The Professor Cube (5x5x5 Rubik's Cube)
The Professor Cube is a 5x5x5 version of a Rubik's cube. If you
already have a solid understanding of the 3x3x3 and 4x4x4 versions,
then the 5x5x5 should be easy enough to solve (this
page gives some hints for the 4x4x4).
This page summarizes some of the techniques I use for solving the 5x5x5
cube. It is not a step-by-step walkthough of a solution.
The cube has six faces, which will be called Up, Down,Front, Back, Right, and Left. Turning a face 90
degrees clockwise is represented by the first letter of the face's name,
in upper case. For example, "R" means to turn the right face 90
degrees clockwise (such that the front right pieces become the top right
pieces). The inner slices are represented by lowercase letters for
the face that they are closest to. For example "r" means to turn
the layer just inside of the right face. There is no notation for
the center slices. A letter followed by a tick mark means to turn
the face counter clockwise by 90 degrees (e.g. R'). A letter
followed by the number 2 means to turn it twice (180 degrees).
Parentheses are sometimes uses to group moves together for easier
Pieces are described by the faces they are closest to. An upper
case letter means the piece is actually on the face, while a lower case
letter indicates that it is one space in from the face. When a
piece is in the middle, no letter is used for that particular
dimension. So, UFR is the top-right corner on the front
face. Moving to the left, we have UFr, UF, UFl, and UFL.
Types of Pieces
The cube contains the following types of pieces:
- 8 Corners (example UFR): these move just like the corners on all
- 12 Middle Edges (example UF) : these move like the edges on a
- 24 Side Edges (example UFr): these move like the edges on a 4x4x4
- 24 Center Corners (example uFr) these move like the centers of a
- 24 Center Sides (example uF): unique to the 5x5x5 cube
- 6 Centers: these never move in relation to one another (like the
3x3x3 cube centers)
- Solve the 9 center pieces on each face (see below)
- Match Side Edge pieces with their corresponding Middle Edges (see
- Solve the cube as a 3x3x3 cube using only face moves (no inner
Solving the Centers
If you are already know some good operators for moving 4x4x4 centers,
then you can solve the 5x5x5 centers by first solving the Center and
Center sides for each face, then using the 4x4x4 operators to move the
Center Corners into position.
Solving the Center Sides without preserving any other pieces is
actually quite simple. The following two sequences should be
r' F r : moves uF to Ur
r2 D r2 : moves Df to Ur
Remember that faces can be turned without disturbing any center pieces
and you can also turn the entire cube to face any way you want, so it
is quite easy to arrange things such that one of the above two
sequences solves a Center Side piece. Do this at most 24 times
and the Center Sides will be complete.
The Center Corners tend to take a few more moves. Initially, I
used the following operators such as:
These are really handy on the 4x4x4 cube if you solve the centers last
because they don't change edges or corners at all. However, for
the 5x5x5 cube we are solving the centers first, so those operators are
- double-center-swap: U2 b'
u'd b U2 b' u d' b (use to exchange Ubr/Ubl with Fur/Fdr)
- single-center-swap: U2 b'
u' b U2 b' u b (use to exchange Ubl with Fur)
- double-center-swap2: r2
u2 r2 u2 (exchange Ufr/Ubr with Dfr/Dbr)
Here's a faster operator for fixing a single center corner.
center-corner-move: d R d' R d
R2 d' - move Rdf to Fdr
Note that it has some side effects. It cycles some side edges on
R and cycles side corners on R, but since we don't care about permuting
the side corners within a single face and we haven't fixed the edges
yet, these side effects are harmless.
Solving the Centers without Operators
The above solution, although effective, can be a bit tedious.
Just like on a 3x3x3 cube most people solve the first layer or two
intuitively before resorting to general purpose operators for the last
layer, it is possible to solve the centers without brute forcing each
individual center side and center corner.
It is quite east to work with 2 faces at a time without distrubing the
centers on the other 4 faces. The key is to do mostly face moves
and always match a slice move with its inverse. Between the slice
and its inverse you have to be careful to only turn a face that
consists entirely of pieces that you are willing to move. For
example, when working on the U and F centers you could do something
U2 F r' F2 r U
Actually, the stuff before r' and after r is irrelevant - it can be any
combination of U and F moves that you want. Since we're only
concerned with the centers, the order of the moves doesn't even matter
since upper centers are only affected by U and front centers are only
affected by F. The important part is that between r and r', you
restrict yourself to turning F.
Matching Up Edges
The goal here is to form edge groups by matching each middle edge with
the two corresponding side edges. One very important thing to
keep in mind is that face moves always move middle and side edges as a
group. Thus, any number of face moves can be made without
disturbing previously matched up edges. However, you still need a
way to move side edges independent of middle edges, and the 4x4x4
cube's edge-3-cycle is your best friend here:
edge-3-cycle: r (U' R U) r' (U' R' U)
This will cycle DFr, UFr, FRu. Actually, you can skip the last
three moves and just do r U' R U r', because the last three moves are
face moves which have no effect on matching of edges. Their only
purpose is to restore edge groups and corners to their original
position. Since we only care about matching up the edges, and not
where the edge group (or corners) wind up, we can skip those last moves.
I usually just pick a piece at DFr, and use face moves to move the
corresponding middle edge to UF. Make sure you get UF flipped the
right way (the front face of DFr should match the up face of UF).
Then examine UFr and put the corresponding middle edge at FR (the F
face of UFr should match the R face of FR). Then execute the
edge-3-cycle and you are 2 pieces closer to matching all of the edge
It is possible to wind up with only two unmatched side edges that need
to be swapped with one another. No amount of manipulation with
edge-3-cycles will be able to solve this problem. Another
operatoin is required. Basically, you need to create an odd
permutation of the edges. Once you do this, you should then be
able to perform one or more 3 cycles to clean things up. My
preferred way of solving this problem is to put the two problematic
edges at uFR and uBR, then do this:
edge-4-cycle: R2 u
R2 u R2 u R2 u R2 u R2.
This cycles uFR, uBR, uBL, and uFL. Since uFR and uBR needed to
be swapped, after the 4-cycle, exacly three side edges will be out of
place and an edge-3-cycle should be able to fix them.