The 5×5 Rubik’s cube is also known as the Professor’s Cube because of its high difficulty level.
The Professor’s Cube is a 98-piece puzzle that can be challenging to complete, but it is doable if you carefully follow the reduction method algorithm. It’s suitable for beginners and people participating in speedcubing competitions in the 5×5 category.
It essentially involves ‘reducing’ the cube to a state that can be solved as if it were a 3×3 cube by solving the centerpieces and pairing up the matching edge pieces.
The best part about a 5×5 is that there are no special or parity cases, making it easier to solve than a 4×4.
To solve the 5×5, follow the steps below:
Step 1: Solving The Centers
The first step to solving the 5×5 involves completing the centerpieces. Unlike the 4×4, the 5×5 and all other odd-layered cubes have fixed center pieces. This means the centerpiece that lies directly in the middle of each side denotes the final color of that side.
The 5×5 has three different types of center pieces that can’t be interchanged, including the middle-fixed, corner, and edge centers.
Start by solving one center. A simple strategy involves solving the inner 1×3 bar made of two edge centers and the middle center, then creating the outer 1×3 bars made of two corner centers and an edge center and attaching these to the first 1×3 bar.
Once you solve the first center, you can solve the pieces of the center on the opposite side in the same manner, ensuring you don’t mess up the completed first center.
After solving the first two centers on the opposite sides, hold them on the left and right-hand sides of the cube and solve the third and fourth centers.
Ensure you solve two adjacent centers as the third and fourth centers.
You’ll notice that your move set gets restricted as you solve more centerpieces.
The following formulas can come in handy:
- r2’Br2Br2’B2r2
- r2’B2
- r2’Br2Br2’B2r2
- r’U’rU’r’U’2r
Step 2: Edge Pairing
The second step in the reduction method is to pair up matching edge pieces. It can be time-consuming but intuitive. On the 5×5 Rubik’s cube, there are two types of edge pieces: the middle edges and the wings.
The middle edges can change orientation or be flipped in their position, while the wing pieces cannot.
First 8 Edges
In all combinations of two colors on the cube, excluding the opposites, you’ll find three edge pieces with those colors.
The goal is to pair these pieces with every color combination to create an equivalent edge piece, as shown below:
The Freeslice method is the most suitable for solving the first eight edges. It involves using one slice, or axis, of the cube as a working zone to help pair middle edges and wings. You’ll use the double layer wide turn around the axis to connect edge pieces and create a solved edge.
After creating the solved edge, you can move it to the bottom or top face and continue working on pairing up more edges using the Freeslice method.
Ensure you don’t change the orientation of any centers when replacing or inserting an edge into the free slice.
Algorithms that may come in handy when inserting an edge from the top-front to the front-right position include:
- RU’R’ – Preserves the edge orientation.
- FR’F’R – Changes the edge orientation.
- RUR’FR’F’R – Flips the front-right edge piece into its position.
Continue pairing up the edge pieces until you have eight solved edges at the bottom and top layers, with four at the bottom and four at the top.
After completing this, perform a slice to restore the centerpieces to their solved positions. You should have only four edges remaining to solve at this point.
The Last Four Edges
You need to find instances where one wing is connected to its corresponding middle edge to start solving the last four edges. You’ll find a situation where the wing and middle piece are connected by the same edge piece but are either:
- Correctly paired with the colors that match each face.
- Incorrectly paired with two colors, creating a checkerboard pattern.
- You can solve the two cases through the following algorithms:
If you have a case where the wing isn’t paired with a middle piece correctly or incorrectly, you can apply any of the above sequences to attach a wing to its corresponding central piece.
Remember, while solving the last four edges, you’re performing the slice-flip-slice sequence to preserve your centerpieces.
You can find a tutorial video on YouTube showing different variations of the above algorithms that you can apply to other similar cases when solving the last four edges.
The Last Unsolved Edge
With the above algorithms and their variations, you can combine the edges block by block and solve all 12 edge blocks if you’re lucky. However, you may have one unsolved edge block that requires you to swap two wing pieces with the following formula:
Rw U2 x Rw U2 Rw U2 Rw’ U2 Lw U2 3Rw’ U2 Rw U2 Rw’ U2 Rw’
Step 3: Solve The 5×5 Rubik’s Cube Like A 3×3 Cube
At this point, you’ve solved the bulk of the Professor’s Cube by solving the centers and pairing the edges. You can now effectively solve the cube like a 3×3 Rubik’s cube. The centers formed on the 5×5 are similar to a single 3×3 cube center, and every group of three edge pieces is similar to a single edge on the 3×3 Rubik cube. The corner pieces are similar on both cubes.
You can follow the basic principles of the layer-by-layer method to solve the 5×5 completely. It involves the following steps:
White Cross
Start with creating a white cross on the white face, paying attention to the color of the side center pieces. It’s usually relatively easy and intuitive without any instructions.
White Corners
To finish the first face, arrange the white corner pieces. Twist the bottom layer until one of the white corners is directly under the spot where it’s supposed to go on the top layer. Useful algorithms include:
- R’D’R
- FDF’
- FLD2L’F’
Second Layer
This step involves completing the first two layers, and you can use the right and left algorithms:
- Right: URU’R’U’F’UF
- Left: U’L’ULUFU’F’
You can apply the algorithm twice if an edge piece is oriented wrong.
Yellow Cross
Make a yellow cross to start solving the last layer. Don’t worry if the pieces aren’t in their final places. Use the algorithm below to go from a dot, an L shape, or a horizontal line.
Apply the permutation three times, twice, or once for the dot, L shape, or horizontal line, respectively.
- FRUR’U’F’
Yellow Edges
Once you make the yellow cross, put the yellow edge pieces in their place to match the colors on the centerpieces through the following algorithm:
RUR’URU2R’U
Orient Yellow Corners
All that’s left is to orient the yellow corners to finish the puzzle. It’s sometimes referred to as “orienting the outer layers.” Hold the cube in your hand with the unsolved corner on the front right top corner and perform the following algorithm twice or four times until the piece is oriented:
- R’D’RD
