Layer-by-Layer 2.0

0 White cross - Layer 1 Tutorial


The goal: place the four edges WR , WB , WO , WG

The goal is the same as the standard version. The strategy, however, is a bit different

We bring the edges with a white sticker up to Layer 3 (the yellow face), making sure they arrive with the white sticker facing up.

Sometimes, when we move from Layer 2 to Layer 3 , this ACTION dislodges an edge we already placed in Layer 1 In that case, we need a short sequence of moves to fix the side effect: put the white edge back.

All this may feel clumsy for the 'white cross'. But it is only to introduce the approach of version 2.0: once you master it, the entire cube is solved.

The strategy:
  • If the edge is on Layer 1 then move it to Layer 2
  • If the edge is on Layer 2 then move it to Layer 3 white sticker up. on the yellow face
  • If the edge is on Layer 3 white sticker faces sideways, then move it to Layer 2

Once the edge reached the Layer 3, white sticker up

  • Rotate the top face to align the edge's side colour with the matching centre.
  • Rotate that face 180° to insert the edge.

 

In a nutshell:
  • F' - a Setup move. It's like bringing an object to the workbench to fix it.
  • (R U' R' U) Does the job keeping side effects contained.
    • R - the Action we want to perform. Has side effects.
    • U' - the Protection protects the action from the next move.
    • R' - the Undo cancels the side effects of R
    • U - the Undo cancels the side effects of U'
  • U F2 - (U F F) Just simple moves to bring the edge to its final position.
Special case: the edge is on Layer 3 and the white sticker faces sideways

 


  • U : Brings the WB edge onto the Blue face at position muf
  • F : Brings the WB to Layer 2 (Once the edge is on the Layer 2 normal strategy applies)

What you learned for the white cross is all you need to solve the entire cube.



'Disclaimer': the proposed strategy is not optimized at all

A better option could have been (for example) (D R' D' R) Didactical constraints suggest the strategy adopted was better (in few sections will be clear why)

1Positioning corners - Layer 1

Tutorial

Here is where this version differs from the standard approach:

the layer will not be fully solved. One corner stays empty, on purpose.

It's a small change, but it will greatly simplify the solving process. That empty corner gives room to move pieces without disturbing the rest of the layer.

At the end of the process the corner at rdf will remains empty on purpose. (One of the reasons will become clear next section.)

The goal: place the three corners RWG , OWG , OWB

Now it is the time to sort out the corner in the Layer 1 but only 3 out of 4 will be sorted and will be done using the same process learned for the 'white cross': action, protection undo undo.

That initial effort now starts paying off.

The strategy:
  • Move any misplaced white corner from Layer 1 , to Layer 3 .
  • Rotate the top face until the corner is directly above the slot where it belongs.
  • Move a white corner from Layer 3 , to Layer 1 .
  • The corner's orientation will result in a very easy way. The next section shows how.


 


In a nutshell:
  • (R U' R' U) Brings the corner to Layer 3 avoiding side effects.
    • R the Action we want to perform. Has side effects.
    • U' the Protection protects the 'action' from the next move
    • R' the Undo cancels the side effects of the first move: R
    • U the Undo cancels the side effects of the second move: U'
  • F' a Setup. Brings the corner, on Layer 3 over its destination (on Layer 3) .
  • (B' R B R') Brings the corner to Layer 1 avoiding side effects.
    • B' the Action we want to perform. Has side effects.
    • R the Protection protects the 'action' from the next move
    • B the Undo cancels the side effects of the first move: B'
    • U the Undo cancels the side effects of the second move: R

  The algorithm: Sledgehammer Tutorial


In the previous section we used 2 different sequences (R U' R' U) and (B' R B R'), sharing the same schema: Action, Protection, Undo, < strong class="mark">Undo.

Action is the rotation we want to do. But that rotation has side effects.

Protection, Undo, Undo is the sequence that fixes the side effect.

As you have seen, this sequence is useful in many cases. It is natural for it to become a regular 'tool'. In fact, it is a well-known algorithm: the 'Sledgehammer'.

Giving a sequence the status of an 'algorithm' has an important meaning: it shifts the attention from the individual moves to the tool. The algorithm allows us to abstract: we know what it does, without worrying about how it does it.

This has already happened: in the '1 Positioning corners' section, when we moved the Red-White-Blue corner from Layer 1 to Layer 3, the second rotation was counter-intuitive. I wanted to move the corner, I knew the Sledgehammer could do it, and I chose to use it.

In that case I used (R U' R' U), but the U' rotation was counter-intuitive. It would have been more intuitive (and correct) to use (R U R' U'), the famous 'Sexy move' (the 'big brother' of the Sledgehammer). The Sexy move is more efficient in many cases, but to avoid introducing too many new concepts, in this tutorial we only use the Sledgehammer.

The Sledgehammer is more than enough to solve the whole cube. Although there are faster algorithms, this one is sufficient for learning the method without unnecessary complications.

The price for this advantage is a greater number of rotations — not that high for a beginner or first-time solver.

For a beginner there is only one must: just get it done! Speedcubing will come later!


They are two variants of the same algorithm, the Sledgehammer

The price for this advantage is a greater number of rotations: not that high for a beginner or first time solver

For a beginner there is only a must: just get it done! Speedcubing will come later!



To choose the right sledgehammer is simple:

The action is the first move of the required Sledgehammer. The rest follows logically.



Thinking in terms of 'Sledgehammer' makes solving the cube easier.



For the sake of correctness

Formally only (R U' R' U) is the Sledgehammer and only (R U R' U') is the Sexy Move. In this tutorial, we use these names more broadly for any sequence with the same Action → Protection → Undo → Undo structure and regardless of the faces involved.

It is not formally correct. It's just a didactic choice to keep things easy.


For those who want to dive deeper

  • Workbench The cubies affected by the 'Sledgehammer'.
  • Rotations How edges rotate.
  • Swap How corners swap together.
  • Arrows Arrows shows how cubies relocate
  • Cycle 'Sledgehammer' repeats itself every 6 iterations
  • Reverse The 'Sledgehammer' cancelling the effect of another
  • Sexy move The big brother of the 'Sledgehammer'.

    Both do the same job, but in a different way: the difference is the second rotation, and therefore the fourth.

    • R U' R' U - Sledgehammer
    • R U R' U' - Sexy Move

    'Sexy move' and 'Sledgehammer' share the same pattern: Action, Protection, Undo, Undo.

    In the first section, after the setup move, if those four rotations seemed unreasonable - you were right! I should have used the Sexy Move (R U R' U') instead of the Sledgehammer (R U' R' U) (For teaching, the Sledgehammer was the right choice).

    In the classic layer-by-layer method, when you need to solve the third layer, one setup move is enough to use the Sexy Move. To use the Sledgehammer, you need two setup moves.

    For speedcubers, when speed matters, the Sexy Move wins.

    Instead the Sledgehammer makes its effects easier to see (better than the Sexy Move). So, in a tutorial, For beginners, when clarity matters, the Sledgehammer wins.


2 Orientation - Layer 1

Once the corner is in place, to adjust orientation just repeat the 'Sledgehammer'.


Corner orientation with the 'Sledgehammer'.

In the previous section, we placed the corner but didn't care about its orientation. It may be in the right slot but facing the wrong way.

Adjusting the orientation is very simple: repeat the same Sledgehammer until the corner is correctly oriented.


 



The 'Sledgehammer' only changes the position of the cubies inside the 'Y' shaped region.
The 'Y' shaped region

The 'Y' shaped region is called the Workbench. This is an important protective feature: it allows you to manipulate cubies while being sure that side effects remain confined within the Workbench.



Just another example:

3 Edges - Layer 2

Tutorial

Now you will see the advantage of not having completed Layer 1  (see above)


The goal: place the three edges RG , OG , OB ,

Same goal as layer-by-layer, except we skip one cubie as in Layer 1 .

The strategy:
  • Rotate Layer 3 to align the edge's side colour with the matching centre.
  • Rotate Layer 1 to bring the sacrificial cubie, the one at rdf under the placing edge.

    Here comes the pay-off from the choice to not complete Layer 1.

    The empty slot at rdf now acts as a sacrificial placeholder. It can be swapped with the RWG corner at rdb by rotating Layer 1.

    The next sequence (the Sledgehammer) will then relocate the sacrificial corner somewhere in the cube. We don't care about it. When the sequence is completed, we will bring the correct corner back to its place.

    Technically, the action of placing the sacrificial cubie in place of the one we want to protect is called a 'setup', and the sacrificial cubie is called a 'buffer'.

  • Move the placing edge from Layer 3 to Layer 2
  • Bring back the sacrificial cubie to its position at rdf

If the placing edge is on Layer 2,

  • Rotate Layer 1 to bring the sacrificial cubie, the one at rdf under the placing edge
  • Run any 'Sledgehammer' Just to bring the edge from Layer 2 to Layer 3 .
  • Bring back the sacrificial cubie to its position at rdf

 



In a nutshell:
  • U2 Setup - prepares the cube for the Sledgehammer
  • D Protect the RWG by swapping in the sacrificial corner at rdf
  • (B' R B R') Sledgehammer - does the job with 'controlled' disruptions.
  • D' Undo - restores the RWG corner to its place.


Special case: the edge to place is trapped in Layer 2.


The same move that inserts an edge can also free a trapped one.

Simply pick any edge that's already on Layer 3 for example the edge OY at position muf and pretend it's the one you want to place onto Layer 2. at position leb occupied by the edge you are really interested in RG

 

Then repeat the technique you just learned. This will move your fake edge down to Layer 2 and bring the edge you actually need up to Layer 3


Believe it or not, the worst is over. 😎

In the classic approach, the third layer introduces several new algorithms at once — which can be a lot to absorb. From now on, this is where the Sledgehammer-based approach really helps: you keep using the same tool you already know, and the rest falls into place.

The Sledgehammer alone solves the rest. No new algorithms needed.

4 First 2 Edges - Layer 3


The Sledgehammer is a powerful tool for keeping the cube under control. But never forget: the Rubik's cube is a wild beast, always ready to strike.


This section is about finding out whether we've fallen into its trap.

We could avoid the trap by analysing the remaining cubies to decide where to place the first yellow edge. But that would require learning a whole new analysis - and then doing it every time. It's simpler to just proceed. If we've fallen into the trap, we'll get out with the Sledgehammer.

The goal: place the two edges OY , YG ,

This could be a good opportunity to test your level of mastery of the Sledgehammer. Have a go at solving this goal in your own way.


Workbench have you seen it yet?



The strategy:
  • Only one of the two edge at a time should be in the 'Workbench'

    That is not a must but is a good practice at least until the 'Sledgehammer' doesn't have any secret

  • Use only the sledgehammers starting from the faces Red or Yellow or Blue
    • Red (R U' R' U) or (R' F R F')
    • Yellow (U F' U' F) or (U' R U R')
    • Blue (F R' F' R) or (F' U F U')

    This prevents disrupting cubies, already placed

  • If the edge is on Layer 3 then move it to Layer 2

    Not mandatory! it is just a good practice, for a beginner, to make thing easier.

  • Orientate the Layer 3 to receive the edge from Layer 2

    Normally the first edge to be placed is the orange-yellow and does not require particularly attention

    When placing the YG the OY , should be placed at position mub

  • If the edge is on Layer 2 then move it to Layer 3 Yellow sticker up.

    It is always possible bring the edge on Layer 3 Yellow sticker up. using only one 'Sledgehammer'. But sometimes is not intuitive

    When is not possible bring the edge on Layer 3 Yellow up directly, using the 'long path' helps!

    For example:
    instead going directly from ref to rus using the sledgehammer (R U' R' U),
    you can go from ref to muf using the sledgehammer (F' U F U'),
    and from muf to rus using the sledgehammer (U' R U R')

    The result is the same: the edge ends up at rus , but a different orientation.


 




In a nutshell:

This part is easy like the white cross. If you've got the idea behind it, you'll soon improvise.

5 The Checkpoint - Layer 3


At this point the edges YG and OY are correctly sorted out. And the last three edges inside the 'Workbench', at muf , rus , ref will tell us whether we've fallen into the trap.


if only one of the edges ( muf , rus , ref ) is in its place, the trap has struck.

Regardless of how the three edges are oriented.

There are many ways to get out of it. This tutorial is committed to the Sledgehammer, and the next section shows how to escape the trap using just the Sledgehammer.

There is also a very elegant and intuitive procedure that involves a 5-cubies rotation

6 'The Trap' - Layer 3 Tutorial


Layer 3 is where most give up, even though the solution is simple.


When positioning the first edge on the third layer, it seems natural to assume it can be placed in any of the four slots.

THAT'S WRONG!

allowed slots
Only two positions are valid - they lead to a successful resolution.

The other two will result in a swap of the last two edges, making the cube seem impossible to solve - until you realise you just need to relocate the already placed edges, OY and YG

And that is exactly why it's called 'the trap'.


To resolve this, simply relocate the two edges OY and YG to their adjacent positions.



 



In a nutshell:



It does not matter how the remaining three edges are arranged.


The trap is escaped by performing the Sledgehammers on the two edges already placed

In this example, for teaching purposes, the three edges have been arranged to make the final result clear


Take a look at this brilliant alternative to escape the trap escape the trap


7 Orientation - Layer 3

Once you've escaped the trap, you need to position the last 3 edges: YB, RY, RB. Any Sledgehammer fits this purpose. Run it until all three edges are in place.


There are only two possible outcomes:


 




In a nutshell:



There is another way to adjust orientation (💥 the Armageddon).


The boring part 🥱

At this point, with at most 5 corners left to place, this might seem like the trickiest part, the one where you could mess things up. But in fact, from here on, the process is so simple and mechanical that it becomes boring.

You will need a moment of concentration to grasp the intuition behind it. But after that, it is all mechanical and left to muscle memory.

8 Completing corners - Layer 3

I found this technique on the internet - no idea who came up with it.

Last effort: placing the final 5 corners

At that point all the edges are sorted out. The corners OYG , RWB , OYB , RYB , RYG still need to be sorted out without damaging what done so far.

The idea is to bring the corners to their correct positions one at a time, using the Sledgehammer's property of swapping two corners

In our case, we are interested in the swap between the corners at positions ruf and rdf .

Although the idea is simple, the execution requires special attention: a Sledgehammer, in addition to the swap that we find useful, also scrambles the other cubies within its Workbench, and that would be a problem.

But there is a fact about the Sledgehammer that helps us: every six repetitions, the Workbench cycles and returns to its original configuration.

Why does that help? Simply because, if we are careful to always use the same Sledgehammer (or its inverse ), we can perform as many swaps as we need, knowing that the other cubies in the Workbench are only in one of six possible configurations. When we have finished the swap operations, it will be enough to repeat the Sledgehammer until the Workbench returns to its initial state.

Good, but there is still a problem: during our corner-placement process, we keep rotating Layer 3 , constantly changing the cubies within the Workbench. We need the cubies in the Workbench, apart from the two corners we are working on, to remain stable!

That is a real problem!

...

💡 The problem is challenging, but the solution is simple: just change the 'old' Workbench to a 'new' one.

Things to know:
  • Cycle - a 'Sledgehammer' repeats itself every 6 times.
  • Swap - 'Sledgehammer' swaps corners.
  • Reverse - Each sledgehammer has its own reverse.
The goal: place the corners OYG , RWB , OYB , RYB , RYG

The goal is the same as the previous version, as well as the tecnique: nothing new.

The strategy:

First of all it is necessary change the workbench from the old one to the new one. and using only the the sledgehammers The new sledgehammer becames: (F' R F R') or (R F' R' F) (Note: both are the inverse of the other) to be sure the workbench will return to its original configuration

  • Check the corner at position rdf
  • Bring the destination of that corner at position ruf with a setup move

    In this example the destination of the RYB is exactly between the edges YB and RY, therefore it is no need to perform the 'setup move' and Layer 3 does not rotate.

  • Swap the corner at rdf with the corner at ruf Using a 'Sledgehammer"

    (The corner at position ruf will be the next corner that will be put in place)

  • To adjust the orientation just keep going with the same 'Sledgehammer'

 


  • (F' R F R') SH RYB goes to its position ruf and corner at ruf goes to rdf
  • U Setup the corner at rub goes to ruf
  • (U F' U' F) Sledgehammer RYG goes to its position ruf and RWB goes to rdf
  • U2 Setup OYB is already in place. A double 'Sledgehammer' will adjust its orientation
  • (U F' U' F) Sledgehammer Moves the OY edge to the next position
  • U Move Brings OY to its correct place.

In a nutshell
  • Position the corners by continuously swapping between the corners at ruf and rdf .
  • Avoid side effects by changing the Workbench from the 'old' one to a 'new' one.
  • To avoid creating chaos in the new Workbench, always use the same Sledgehammer (R F' R' F) or its inverse (F' R F R').
  • Once the corners are in place, repeat the Sledgehammer until the Workbench is restored to its original state.

9Corners Last 2 - Layer 3
The final hurdle: two corners correctly placed but incorrectly oriented

You know it by now: the cube is a wild beast, and this is its final twist. But it is a beast that is now tame and no longer frightening. We already know how to react.

Changing the 'Workbench' to this and using only the the sledgehammers (D' R D R') or (R D' R' D) (Note: both are the inverse of the other) to be sure the workbench will return to its original configuration will definitively complete the cube.

Things to know:
  • Cycle - a 'Sledgehammer' repeats itself every 6 times.
  • Swap - 'Sledgehammer' swaps corners.
  • Reverse - Each sledgehammer has its own reverse.


This sequence uses the same 'Sledgehammer'

 

  • (D' R D R')2 Sledgehammer Adjusts orientation of corner RWB at rdf
  • F Setup moves corner RYB from ruf to rdf
  • (D' R D R')4 Sledgehammer Adjusts the orientation of ruf
  • F' Setup Final rotation. Cancels the rotation from step 2 (F)
Note:

Repeating the 'Sledgehammer' 6 times returns the 'workbench' to its original state. The first 2 repetitions adjust the orientation of the corner RWB

Since after 6 ripetition of the same 'Sledgehammer' the cube restores its original state the same 'Sladgehammer' will be repetead other 4 times and the cube will be finally solved

This sequence uses a 'Sledgehammer' and its reverse

 


  • (D' R D R')2 Sledgehammer Adjusts orientation of corner RWB at rdf
  • F Setup moves corner RYB from ruf to rdf
  • (R D' R' D)2 Sledgehammer Adjusts the orientation of ruf
  • F' Setup Final rotation. Cancels the rotation from step 2 (F)
Note:

The second 'Sledgehammer', the inverse of the first, cancels the effect of the first one and the cube returns to its original state in only 2 iterations.

How to reverse: Perform the moves in opposite order and opposite direction. If the move was D', the reverse is D. E.g. (D' R D R') ⬄ (R D' R' D)


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