4 Ways to Solve the Rubik's Cube with the Layered Method

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-01-17 17:31

The Rubik's Cube can be very frustrating and it can seem almost impossible to get it back to its starting configuration. However, once you know a few algorithms, it's very easy to fix. The method described in this article is the layered method: we solve first one face of the cube (first layer), then the middle one and finally the last one.

Steps

Method 1 of 4: First layer

Step 1. Familiarize yourself with the notations at the bottom of the page

Step 2. Choose to start with a face

In the examples below, the color for the first layer is white.

Step 3.

Solve the cross.

Place the pieces at the four edges that contain the white in place. You should be able to do it yourself without the need for algorithms. All four board pieces can be placed in up to eight moves (five or six in general).

Insert the cross at the bottom. Rotate the cube 180 degrees so that the cross is now on the bottom

Step 4. Solve the four corners of the first layer, one by one

You should also be able to place corners without the need for algorithms. To get started, here's an example of how a corner is solved:

At the end of this step, the first layer should be complete, with a solid color (in this case white) at the bottom

Step 5. Verify that the first layer is correct

You should now have the first layer complete and look like this (from the bottom side):

Method 2 of 4: Middle Layer

Step 1. Put the four edges of the middle layer in place

Those border pieces are the ones that don't contain yellow in our example. You only need to know an algorithm for solving the middle layer. The second algorithm is symmetric to the first.

• If the edge piece is in the last layer:

  									(1.a)
  									(1.b) symmetrical of (1.a)

• If the edge piece is in the middle layer, but in the wrong place or in the wrong orientation, simply use the same algorithm to put any other edge pieces in its position. The edge piece will then be in the last layer and you just have to use the algorithm again to place it correctly in the middle layer.

Step 2. Verify correct placement

The cube should now have the first two full layers and look like this (from the bottom side):

Method 3 of 4: Last layer

Step 1. Swap the corners

At this point, our goal is to put the corners of the last layer in their correct position, regardless of their orientation.

• Find two adjacent corners that share a color other than the top layer color (other than yellow, in our case).

• Turn the top layer until these two corners are on the correct color side, facing you. For example, if two adjacent corners both contain red, turn the top layer until those two corners are on the red side of the cube. Note that, on the other side, both corners of the upper layer will also contain the color of that side (orange, in our example).

  

• Determine if the two corners of the front side are in their correct position and swap them if necessary. In our example, the right side is green and the left side is blue. So the front right corner must contain the green and the front left corner must contain the blue. If not, you will need to swap the two corners with the following algorithm:

  Swap 1 and 2:

  (2.a)

• Do the same with the two corners on the back. Turn the cube to put the other side (orange) in place in front of you. Swap the two front corners if necessary.

• Alternatively, if you notice that both the front and rear pair of corners need to be reversed, this can be done with just one algorithm (note the enormous similarity with the previous algorithm):

  Exchange 1 with 2 and 3 with 4:

  (2.b)

Step 2. Orient the corners

Locate each top colored label in the corners (yellow in our case). You only need to know one algorithm for orienting corners:

(3.a)

• The algorithm will rotate three corners on themselves at once (side up). The blue arrows show you which three corners you are turning and which direction (clockwise). If the yellow stickers are placed in the manner indicated by the images and you run the algorithm once, you should end up with four yellow stickers on top:

• It is also convenient to use the symmetric algorithm (here the red arrows are turned counterclockwise):

  (3.b) symmetric of (3.a)

• Note: Running one of these algorithms twice is equivalent to running the other. In some cases, it will be necessary to run the algorithm more than once:

• Two correctly oriented corners:

  	=		=		+
  	=		=		+
  	=		=		+

• No corner oriented correctly:

  	=		=		+
  	=		=		+

• More generally, (3.a) applies in these cases:

Two correctly oriented corners:
No corner oriented correctly:

Step 3. Swap the edges

You only need to know one algorithm for this step. Check if one or more edges are already in the correct position (orientation doesn't matter at this point).

• If all the edges are in their correct position, you are ready for this step.

• If only one edge is positioned correctly, use the following algorithm:

  (4.a)

• Or its symmetrical:

  (4.b) symmetric of (4.a)

  Note: executing one of these algorithms twice is equivalent to executing the other.

• If all four edges are positioned incorrectly, run one of the two algorithms once from either side. You will have only one corner positioned correctly.

Step 4. Orient the edges

You need to know two algorithms for this last step:

		Dedmore model to H.
											(5)
		Fish model of Dedmore
													(6)

• Note that DOWN, LEFT, UP, RIGHT is the recurring sequence for most of the H and Fish Dedmore algorithms. You really only have one algorithm to remember:

  (6) =

  + (5) +

• If all four edges are flipped, run the H-type algorithm from each side and you will need to run that algorithm one more time to solve the cube.

Step 5. Congratulations

Your cube should now be solved.

Method 4 of 4: Notations

Step 1. This is the key to the notations used

• The pieces that make up the Rubik's cube are called cubies and the color stickers on the pieces are called facelets.

• There are three types of pieces:

  • THE center pieces, in the center of each face of the cube. There are six of them, each have a facelet.
  • The corners or corner pieces, at the corners of the cube. There are eight of them and they each have three facelets.
  • THE edges or edge pieces, between each pair of adjacent corners. There are 12 of them and each has 2 facelets

• Not all cubes have the same color combinations. The color scheme used for these illustrations is called BOY, because the Blue (blue), Orange (orange) and Yellow (yellow) faces are clockwise.

  • White is opposed to yellow;
  • Blue is opposed to green;
  • Orange is opposed to red.

  Step 2. This article uses two different views for the cube:

  • The 3D view, showing the three sides of the cube: front (red), top (yellow) and right (green). In step 4, the algorithm (1.b) is illustrated with a photo showing the left side of the cube (blue), front (red) and top (yellow).

    

  • The view from the top, which shows only the top of the cube (yellow). The front side is at the bottom (red).

    

  Step 3. For the top view, each bar indicates the location of the important facelet

  In the photo, the yellow facelets of the top side on the back are on the top (yellow) side, while the yellow facelets of the top front corners are both located on the front side of the cube.

  

  Step 4. When a facelet is gray, it means that the color is not important at that time

  Step 5. The arrows (blue or red) show what the algorithm will do

  In the case of algorithm (3.a), for example, it will rotate the three corners on themselves as shown. If the yellow facelets will be like the ones drawn on the photo, at the end of the algorithm they will be on top.

  

  • The axis of rotation is the large diagonal of the cube (from one corner to the opposite corner of the cube).
  • The blue arrows they are used for clockwise turns (algorithm (3.a)).
  • The red arrows they are used for counterclockwise turns (algorithm (3.b), symmetrical to (3.a)).

  Step 6. For the top view, the blue facelets indicate that an edge is incorrectly oriented

  In the photo, the left and right edges are both correctly oriented. This means that if the top face is yellow, the yellow facelets for those two edges will not be on the top, but on the side.

  

  Step 7. For move notations it is important to always look at the cube from the front

  • The rotation of the front side.
  • The rotation of one of the three vertical lines:
  • The rotation of one of the three horizontal lines:
  • Some examples of moves:

  START

  Advice

  • Know the colors of your cube. You need to know which color is on the other face and the order of colors on each face. For example, if white is on the top and red in the front, then you should know that blue is on the right, orange is on the back, green is on the left and yellow is on the bottom.
  • You can start with the same color to help you understand where each color goes or try to be efficient by choosing a color for which it is easier to solve the cross.
  • Practice. Spend time with your cube to learn how to move the pieces. This is especially important when you are learning how to solve the first layer.
  • Locate all four edges and try to think ahead of time how to move them into place, without actually doing it. With practice and experience, this will teach you ways to solve it in fewer moves. And in a contest, participants only have 15 seconds to inspect their cube before the timer starts.

  • Try to understand how algorithms work. While running the algorithm, try to follow the key pieces all around to see where they go. Try to find the pattern in the algorithms. For instance:

    • In algorithms (2.a) and (2.b) used to permute the corners of the upper layer, four moves are performed, at the end of which the pieces of the lower and middle layers are back in the lower and intermediate layers. You then have to flip the top layer and then reverse the first four moves. Therefore, this algorithm does not affect the layers.
    • For algorithms (4.a) and (4.b), note that you are transforming the top layer in the same direction that is needed to activate the three edges.
    • For algorithm (5), the H-shaped Dedmore model, one way to remember the algorithm is to follow the path of the top right flipped edge and the pair of corners around it for the first half of the algorithm. And then for the other half of the algorithm, follow the other inverted edge and the pair of corners. You will notice that five moves are performed (seven moves, counting the half turns as two moves), then half a turn of the upper layer, then the inversion of those first five movements and finally half a turn of the upper layer.

  • Further progress. Once you know all the algorithms, it is recommended to find the fastest way to solve the Rubik's cube:

    • Solve the corner of the first layer along with its mid-level border in one go.
    • Learn additional algorithms to orient the corners of the last layer in the five cases where two algorithms are needed (3.a / b).
    • Learn other algorithms to permute the edges of the last layer in the two cases where no edge is positioned correctly.
    • Learn the algorithm for the case in which all the edges of the last layer are upside down.
  • Further progress. For the last layer, if you want to solve the cube quickly, you will need to do the last four steps two by two. For example, permute and orient corners in one step, then permute and orient edges in one step. Or you can choose to orient all corners and edges in one step, then permute all corners and edges in one step.
  • The layer method is just one of many existing methods. For example, the Petrus method, which solves the cube in fewer moves, consists of building a 2 × 2 × 2 block, then expanding it to a 2 × 2 × 3, correcting the orientation of the edges, building a 2 × 3 × 3 (two solved layers), placing the remaining corners, orienting those corners, and finally placing the remaining edges.
  • For those interested in solving the cube quickly or for those who simply don't like the difficulty of turning pieces, it's a good idea to purchase a DIY kit. Speed Cubes have rounder internal corners and allow you to adjust tension, making it much easier to move pieces. Also consider the possibility of lubricating the cube with a silicon-based oil.