How to solve the 5x5x5 Rubik’s Cube
I believe that anything can be explained in words, which is a good thing because I can’t do graphics. This document will hopefully explain to you how to solve the toughest Rubik’s Cube, the 5x5x5, also called the “Professor’s Cube,” with its 98 cubies. This document is long: it takes me a good ten minutes to solve a mixed up 5x5x5, so it certainly will take me longer than that to tell you how to do it yourself. I assume that you already know a good solution for the normal 3x3x3 cube. In fact, most of the moves to solve the 5x5x5 are moves for solving the 3x3x3, and you will be happy to recognize them when they come up. This solution requires a few more moves than the 3x3x3, but not many, and so it is a solution that is easy to remember. That’s good, since it certainly is not efficient. This document is a work in progress. By mailing me any comments, I can make this document better, and I will thank you for it.
Buying a cube
The most common question I get is about where to purchase a 5x5x5 cube. Meffert sells them, and as of 2/26/2004, two people have told me that they now sell East Sheen 5x5x5 cubes that are slightly larger than a normal cube and work quite well. Apparently the East Sheen cubes can be easily disassembled and reassembled.
Not too much help
If you still want to solve the cube on your own, but you just don’t feel like you have a good way of breaking down the solution, then just read the next section and then read names the eight steps of my method.
There are six distinctly different kinds of cubies on the 5x5x5. Naturally there are 6 Center cubies, and right next to each Center are 4 Cross cubies. Diagonally from each Center cubie are 4 Point cubies. Each side of the cube has five cubies along it: Corner, Wing, Edge, Wing, Corner. There are 8 Corners, 12 Edges, and 24 Wings.
- When your cube is sitting on the table, the face on the table is the Down face, and its opposite is the Upper face. The face on the side that you are looking at is the Front face, and opposite it is the Back face. On the left is the Left face and on the right is the Right face.
- When you rotate a face of the cube, you may rotate it clockwise either one, two, or three turns, so I will notate a face turn with the first letter of the face name followed by either a one, two, or three indicating the number of clockwise quarter turns to make. Yes, I know that turning a face three quarter turns is the same as turning a face one quarter clockwise, and I encourage you to do so. It just makes my notation easier.
- When you rotate a face on a 5x5x5, you could either rotate one layer or two layers. When I notate a face turn of one layer, I’ll lower-case the face name. When I notate a face turn of two layers, I’ll upper-case the face name.
- For a few examples: R2 means “turn the two layers on the right face two quarter turns;” f1 means “turn one layer of the front face one quarter turn clockwise;” u3 means “turn the one layer of the upper face one quarter turn counterclockwise.”
- Often we rotate the layer in the middle, and I will indicate such a move with the letter e for equator move. I will indicate a number following the letter e for how many clockwise rotations you need to make, looking at the cube from the top. Further, I will not consider the position changed by this layer twist — an e1 move will shift the Center that was in the Front face to the Left face, and the Points, Wings, and Corners which were on the Front face are still on the Front face.
- I will often ask you to twist a face so that a cubie is in a particular position. I will refer to such a twist by describing where I want you to move the cubie and by replacing the number of twists with x. So, if I ask you to move a cubie to the upper left by using single layer face twists, I’ll also denote the rotation with fx, which may mean f1, f2, f3, or no twist at all, depending on the original location of the cubie in question.
- Naturally the names of the faces are entirely relative, so sometimes I’ll indicate that the same move applied to other faces.
On most cubes, blue is opposite white. If yours is non-standard, just mentally substitute whatever color is opposite white on your cube for “blue.” I use White as my initial Upper face as a hold over from speed cubing, in which having the same Upper face each time makes it easier to see the patterns that I am use to seeing.
First Step — White Points
Ignoring everything else, get the four white Points next to the white Center.
Second Step — Blue Points
The blue Points are now either on the sides or on the Down face. You can move the blue Points to the Down face by first lining them up on the right side of the Front face and having any blue Points already on the Down on the right side of the Down face. Using R3-d2-R1 you can move two Points to the Down face, or R3-d1-R1 to move one to the Down face.
Third Step — Remaining Points
To solve the remaining 16 Points, you must use successive Dx and fx moves. Rotate Dx freely to get Points next to their Centers and fx to put the Points up to the upper layers. When moving Points to upper layers that have already been filled with the correct Points, first rotate the upper Points with f2 and then use Dx to move the needed Points over to their Center and use fx to put the needed Points on the upper layers, and lastly bring the lower layers back with Dx. Often near the end of this process, you will have three solved Points on one face and three solved Points on another face, and you need to switch the unsolved Points. If, for example, these two faces were the Left and Front faces, you would rotate fx so that the unsolved Point is in the upper right. Then you would rotate lx so that the other unsolved Point is in the lower left of that face. Then use D1-f1-D3 to switch these Points.
Fourth Step — White and Blue Crosses
There are four white Crosses and four blue Crosses to be solved. Turn ux so that an unsolved Cross on the Upper face is on the right side, turn dx so that an unsolved Cross on the Down face is also on the right side, opposite the one on the Upper face. If you are moving a white Cross into place, put it on the right side of the Left face by using as many lx and ex moves you need to, as long as you never separate the Points from each other. Don’t worry about moving around the green, red, yellow, or orange Centers. Then move R3-e3-R1. If you are moving a blue Cross into place, put it on the blue Cross on the Left face on the left side and use R3-e1-R1. At the end of this process, you will probably have one Cross left over. Let’s say it is a white Cross. Turn dx so that the unsolved Cross is on the right side of the Upper face. Turn ex and fx as needed to move the white Cross to the left side of the Front face. Then turn R3-F2-e3-F2-e1-R1. This move will be used again in the next step, although in a stripped down form. You should have a block of nine solved white cubies on Upper and nine solved blue cubies Down.
Fifth Step — Remaining Crosses
To solve the 16 remaining Crosses, use ex and fx moves, making sure to not separate the Points from each other. Move Cross cubies between like Points on the upper and lower layers of as many of the faces as possible. Often this will just put one Cross into place, but look for places where two like-colored Crosses are on the same face, move them to the equator, use ex to get them both to the right face, and use f1 to put both Crosses above and below the equator. There are two main moves I use to put the remaining Crosses into place. To rotate around six of the Crosses in the equator, use F2-e1-F2-e3. You will notice that this move can take a Cross from one side of the cube to the opposite side, but will never switch to an adjoining side. By setting up unsolved cubies in sets of six in the equator by using fx moves, you can get many of the Crosses into place. Between such moves, you can do simple f1 and f3 moves to bring other unsolved Crosses into the equator. At some point, you will probably need to switch cubies to adjacent faces. One way to do this is to switch a pair on one face with a nearby face with e1-f1-e3. Another move will swap a equator Cross with the Cross that shares the same Edge cubie, and will do the same to the other equator Cross on the same face. So, position the cube so that the Front face has the two Crosses you wish to switch with the Crosses on the front Left face and the front Right face. The move is e1-L2-e3-L1-e3-L1-e3-L2-e1-L1-e1-L1. On occasion you will have the ugly situation of having to swap only two Crosses with each other, rather than doing two swaps at the same time. To do this, you will have to still use this same move, but first do a pre-move so that the other Crosses that swap are the same color. So, if you position the cube with one Cross on the Front left and the other on the Left front, do U3-r3, then do the swap move, and the undo the pre-move with r1-U1. You should have all the Centers, Points, and Crosses solved.
Sixth Step — Wings to Edges
Each Edge has two associated Wings, and they are not interchangeable. For this step, ignore completely how the Edges and Wings are positioned around the now-solved center blocks. This step is only involved in bringing the Wings to their associated Edges. Position an Edge that has an unsolved left Wing at the UpperFront edge. Find that left Wing and move it with one layer face moves to be on the UpperBack edge on the left side. For such positioning, you should never need to break up any of the solved Points, Crosses, and Centers. You can tell that you have the correct Wing opposite the correct Edge because L2 move would join them, although it would mess up the center blocks. To join them, you will also need an unsolved Wing on the Upper Back Left edge. Then do L1-f3-l1-f1-L3. This actually rotates three Wings, so if you set up before this move better, you can get two Wings into place with each move rather than just one. Half the time, using this move over and over will be sufficient for getting all the Wings into place with their Edges. The other half of the time, the “parity” is off, and you will end with just two edges needing to be switched. This move will never switch them, and you will need to “fix the parity.” Put the two edges on the top face, with one edge at the front and one at the back, both on the left side. Then do R1-u2-R1-u2-R1-u2-R1-u2-R1-u2. This will fix one of them, but mess up two other edges. You will now be able to rotate those three edges into place with the L1-f3-l1-f1-L3 move that you did before. (Thanks to Gary Briggs for the parity fixing move.)
Seventh Step — Solve the 3x3x3
Use your favorite solution to the 3x3x3 now by just using one layer face moves. Now that the Wings are joined to the Edges, and the Centers are joined to their Crosses and Points, those parts of the puzzle can be moved together. I prefer a top corners, bottom corners, top and bottom edges, then middle edges approach, of course.
In this solution, I have given mainly a strategy and a few memorized moves for solving the 5x5x5 cube. I have given several key examples, but I have not spelled out every way of using those example moves. For example, I have given several moves which clearly can be done in reverse or in mirror image. While I hope to improve this document’s clarity, I suspect that a complete cookbook would make solving the cube boring and would make this document too long. I hope you will enjoy solving this cube as much fun as I have. I also hope that you will give me feedback about how helpful this page was and how to improve it.
I have marked all of the cubies on one of my cubes so that they are all different. In this case, I cut off the corners of the stickers on each face so that all of them have the same corner cut. For example, when the cube is solved the red face has all nine cubie stickers missing the upper left corner. Thus, I cannot possibly have the parity problem, which is caused by two equally colored crosses or points that are switched. But I also have to worry about getting them into the right places, and even have to get the centers rotated correctly. If you want a new challenge, you may try modifying your own cube.