Swap edges

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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):

Introduction

SwapT.png

A common tricky configuration arises when all edges are correctly positioned, except for two edges swapped together.

The Workbench approach, calls this configuration 'The trap' .

Many algorithms are available to resolve this setup.
(This page is a collection of them. Some are just algorithms. For some of them, an intuitive approach is provided.)

- rotations 4 + 3

Consider this sequence of numbers:
1 2 3 4 - If we rotate all four numbers we get:
2 3 4 1 - Then reverse the last three numbers, and we get:
2 1 3 4 - We've effectively swapped the '1' and '2'.

Therefore a rotation of 4 items and a (counter) rotation of 3 items can produce a swap between two items, (specifically ‘1’ and ‘2’)

The same principle applies to the cube configuration with two edges swapped:

  • The 1st rotation (that affects 4 edges) is simple: it’s a single rotation that shifts each edge on a face to the position of its direct neighboring edge.
  • The 2nd rotation, although conceptually straightforward, involves a set of standard moves that affect only three edges instead of the usual four.

As always there are many different options to get the requested rotation of 3 edges. The following is one of them

There are many ways to achieve this second rotation, but here's one example:

  • U - This is the rotation that affects 4 items (edges)
  • R U R' - This shifts the YG edge to the position of the OY one.
  • U R - This shifts the OY edge to the position of the RY one.
  • U2 R' - This shifts the RY edge to the position of the YG one.

This page provides an interactive 3D example in a way that’s easier to follow.

- The Trap

Here's a different way to look at it, and it's actually quite revealing.

PositionsOK.png

When you start placing the last layer's edges, it's important to choose the right slot for the first one. There seem to be four options, but really, there are only two. The other two choices will always force you to swap two pieces.
Within this perspective, there's nothing the player can do until they realize that it's not the two swapped edges that are out of place, but the two edges (only apparently) correctly positioned.

Obviously, there's a way to determine what the correct position would be (it's a matter of parity). However, getting out of the trap is so simple that it's less demanding to move on and solve the problem when, and if, it arises.

This page provides an interactive 3D example in a way that’s easier to follow.

- Rotation of 5

RotationOf5.png

For this final perspective, having the cubies arranged slightly differently is useful. (This is another example of how layer-by-layer methods, while excellent for speedcubing, can sometimes obscure the underlying mechanics of a solution.)

If we focus on the five edges: RY, YG, OY, RB, and YB, we can see that they’re all in the correct relative positions. Each edge has the neighbor it should have:
RY is preceded by YB and followed by YG,
YG is preceded by RY and followed by OY,
and so on.
A simple rotation of these five edges is enough to resolve the swap of two cubies, as it brings all the third-layer cubies into alignment on the third layer and places the RB edge in its correct spot.
After rotating these five cubies, the cubies on the third layer will be in the correct relative position but in the wrong absolute position. However, one additional rotation will restore everything.

This page provides an interactive 3D example in a way that’s easier to follow.

- Other solution

This section provides a list of other approaches found along the web. (anybody knows new solution, please add to this list)