Solving the Magic Cube: Helpful Steps and Tips

The Rubik’s cube was invented by Ernő Rubik in 1974, taking inspiration from smoothed pebbles in the Danube River, in order to help explain three-dimensional geometry. I started doing the Rubik’s cube when I was in Germany in 2007. I was on a four or five hour train ride to Berlin from Oldenburg and had time to kill. A friend of mine could do it so she gave me a few hints to start me on my way. My fastest time is 53 seconds (which is a far cry from the world record) but it’s been ages since I had the ability to work it that fast. Recently, I only pull the cube out on occasion to impress people at parties or just to exercise my brain. Now I’m ready to lay some knowledge down for you to pick up.

Stage 1: The Terminology

Middle Pieces

The middle pieces never move.  The cube will always appear the same when solved because the blue side will never touch the green side, the white side will never touch the yellow side and the red side will never touch the orange side (See Figure 1).

Figure 1. The middle pieces are indicated with red white and blue. These pieces never move.

Edge Pieces

The Edge pieces are the 12 pieces that form the sides of each square on each side.  They have two colors and you can move these pieces (See Figure 2).

Figure 2. The edge piece is indicated by red and blue. There are 12 of these moving pieces.

Corner Pieces

The corner pieces are the 8 pieces that form the corners of the square on each side.  They have three colors and you can move these pieces (See Figure 3).

Figure 3. The corner piece is indicated by the red, blue and white. There are eight of these moving pieces.

Up, Down, Right, Left, Front, Back and Inverted Turns

For the sake of leaving confusion out of the equation the Up side will always refer to the white side, and the Down side will be yellow.  Up and Down can also be commands for turning the Up or Down side, respectively.  Right, Left, Front and Back refer to the side the user turns.  There will be no color associated with right, left, front or back because this changes as we progress.  All turns should be assumed to be clockwise unless indicated by an “i,” which represents an inverted turn or a counterclockwise turn. All turns indicated are a quarter of a full turn unless otherwise stated.  A full turn returns the side to its original position; a half turn rotates the side 90 degrees.

Middle Row

The middle row will always refer to the band of non-Up, non-Down side colors: blue, red, green, and orange.  It is the collection of edge and middle pieces in the middle of the Rubik’s cube (See Figure 4).

Figure 4. The middle row is this band of edge and middle pieces.

Position

This is where the piece belongs in relationship to the cube.  For example the orange/green/white corner piece belongs in the corner where the orange green and white sides of the cube meet (See Figure 5).  Therefore a piece can be in the correct position.  This also refers to whether or not the colors are correctly aligned based on the colors of the middle pieces, which again don’t move (See Figure 6).  Therefore, the colors can be in the correct position as well.

Figure 5. This piece is in the correct position.

Figure 6. These colors are in the correct position.

Other Helpful Information

Specific examples will be used throughout this post in order to better explain the concept.  Because the Rubik’s cube is so dynamic, the one you are working on will most likely appear completely different from the one discussed.  The point is to see the pattern presented here, focus on the end result and don’t get bogged down with details.

Stage 2: The Completion

Step 1 – Solving the Down Cross

The first two steps are the most important and the most difficult things you must do to solve the Rubik’s Cube.  Start by solving the Down cross.  As stated before in the Terminology section, the Down side always refers to the yellow side and the middle piece will never move from its current location.

Take your Rubik’s Cube and hold it so the side with the yellow square in the center (the Down side) is facing up.  Locate on the cube all of the other edge pieces with yellow on them (ignore the yellow corner pieces for now).  Find the orange and yellow edge piece and turn the sides until the piece is on the edge of the orange and white sides.  Turn the Up side (the White side) one quarter turn, invert turn the left side and turn the right side.  Now invert-turn the orange side.  If you have followed the instructions, the yellow/orange edge piece should be lined up on the yellow/orange side (See Figure 7).

Figure 7. The yellow/orange edge piece is in the yellow/orange position.

For the rest of the edge pieces, you will have to use these steps, logic and reason to keep the yellow/orange edge piece in its place and solve for the other three edge pieces.  The end product should look something like Figure 8.

Figure 8. The Down cross is complete. The edge pieces are in the correct position.

Step 2 – Filling in the Corners

Now hold your completed Down cross so it faces up.  Locate the yellow corner pieces.  Find the yellow/red/blue piece and line it up on the cube so that it is in the white/blue/red corner position (See Diagram 1).

If the yellow side of the corner piece is on the blue side of the cube, i-turn the Up side, i-turn the right side, turn the Up side, turn the right side (See Diagram 1).

Diagram 1. This shows the sequence necessary to solve for the corners on the Down side with the yellow side of the yellow/red/blue corner piece starting on the blue side of the cube.

If the yellow side of the corner piece is on the red side of the cube, turn the Up side, turn the Left side, i-turn the Up side, i-turn the Left side (See Diagram 2).

Diagram 2. This shows the sequence necessary to solve for the corners on the Down side with the yellow side of the yellow/red/blue corner piece starting on the red side of the cube.

If the yellow side of the corner piece is on the white side of the cube, you must manipulate the cube so that it is in one of the above positions.  Continue following these steps and manipulating the cube until the other three yellow corner pieces are solved and the Down side is complete (See Figure 9).


Figure 9. The Down side is complete. Notice the “T” shape on all sides of the cube.

Step 3 – Working Out the Middle Row

The next thing to do is to solve for the four edge pieces in the middle row.  Hold the cube so that the Up side faces up and locate the four-listed edge pieces.  Start by finding the red/blue edge piece.

If the red side of the edge piece is on the Up side of the cube, line up the blue side of the edge piece with the blue side of the cube.  Hold the cube so that the red side is facing you, i-turn Up, i-turn Front, turn Up, turn Front, turn Up, turn Right, i-turn Up, i-turn Right (See Diagram 3).

Diagram 3. This shows the sequence necessary to complete the middle row with the red side of the edge piece on the Up side of the cube as a starting point.

If the blue side of the edge piece is on the Up side of the cube, line up the red side of the edge piece with the red side of the cube.  Hold the cube so that the red side is facing you, turn Up, turn Right, i-turn Up, i-turn Right, i-turn Up, i-turn Front, turn Up, turn Front (See Diagram 4)

Diagram 4. This shows the sequence necessary to complete the middle row with the blue side of the edge piece on the Up side of the cube as a starting point.

If the blue side of the edge piece is on the red side of the cube and the red side of the edge piece is on the blue side of the cube (in other words the edge piece is in the right position on the middle row but the colors are wrong) then perform either of the above maneuvers to free the piece.  Then line it up according to the above instructions and follow the method again.

Find the rest of the middle row pieces and do the above maneuvers to complete the middle row until your cube looks like Figure 10.


Figure 10. The middle row is complete.

Step 4 – Solving the Up Cross

If your cube looks like Figure 11, hold the cube so that the Up side is up and in the same position as it is in Figure 11.  Turn Front, turn Right, turn Up, i-turn right, i-turn Up, i-turn front (See Diagram 5).

Figure 11. This shows one starting position for solving the Up cross.

If your cube looks like Figure 12, hold the cube so that the Up side is up and in the same position as it is in Figure 12.  Turn Front, turn Right, turn Up, i-turn right, i-turn Up, i-turn front (See Diagram 5).

Figure 12. This shows one starting position for solving the Up cross.

Diagram 5. This shows the sequence necessary to complete the Up cross starting with any position.

Once your cube has an Up cross you will have to position the edge pieces so that the colors line up with the correct side.  To do this line up the Up side so that only one color is in the correct position.  This will not work if more than one color is in the correct position (if all four edge pieces and colors are already in the correct position skip to step 5).

Hold the cube so that the correctly aligned color is facing you (See Figure 13).  Turn Up, turn Right, turn Up, i-turn Right, turn Up, turn Right, turn Up, turn Up, i-turn Right (See Diagram 6).  Then repeat this sequence until all colors in the Up cross line up with the corresponding side and your cube looks like Figure 14.

Figure 13. This shows the correct way to hold the Rubik’s cube before finishing the Up cross.

Diagram 6. This shows the sequence necessary to complete the Up cross. Every other turn is a clockwise Up side turn with the last showing two turns. The Right side turns alternate between clockwise and counterclockwise starting with clockwise.


Figure 14. This shows the completed Up cross with all colors and pieces in the correct positions.

Step 5 – Positioning the Corners

Look at all the Up side corner pieces.  Decide if any of the corner pieces are in the correct position.  If no pieces are in the correct position hold the cube so the Up side is up; it doesn’t matter which side faces you.  Turn Up, turn Right, i-turn Up, i-turn Left, turn Up, i-turn Right, i-turn Up, turn Left (See Diagram 7).

Diagram 7. This shows the sequence necessary to position the corners properly. The outcome shown in the diagram is not the only outcome possible, there are many outcomes.

Re-evaluate the cube.  Are any of the corner pieces in the correct position?  If none are, repeat the above sequence until at least one corner piece is in the correct position.

When one corner piece is in the correct position hold the cube so that Up side is up and the piece that is in the correct position is in the lower right hand corner of the cube (See Figure 15 ).  Repeat the above sequence.  Check to see if all the corner pieces are in the correct positions.  Do the sequence until they all are.

Figure 15. This shows the correct position for a corner piece and the way to hold the cube before positioning the remaining three corner pieces.

Step 6 – The Big Finish

Look at the Up side and the corner pieces.  Are any of the colors of the corner pieces in the correct position?

If none are it does not matter how you hold the cube to do this sequence.  If one of the corner pieces does have it’s colors in the correct position start by holding the cube with the Up side facing up and that piece in the lower right hand corner of the Up side (See Figure 16).

Figure 16. This shows the proper way to hold the cube before completing the cube if one corner piece has the colors in the correct position.

There are two ways for two corner pieces to appear on the cube with the colors in the correct position.  The first way is shown in Figure 17 and should be held as Figure 17 appears.

Figure 17. This shows the correct way to hold a Rubik’s cube before finishing the cube when two corner pieces have the colors in the proper position in the shown arrangement.

The second is shown in Figure 18 and should be held as Figure 18 appears.

Figure 18. This shows the correct way to hold a Rubik’s cube before finishing the cube when the corner pieces have the colors in the proper position in the shown arrangement.

This final step is easy to get lost in, so PAY ATTENTION to the colors.

Start by turning the Up side.  This is the sequence: i-turn Right, i-turn Down, turn Right, turn Down (See Diagram 8).  Repeat this sequence until the white edge piece and the white corner piece line up and they are on the Up side of the cube.

Diagram 8. This shows the sequence necessary to complete the Rubik’s cube. This particular sequence is sometimes repeated a number of times, other times only one time will be necessary.

Then turn the Up side again and repeat the above method until the Up side is completed.  If everything worked out nicely your cube may need a few turns to get the rows lined up, but it should be complete and look like Figure 19.


Figure 19. This shows a solved Rubik’s cube. All color sides are completed.

Stage 3:  The Tips and Techniques

Seeing the Big Picture

Solving a Rubik’s Cube is about noticing patterns and learning how to manipulate the changing sides so that the result is what you want.  You will never solve the same Rubik’s cube twice.  It may be the same device but the colors will never be scrambled in the same order.  Finally, keeping track of which step you’re on and knowing how to go back to where you made the mistake is key.  Pay attention to the way the cube changes when you turn a side.

Decreasing Your Time

There are many ways to decrease your time.  The best way is to practice; the more you do the cube the more likely you are to be able to solve it and to solve it fast.  Also when you practice you learn about the dynamics of the cube, how it changes, why certain maneuvers work, etc.  The more you know about the cube the more likely you will be able to skip steps or do more than one step at a time.

Alternative Method

The above method is meant for beginners.  Once you have been playing around with the cube for a while you begin to discover new ways to complete it.  The following way does not go into as much detail as the above method because it is meant for those who are familiar with the movements of the cube.

Start by solving the orange/green/yellow 2x2x2 cube.  Then solve the red/green/orange/yellow 3x2x2 box.  Then add the blue side until you have a 3x3x2 box.  Finish by solving the white side in the same way you would solve in the beginner’s method.

Other fun ideas include solving the cube with flowers on each side like in Figure 20, and mixing up one cube and trying to match it using another cube.

Figure 20. This represents one of many other fun ways to solve the Rubik’s cube.

(***Update 09/05/12: Although I loved my time at WordPress, I found it was my time to move on. I am now at Blogger; I believe it to be a better fit for me personally. If you subscribe, or want to subscribe, to this blog, please be sure to subscribe to the new one. Here’s the link.)

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