Solving the 4 x 4 Cube

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Kerry Sanders
6 years ago
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1 Solving the 4 x 4 Cube How to Reference and Talk About the Cube: Like the 3 x 3 cube, we will refer to three main types of pieces centers (4 per side), edges (2 per edge) and corners. The main approach we will use in solving the 4 x 4 cube is to essentially turn it into a 3 x 3. First we will correctly place and solve all the centers, then we will match up all edge pieces, finally we will finish the cube like a 3 x 3. Labeling the Cube: Up Face U 2 nd Layer from top u Back Face B 2 nd Layer form back b Left Face L 2 nd Layer form left l Right Face R 2 nd Layer from right r Front Face F 2 nd Layer from front f Down Face D 2 nd Layer form bottom d

Movements on the cube: To make life easy we will use a notation involving U, Dd, R, L, Ff, Bb to signify which face or layers will be turned. We either turn a face clockwise or counterclockwise.

2 Movements on the cube: To make life easy we will use a notation involving U, Dd, R, L, Ff, Bb to signify which face or layers will be turned. We either turn a face clockwise or counterclockwise. To decide which way to turn a face imagine you are looking directly at the face when turning. Ex) Rr means turn the two Right most layers clockwise R r means turn the two Right most counterclockwise *again to help determine which way is clockwise and which way is counterclockwise imagine you are looking directly at the Right face.

3 Solving the Centers

4 The first trick in solving the centers is to realize that unlike the 3 x 3 cube the centers of a 4 x 4 can move. Thus not only do we need to match the center colors together but we must also make sure that they are on the correct face. When solved the color scheme of this cube will match the color scheme of a 3 x 3. In other words red will be opposite orange, white will be opposite yellow, and blue will be opposite green. In addition to this we must be aware of how the red, white, and blue faces sit in relation to each other. One easy trick is to realize that when looking at the red, white, and blue faces, the colors must go from red, to white, to blue in a clockwise fashion. White Face Blue Face Red Face When placing the centers you must make sure that the correct color is being placed on the correct face.

5 Connecting two Center Pieces The technique shown here will connect two center pieces together without disrupting any other centers that are already finished. Position the center to be placed directly below the space it is to occupy. This is called having the same relative position. Swing the center piece up into place. Rr Swing the now connected center pieces out of the way U Bring the two most right layers back down thus restoring all other centers. R r

6 Connecting the 3 rd Center Piece Again what is shown here will only affect the pieces involved. All other centers will remain unchanged. Position the center to be placed so that it is below the two centers already established. Remember that turning any of the outside faces (U, D, R, L, F, B) will not disrupt the centers. Only by turning an inside layer will the centers be disrupted. Rr Swing the center piece up onto the desired face. This will also move the two centers already established off of the face, but we will bring them back. Swing the center piece out of the way. U Bring the two most right layers back down thus restoring all other centers and bringing back the previously two displaced center pieces. R r

7 Connecting the 4 th Center Piece Once again what is shown here will only affect the pieces involved. All other centers will remain unchanged. Position the center piece so that it has the same relative position as the corner of the L formed by the three centers already placed. Rr Swing the center piece up onto the desired face. This will also move two of the centers already established off of the face, but we will bring them back. Swing the two center pieces out of the way. U Bring the two most right layers back down thus restoring all other centers and bringing back the previously two displaced center pieces. R r Repeat this process to correctly place all center pieces making sure that all each colored center sites on the correct face.

8 Pairing the Edges

9 Now that the centers are all placed, each group of four center pieces will act as one piece. The next step is to pair up the various edges so that each edge pair will act as one piece. When this is complete your cube can be thought of as a 3 x 3 cube. The will be 12 edge pairs that need to be matched up. For example there are two edges that have red and white as their colors, two edges that have blue and yellow as their colors, and so on. Since the centers of the cube are already established we do not want to mess this up. Throughout this process there are two things we need to understand: Turning the outer faces (U, R, L, F, B, D, U, R, L, F, B, D ) will not affect the centers and are safe moves. If any of the interior layers are turned they will need to be turned back to restore the centers. As we match up one edge pair another edge pair will be disrupted. When the edges on the front face are paired the edge pair on the right side of the top face will be disrupted. When the edges on the front face are paired the edge pair on the left side of the top face will be disrupted. The trick is to place an edge pair on the top face that is not yet properly paired up. This way is does not matter if it is disrupted.

10 If the edge piece on the right side of the front face is showing white on the front face and blue on the right face, then then edge piece on the left side needs to show blue on the front face and white on the left face. Start Position To begin matching an edge pair, you need to place the pair to be matched on the front face as shown. As well, the color of one edge facing you needs to match the color on the left or right face of the other edge piece. For example if you are matching the blue white edges, one edge needs to have its blue face and the other needs to have its white face towards you on the front face. If the edge piece on the right side of the front face is showing white on the front face and blue on the right face, then then edge piece on the left side needs to show blue on the front face and white on the left face. When the edges on the front face are paired the edge pair on the right side of the top face will be disrupted. The other thing to be aware of is that one of the edge pairs on the top face will be disrupted and so you need to make sure that the edge pair in this location is not one that you care about. Place an edge pair in this location that is not properly matched When the edges on the front face are paired the edge pair on the left side of the top face will be disrupted. *Remember that you can turn any of the outside faces without disrupting the centers.

11 Uu Place the edge to be paired together on the front face so that they are across from each other. The colors showing on front face of the two edge pieces should be different. As well, make sure that the edge pair highlighted on the top face is not one that needs to be kept. Swing the top edge piece over so that is matches up with the other corresponding edge piece. This will disrupt the centers, but they will be restored. U u Bring the newly matched edge pair up to the top face. L R U L Swing the edge pair to the front face so that it is out of the way. Bring down the edge pair that was highlighted on the top face in the first step. (It will now be split apart as we restore the centers.) U R

12 U u Restore the centers. (This will disrupt the edge pair that was highlighted on the top face in the first step. Uu Repeat this process until as many edge pieces can be matched as possible. At the end of the process you will have three edge pairs that need to matched. Complete the process on last time and one of two things will happen: As you match the edge pair the other two edge pairs will also match up. In which case this stage is complete. After matching the edge pair, you are still left with two edge pairs that need to be matched. If the second case happens here is what you can do to match the remaining two edge pairs. Place the edges to be matched across from each other so that the same color of each pair to be matched shows on the front face. For example, if the blue white edges and the red yellow edges need to matched, then you might place the blue white edges across from each other so that blue is the color of both edge pieces showing on the front face and below that will sit the red yellow edges with both of these showing yellow on the front face. Once properly orientated perform the following algorithm to match the remaining two edge pairs. Dd, R, F, U, R, F, D d

13 Finishing the Cube

Your cube should now resemble a 3 x 3 cube.

each edge pair will act like the edge piece on the 3 x 3, and the corners will

By restricting our movements to the outer faces only (U, F, R, L, D, B, etc.

14 Your cube should now resemble a 3 x 3 cube. Each group of four center pieces will act like the center piece on the 3 x 3, each edge pair will act like the edge piece on the 3 x 3, and the corners will act like corners. By restricting our movements to the outer faces only (U, F, R, L, D, B, etc.) we will not disrupt the centers or the edge pairs that we have established. To finish the cube we will now solve like we do a 3 x 3 cube. Takes the place of Takes the place of

15 Parity Problems Because the centers in a 4 x 4 are not fixed and can move in relation to each other (this does not happen with a 3 x 3 cube), some arrangements may present themselves that would never occur on a 3 x 3 cube. There are two main parity problems that we may encounter. 1 st Parity Issue When flipping up the edges on the last face on a 3 x 3 cube there will always be an even number of edges to flip. On a 4 x 4 cube there may be an odd number of edges to flip up. If this happens flip up as many edges as possible using the same technique used on the 3 x 3 cube. This will leave one edge pair that still needs to be flipped up. To flip up the last edge pair on the final layer of the cube hold the cube as shown and perform the following algorithm. (Rr)2, B2, U2, Ll, U2, R r, U2, Rr, U2, F2, Rr, F2, L l, B2, (Rr)2

2 nd Parity Issue The second parity issue you may encounter occurs when you are placing the edges of the last layer into their correct positions.

On a 4 x 4 cube you may encounter a situation where 2 of the edges are correctly placed and 2 are not.

16 2 nd Parity Issue The second parity issue you may encounter occurs when you are placing the edges of the last layer into their correct positions. On a 3 x 3 cube you will always arrive at a stage where one edge is correctly placed and 3 edges are not. Those 3 edges can then be rotated to sit where they need to. On a 4 x 4 cube you may encounter a situation where 2 of the edges are correctly placed and 2 are not. What you want to do this time is rotate the edges so that the two edges that are not correctly placed are across from one another. This can be done using the algorithm to rotate the edges of a 3 x 3 cube. Edge pair needs to be on the front face To correctly position the last two edge pairs, hold the cube so that the edges to be positioned are on the top face where one pair is located on the top of the front side and the other is located on the top of the back side. Then perform the following algorithm. l2, U2, l2, (Uu)2, l2, u2 Congratulations your cube is solved!

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