Workbench

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The 'Workbench' method
Workbench.140x140.png
Information about the method
Proposer(s): Vincenzo S.
Proposed: 2024
Alt Names: slow-solving method,
Variants: none
No. Steps: 4
No. Algs: 1
Avg Moves: unknown
Purpose(s):

Glossary

For those new to the Rubik's cube this may help:
A 3x3x3 cube is a regular geometrical object with 8 corners, 12 edges, 6 faces and 6 Centers. Cubie(s) are organized into Layer(s) or (more generally) 'Slice(s)' and Rotation(s) (also called 'move'(s), Each rotation identifies a slice (the cubies moved by the rotation). Rotations are organized in Algorithms (one of them is the 'Sledgehammer' used here). There are many strategies to solve the Rubik's cube, called Method(s)

Practising the cube. (Hover on the elements of the page and wait for the tooltip, the floating popup message.)
Arrows (Explains the arrows that appear when hovering over the button on the table to the right of the page.)

This page could help

Introduction

The 'Workbench' is a new approach to the Rubik's Cube that relies only on the 'Sledgehammer'.
(It belongs to the family of simplified methods for beginners, such as Sexy_Method, 8355 Method, Less is More and Y-Move Method. , the latter being the one it most closely resembles, including in name. The original name of the 'Workbench' method was the 'Y Method'.)

Workbench.140x140.png

The 'Sledgehammer' affects seven cubies in a Y-shaped area called the 'Workbench'.
(This area serves as a useful workspace for positioning cubies, which explains the name.)

The 'Tripod' refers to the region consisting of all the cubies that do not belong to the 'Workbench' (the cubies shown in grey in the picture)

- YouTube video on the 'Sledgehammer'
- Live interactive 3D 'Sledgehammer' tutorial

The Strategy

The strategy of the 'Workbench' method is simple, it's something we've always done: first, define a workspace where we can do whatever we need without worrying about making a mess.
Then
- bring the object we want to 'work on' into our workspace,
- fix it,
- return it to its place.

Talking the language of the Rubik's cube: The 'Workbench is our workplace
- A 'setup move' brings a cubie (from the 'tripod') into the 'Workbench'
- A 'Sledgehammer' 'fixes' the cubie.
- An 'Undo Move' returns the cubie to its place.

That's the 'Jolly move':

'setup-move' + 'Sledgehammer' + 'undo-move'.

The 'Jolly move' can:
- Bring every edge or corner (already into the 'Workbench') to its final place. In that case is named 'Delivery' move.
- Bring every edge or corner onto the 'Workbench'. In that case is named 'Setup' move.
- Set the orientation of every cubie (edge or corner).
- Escape 'the Trap' (explained in the next step)
- Complete the corner (explained in the last step)

This video presents the 'Jolly move'.
This page shows that the 'jolly move' can place both edges and corners.
This page shows that the 'jolly move' can even adjust the orientation of the cubie

(Dividing the cube into two regions, 'The Workbench' and the 'Tripod', simplifies Rubik's Cube manipulation by isolating undesirable side effects in the 'Workbench', enabling a straightforward path to complete the 'Tripod'.)

The Flow

The 'Jolly move' is so effective that the entire Rubik's cube can be solved using only a sequence of 'Jolly moves' divided into three steps: (An intuitive evidence is provided in the 'About the 'Jolly move' chapter, in the 'Extra' section later on.)

1. Complete the Tripod (the cubies outside the 'Workbench').
2. Avoid 'the trap'.
3. Change of perspective.
SolverSmall.png

Try the Solver to see the 'Jolly move' solving the cube
(The 'Jolly move' is the 'engine' that allows a machine to mechanically solve any scrumble, explaining every single step.)

Complete the 'Tripod'

WorkbenchT.png

The 'Tripod state' is the configuration where all the cubies external to the 'Workbench' are correctly placed. The player can choose any flow.

Starting with the cubies already inside the workbench makes things even easier.

Avoiding the 'Trap'

SwapT.png
PositionsOK.png

The 'Trap' is when the last two edges are swapped. (This configuration is related to the concept of 'parity'.)

It is a particularly tricky configuration because it cannot be solved until one realizes that the problem is not the two cubies that have swapped places, but two other cubies that appear to be in the right place.

When positioning the edges on the last layer, it seems like there are four possible positions, but in reality, only two are correct, while the other two set the trap.
To escape the trap, you just need to move two cubies (those already placed) to the next position. Once the trap is avoided, all cubies will be in their correct places.

This video shows this concept and how to escape the trap:

There are also these 2 interactive pages that show two different approaches:
the 'sledgehammer' approach
A much more elegant approach

Possible outcomes

To complete this section remains to analyze these cases:

  • last 2 edges in the right place but with the wrong orientation:
OrientationAll.png

The 'workbench' contains 3 edges: two with the wrong orientation (Cubie Red-Yellow and cubie Yellow-Blue, in the picture) one correctly oriented (cubie Red-Blue). So to solve this configuration is enough move the correctly oriented cubie choosing one of the two 'Sledgehammers' that start rotating it and then choose the 'Sledgehammer' that brings it back. Done!


These pages show:
- The 'Sledgehammer' approach
- The 'intuitive' approach
- The 'intuitive' approach (the same as before but step by step)
- Using a sledgehammer to crack a nut. iterating 3 times the 'Flat orientation' solve the problem


  • The three edges inside the workbench are in the wrong place and sticker of the same color on the same face
SolidRotation.png

(Blue sticker on the Yellow face; Yellow sticker on the Red face and Red Sticker on the Blue face) The solution is to choose one cubie and bring it to its position running on the longest path. So the first 'Sledgehammer' brings that edge not to its place but to the other place. Now the second 'Sledgehammer' brings the cubie to its place.
Done

This page shows:
- The 'Sledgehammer' approach


  • All the other configurations

The easiest solution is to run any of the 6 'Sledgehammers' if the edges are not placed then the result will be one of the two previous cases.
(You can follow a different approach: there are 6 different 'Sledgehammers' one can start with. Only 2 of them has the first move that brings a cubie onto its place correctly oriented and (between these two 'Sledgehammers') only one has the second move that brings at least one sticker to the correct face. That is it!)

(It is possible to avoid falling into 'the Trap', but it's simpler to just get out of it, keeping the method straightforward.)

Change of perspective

Last5.png

At this point, the only cubies left to position are the 4 corners inside the 'Workbench' + 1. Now the space for maneuvering is very limited. Continuing could be particularly challenging (though a correct combination of 'Sledgehammers' can solve it, it's not worth the trouble: there is a simpler strategy).

Once you realize that a new 'Workbench' can be used, this final phase becomes quite simple, even mechanical.

This video shows how to positioning the 5 corners

This page shows how to position the first 3 out of 5 corners.
This page shows how to positioning the last 2 corners.

Pros

Simplicity: The ability to use the same tool (the 'Sledgehammer') to solve all configurations is certainly the greatest advantage of this method.
Support: The suggested videos and websites offer a variety of resources to help users learn how to manipulate the cube.

Cons

Slowness: Using a single algorithm simplifies the process, but inevitably slows it down.
Cumbersome: The solutions provided can sometimes be excessively long. There are many shortcuts that an experienced player will be able to discover over time.

Extras

About the 'Jolly move'

The following list shows the sequence of 'Jolly moves' used to solve the default configuration in the Solver:

      ┌── Setups the cube for the 'Sledgehammer'
      │          
      │          ┌── Executes a 'Sledgehammer'
      │    ┌─────┴──────┐ 
      │    │            │    ┌── Restores the cube
      │    │            │    │
 1)   E2   ( U  F' U' F )    E2
 2)   M2   ( U  F' U' F )    M2
 3)   E    ( U  F' U' F )    E'
 4)   E2   ( R' F  R  F')    E2
 5)   U2
 6)   D    ( R' F  R  F')    D'
 7)   M    ( U' R  U  R')    M'
 8)   E'   ( U  F' U' F )    E
 9)   E'   ( R' F  R  F')    E
10)   U
11)   D'   ( F  R' F' R )    D
12)   E    ( U  F' U' F )    E'
13)        ( U  F' U' F )
14)   S'   ( R' F  R  F')    S
15)   S    ( U  F' U' F )    S'
16)   E    ( U' R  U  R')    E'
17)   E    ( R' F  R  F')    E'
18)   U
19)   S    ( U' R  U R' )    S'
20)        ( U  F' U' F )
21)        ( R' F  R  F')
22)        ( F' U  F  U')
23)        ( F  R' F' R )
24)   U2   ( R  F' R' F )3   U2
25)        ( F' R  F  R')
26)   U'   ( R  F' R' F )3   U
27)   U    ( R  F' R' F )3   U'
28)        ( R  F' R' F )
29)        ( R  F' R' F )
30)        ( R  F' R' F )
31)        ( D' R  D  R')2
32)   F    ( R  D' R' D )2   F'

This list clearly shows that the 'Jolly move' (the 'Sledgehammer') is all needed to solve the Rubik's Cube.

Each step results in a cubie:
- Changing its position;
- Changing its orientation.
These two simple actions are the building blocks of the 'Workbench' method.

They form an abstraction layer that lets the player focus on 'what to do' rather than 'how to do' when solving the cube, making the 'Workbench' approach much simpler.

The Solver could serve as a good tutorial to see the 'Jolly move' in action.

Super Jolly move

Appending an 'undo-Sledgehammer' to the 'Jolly move' we get a very interesting trigger:

'setup-move' + 'Sledgehammer' + 'undo-move' + 'undo-Sledgehammer'

- The 'setup move' brings a cubie into the 'Workbench';
- The 'Sledgehammer' performs the necessary operation;
- The 'undo-move' reverses the first move.
- The 'undo-Sledgehammer' reverses the previous 'Sledgehammer'.
('Undo Sledgehammer' is the reverse of the previous 'Sledgehammer'.)

This trigger applies a rotation to 3 edges or 3 corners while keeping the 'Workbench' region (the working place) unaffected.

This page shows a 'Sledgehammer' and its reverse.

This page shows the 'Super Jolly' in action:

Flat orientation

These three 'Sladgehammers': (U F' U F)(F R' F' R)(R U' R' U)
Where the next 'Sledgehammer' continues the previous: (U F' U F2 R' F' R2 U' R' U) Have the interesting property of rotating only the cubies (inside the 'Workbench') on the yellow face so:
- 2 Iteration of this trigger rotate only the corner
- 3 Iteration of this trigger rotate only the edges

This page shows the The 'flat orientation' in action:

'The 'Super Jolly' move and the 'Flat Orientation' together are the only transformations needed to solve the Rubik's Cube. That proves the 'Sledgehammer' alone can solve the Rubik's cube.
(yet to be proven for larger cubes like 4x4x4, 5x5x5, etc.)

(A funny thing is that these 3 'Sledgehammers' (U F' U F)(R U' R' U)(F R' F' R) do nothing!)

Disclaimer

After nearly 50 years since the invention of the Rubik's cube, and with hundreds of millions of people solving it at various levels, it is difficult to claim that something entirely new has been invented. The 'Workbench' method combines already-known solutions with personal insights.

Creating a unique and coherent system is the innovation introduced by the 'Workbench' method.

Video tutorials

External links