to create a 3 on any face, then break up the pair on the U-layer and form a pair with different pieces.



*2x Faces of Opposite Colours*

Rotate the D-layer until the last unoriented cubie has its D sticker is facing you (ie. the D sticker is on the front face).

Rotate the top layer so that the pair is on the opposite side of the D-sticker facing you. For example, if unoriented cubie on the D-layer has its D colour on the left of the front face, then place the pair in the top face on right.

Twist the front face to create exactly two pairs. One on U and one on D. 

Now twist the top layer to create to create two more pairs, one on the left face, and one on the right.

Finally twist the front face again to join up the pairs and create two opposite faces of opposite colours.



*Permutation*

From here, the term 'pair' means two matching corner pieces, such that all adjoining stickers match up.

In this step, only use R2 and U moves!

Create a pair in D, hold in DL. Pair up the other D-layer pieces in U, then send to D, finishing the D-layer.

At this point the U layer may be complete, and you are done ... otherwise do the following:

If the U-layer has a pair, rotate the U-layer so that the pair is in the left side.
Bring a complete D-layer pair into the U-layer, and place it in the back.
Break up that pair with R2 so that one of the pieces drops down into the front-right position of the D-layer.
Now rotate the top layer, and then do R2, so that the other D-layer piece moves from the U-layer, into front-right and its correct position.

Rotate the cube, so that the pair in DF is now in DL. Now solve the rest of the D-layer as before and the U-layer will magically solve itself 

If the U-layer has no complete pair, then follow the previous instructions to create a pair in the U-layer.


Edges Phase

This phase follows an approach based on Roux, and is described in an older thread here.

Before starting on the edges phase, use slice turns to ensure all the centres are in their correct locations with respect to the corners.



*6x F2B Edges*

The goal is to solve 3x L and 3x R edges to create 1x2x3 blocks on L and R.

Find an F2L edge (excluding DF and DB) in the M-slice. Rotate the M-slice so that the edge occupies the D-layer.
Depending on the side the edge belongs to, rotate L or R and then U, so that the edge's home position is in either UF or UB. Move the M-slice to place the edge. If the edge is placed, but flipped, then undo the M-move and do U2. The edge can now be correctly placed with an M-move. Finally undo the top move, and the side move.

If no F2B edges are in the M-slice, then use the approach above to move an edge from the L/R layer into the M-slice.

Finish by rotating the M-slice so that the U/D layer centres are in their correct positions relative to the corners.



*Edge Orientation*

The final 6 edges belong to either the U or D-layers. They are defined as 'oriented' if their U or D stickers are on the U or D faces. The goal is to orient the remaining 6 edges. 

An M slice quarter turn temporarily flips the orientation of all edges in the M-slice. However, as soon as the M slice is turned to re-align the centres, all edges flip back again. If a U-turn is done before undoing the M-move, then two edges in the M-slice and two edges in the U-layer will have their orientations flipped.

Use a series of M and U moves to orient all six edges.

If you have 6 misoriented edges, any M U M series of quarter turns will create a 2 edge case.

If you have 2 misoriented edges, position them so that one will have its orientation preserved, while the other will be flipped and do the M U moves. This will create a case with 4 misoriented edges.

If you have a 4 misoriented edges, position them so that one is in the D-layer, while the other three are in the U-layer. 3 simple M U moves will orient all four edges from there.



*Solve RU and LU*

At this stage, be careful not to flip the edge orientation. This can be done by ensuring only M2 and U moves are made.

To solve RU and LU, first place them in the DF and DB positions. If it is not possible to do this using only M2 and U moves, then place one of them in the DB position, and the other in the UF position. Now do an M move so that the D-layer centre moves into the front face. Do U2 to place the edges next to each other, and then undo the M move.

Once the edges are in the DF and DB positions, rotate the U-layer, use M2 to place them, and then undo the U rotation.



*Solve the M-slice Edges*

Use M moves and U2 to solve four remaining M-slice edges.

I'll leave you to work out the details 




Example Solve

Scramble: D2 L2 F2 D R2 U' L2 F2 D2 U' F' L U' B' D2 U R2 B L2 B 

Solution: click for animation...

3+2:
Pair of opposite colours: *y*
Pair of opposites on top face: *R U2 R' U*
3 on bottom, pair top: *R U' R*

2 Opposite Faces:
D-layer corner in front-right, sticker facing front so move to front left: *y* 
2x pairs on top: *L'*
2x pairs on F/B: *U*
Join pairs: *R x*

Permutation:
Complete Pair in DL: *y U2 R2 y*
Second D-layer pair in U: *U R2 U' R2*
Move into D to complete layer: *U' R2*
Move unsolved cubies into R: *U*
Move pair from D into UB: *R2 U'*
Break up pair: *R2*
Place one D corner: *U R2*
Rotate cube to preserve alternative pair in DL: *y*
Solve D-layer again: *R2 U R2 U' R2*
AUF: *U'*
Solve Centres: *S E*

F2B:
DL: *L2 U M2 U' L2*
BL: *L U' M' U L'*
FL: *M L' U' M' U L*
DR: *M2 R2 U' M2 U R2*
FR: *R U M' U' R'* 
Bring piece into M: *U' M U*
BR: *R' U' M2 U R *
Align centres: *M*

Edge Orientation:
Flip 2: *M U' M*
Flip 4: *U2 M U M*

UL and UR:
Place in D: *U' M' U2 M U*
Solve: *U' M2 U*

M-slice:
*M U2 M' U2 M2*


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## StachuK1992 (Jul 21, 2010)

Could you possible provide an example solve? I'm a tad bit confused on some parts.

Edit:
Cool, the example clears it up a lot. Cool idea, I guess.


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## Daniel Wu (Jul 21, 2010)

I'm a bit confused on corners, but I'm sure I can work it out if I reread. Anyway, it's corners first, solve roux blocks around the corners, and the L6E roux style, right?


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## StachuK1992 (Jul 21, 2010)

rickcube said:


> I'm a bit confused on corners, but I'm sure I can work it out if I reread. Anyway, it's corners first, solve roux blocks around the corners, and the L6E roux style, right?


From what I can tell, it's like Corners-First, Roux, and Salvia had a...strange encounter of sorts.


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## Cride5 (Jul 21, 2010)

Stachuk1992 said:


> Could you possible provide an example solve? I'm a tad bit confused on some parts.



I've edited in an example for you, hope it helps..



Stachuk1992 said:


> rickcube said:
> 
> 
> > I'm a bit confused on corners, but I'm sure I can work it out if I reread. Anyway, it's corners first, solve roux blocks around the corners, and the L6E roux style, right?
> ...



It's quite a mishmash of methods really. Opposite faces uses concept from Guimond, but broken down into specific steps for an intuitive approach. Permutation uses sq-1 style solve, but using property of CP preservation when only R/U turns are used. F2B uses similar concept to M2 BLD method. Final steps are LSE from Roux.


I think I would still teach [wiki]sexy method[/wiki] to beginners, since the single 4-move alg is pretty easy to remember and makes the solve a whole lot easier. I would probably teach this to someone who is interested in cube theory. I'm sure it would definitely be suitable for a more 'switched on' beginner though.


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## Kynit (Jul 22, 2010)

What exactly do you mean by opposite colours? Corners that belong on U and D faces? Or completely non matching?


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## Cride5 (Jul 22, 2010)

Kynit said:


> What exactly do you mean by opposite colours? Corners that belong on U and D faces? Or completely non matching?



Colours which belong to opposite ends of the cube, yes U/D would be opposites. I'll update the tutorial to clarify..


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## Kynit (Jul 22, 2010)

Oh, that extra line completely clears it up! I was thinking only opposites


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## Ordos_Koala (Feb 6, 2011)

nice tutorial, everyone can learn something useful everyday  I'm going to learn Roux


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