How to Solve a 5x5 using the Reduction method

In this tutorial we will solve a 5×5 using the Reduction Method.

You will need to know how to solve a 3×3 to complete the final stage.

There are four parts:

  1. Solve the Centers
  2. Pair the Edges
  3. Solve like a 3×3

PART 1 – Solve the Six Centers

Unlike a 4×4, each center now has 9 pieces instead of 4. The easiest way is to build the centers one row at a time. This tutorial will solve the six centers of a 5x5 in the following order:

  1. White
  2. Yellow
  3. Green
  4. Orange
  5. Red and Blue

IMPORTANT: This step is generally done intuitively. The concept explained in this 5x5 tutorial is to make a "line" (3 centers pieces together) and then put the lines together to form a center. 

STEP 1 – Solve the White Center

Instead of making a 2-piece bar, make a 3-piece line.

  1. Find two white edge-center pieces. 
  2. Turn the outer layers so that one piece is above the center and the other is below it. When you move the inner layers together, the two pieces should line up to form a line. You may need to turn the outer layers 1, 2, or 3 times, depending on the position of the white center pieces.
  3. Use the inner layers to join the two pieces into a 3-piece line as shown in the image below.
  1. Turn your cube so that the White line is on top. 
  2. Now make the second white line. This time, join two white corner-center pieces with one white edge-center piece using the same method. Then join this line to the first one.
  1. Finally, make the third white line using the same concept on the opposite side. Join this last line with the two lines on top to complete the white center.

 

STEP 2 – Solve the Yellow Center

Hold the cube with the completed white center on the bottom and the yellow center on top.

Turn the cube so that a yellow edge-center piece is on the front face.

The concept for making the first yellow line is as follows:

  1. Turn the front face so the yellow edge-center piece is to the left or right of the center.
  2. Move the column containing the yellow edge-center piece up to connect it with the yellow center.
  3. Turn the top layer so the yellow line is vertical.
  4. Return the column containing the white line back to the completed white center.

The image below demonstrates this concept. Repeat these steps with a second yellow edge-center piece to create a 3-piece yellow line.

Use the middle layer to make the second yellow line. 

Join the two yellow lines on the top face using the steps shown in the image below.

 

Repeat the above steps to make the third yellow line on the opposite side.

Finally, join the third yellow line to the top face using the steps shown in the image below.

STEP 3 – Solve the Green Center

  1. Hold the cube so that the completed white center is on the bottom and the completed yellow center is on the top.
  2. As before, make a green center line using the inner horizontal layers.

  1. Turn the layer containing the green line so that it is horizontal.
  2. Make the second green line using the inner horizontal layers, leaving it in a vertical position.
  3. Turn the layer so that the second green line is horizontal, either above or below the first line.
  4. Join the two green lines together.
  1. Repeat this process to make and join the third green line, completing the green center. While making the third line, you will probably separate the two completed green lines. Don't worry—once the third line is complete, you can reconnect all three lines to finish the green center.

STEP 4 – Solve the Orange Center

Hold the cube so that the completed green center is on the bottom, the completed yellow center is on the left, and the completed white center is on the right.

Build the first orange center line by bringing an orange edge-center piece from the top layer into the front face to connect with the orange center. Turn the front face so the 2-piece line is vertical, then restore the green center by turning the layer back.

Repeat the process with the other orange edge-center piece to complete the orange center line. Turn the completed line so that it is in a vertical position.

Now hold the cube so that the orange center line is at the back, while keeping the green center on the bottom.

Make the second horizontal orange line on the front face by bringing the required pieces down from the top or back layer. Turn the line so it is vertical before restoring the completed centers.

Use the steps shown in the image below to join the two orange lines without disturbing the completed centers.

Repeat the process to make the third orange line. Then join it to the orange center using the steps shown in the image below. Before joining the line, make sure it is in the same column as the second orange line on the top layer.

STEP 5 – Solve the Last two centers (Red and Blue)

IMPORTANT: This step is generally done intuitively. The concept is to make a line with 3 pieces together, but it can be restrictive to do it without messing up the other centers.

If you get stuck on the last two centers, you can swap two center pieces using a simple sequence of moves called a commutator.

  • Hold the cube so the two center pieces you want to swap are on the Top (U) and Front (F) faces.
  • Rotate the Top (U) and Front (F) faces until the two pieces are in the same column. We recommend using the right-hand column.
  • Move that column up one turn.
  • Turn the Top (U) face anti-clockwise (U').
  • On the top face, you'll now see a missing center piece. Move that column up one turn.

Now reverse the moves:

  • Turn the Top (U) face clockwise (U).
  • Move the first column down one turn.
  • Turn the Top (U) face anti-clockwise (U').
  • Move the remaining column down one turn.

The two center pieces will now be swapped.

Hold the cube so the two remaining unsolved centers are on the Front (F) and Top (U) faces. 

Find pieces of the color that belongs on the Front face. The same concept applies where you move the lice from the top to the front face. Turn the front face so that you can restore the layer without breaking the line.  

Repeat this bar-building process for the final two centers.

If you get stuck then you can swap individual pieces between the top and front layers using a basic commutator algorithm.

Hold the cube so that the two centers you want to swap is in the top and front layers "U" and "F".

  1. Put the two centers that you want to swap in the same column by rotating the top "U" and front "F" layers. We recommend putting it to the right side of the cube.
  2. Move the column with the swapped centers up once.
  3. Move the top layer anti-clockwise (U')
  4. Move the column with the piece that you are swapping up.

Then perform the opposite:

  1. Move top layer clockwise (U)
  2. Move the same column from step2 above down
  3. Move top layer anti-clockwise (U')
  4. Move the column from step3 above down

 


PART 2 – Pair the 12 Edges

The second part of solving a 5x5 is to pair three edges with the same colours together. There are 12 edge pairs in total to make.  The goal of this part is to reduce the 5x5 to a 3x3. So you can then solve it like a 3x3.

For 5x5 each edge contains three pieces. At a beginner level you will pair the wing edges with the corresponding center edge. As you become more comfortable you will be able to pair both wings to the center simultaneously. 

The Concept:

5x5 Edge Pair Concept

Move the edges that you want to pair into the front-left and front-right positions of the cube. This will enable you to make and store the pair, without disturbing the rest of the cube.

The secret of this step is to always bring an unpaired edge back into the front right slot so that solved pieces are not disturbed when you restore your centers after an edge pair.

Pair the Wing Edges

  1. Choose two edges that you want to pair. The goal is to move two edges with the same colours into the front left and right spots by turning the outer layers ONLY.

    IMPORTANT: Do not turn any inner layers for this step.  This will break the centers you made in part 1.

  2. Slice the inner layer to match the edges.
  1. Store the edges in the top layer. be sure to bring an unpaired edge back down.
  1. Restore the centers

Repeat until every edge has matching wing pieces. Continue until all 12 edges are paired.

Last Two Edges - Parity

If you have solved all your edges and you have ONE edge that is unsolved where the center or wings are flipped then this is Edge Parity on a 5x5.  This is because the two "wings" need to be swapped.  

5x5 Edge Parity Solution

PART 3 – Solve Like a 3×3

5x5 Reduction to 3x3

Once all the centers are solved and all edges are paired you have effectively reduced the 5x5 to a 3x3 and the cube behaves exactly like a 3×3. Solve it using your normal 3×3 method.

5x5 (Professor’s Cube) Print Friendly Guide


5x5 (Professor’s Cube) Algorithm Sets