Why can't I solve my magic cube

Rubik's Cube

What is the Rubik's Cube?
 

......The Rubik's Cube is a rotating puzzle in the shape of a cube. It is also called the Magic Cube or Rubik's Cube after its inventor.
At first glance, the Rubik's Cube consists of 27 individual cubes that together form a large 3x3x3 cube.

......In reality, however, it only consists of 21 parts, namely 1 axis system (with 6 fixed, single-colored middle pieces and the central single cube), 8 three-colored corner pieces and 12 two-colored edge pieces.

......The colors of my cube are white / yellow, orange / red and green / blue (here orange = pink).

When released, all side surfaces are monochrome.

Even after a few careless rotations of levels, the cube is colored.



The basic problem is to arrange the colored cube in such a way that the side faces are again monochrome at the end.

SPIEGEL solution, slightly changed
introduction Top
The Hungarian professor of physics and design Ernö Rubik invented the cube in 1974. Around 1980 the Rubik's Cube spread like a virus in the world. Around 100 million cubes were sold around the world in the early 1980s. Everyone who had it tried to judge it. But most of them couldn't get past a level or two on their own. The SPIEGEL-Magazin deserves the credit for making the first generally understandable solution available to a broad public in Germany (4/1981). It is still relevant today. The science journalist Albrecht Kunkel (copyright SPIEGEL) was behind the solution.

The magazine "bild der Wissenschaft" was faster (11/1980), but had too little picture and too much science ;-).

I replaced step 2c with my own sequence of moves because the mirror solution also brings a second corner piece up (left) and displaces the possibly already correct corner piece (Stefan, thanks for this hint).

The following overview describes the procedure. Aligning the cube is done in seven steps.
(Figures 4 and 6 can also look different.)

......The rotations of the cubes are shown below with 3x3 squares and an arrow. The square is always the front square. The arrow describes a quarter turn of the marked plane in the direction of the arrow. The arrows always lie in the plane to be rotated.
Two examples show the meaning of the squares with arrows.
...... It's more practical. .................................................. ....................

One principle should be remembered for the following seven solution steps: During the turning sequences, you must not turn the cube itself, only individual levels. In other words: the orientation of the cube in space remains constant while it is being rotated.


Building the first levels Top
To align the first two levels, hold the cube so that the white center piece is always on top.
Step 1: Straighten edges

Find the blue / white edge piece and turn it towards the front, bottom center. There are two possibilities.
1a) white is below

1b) white is in front
Proceed in the same way with the orange, green and red sides.
You have to make sure that you don't destroy the resulting white cross again when you switch to a new color.
Result: Now there is a white cross on the top. Its side colors match the center colors of the cube sides.
 
 

2nd step: Straighten corners
There are four corner pieces, each with a white surface. The cube is initially held again with white on top and blue in front. The example is corner piece white / red / blue, which should be brought to its correct place at the top right in the front.
You first bring this corner piece to the lower left in front. There are three options 2a), 2b) and 2c).
2a) white is on the left

2b) white is in front

2c) white is below
The three remaining corner pieces with white surfaces are treated according to the same scheme.
Result: The upper level is now completely white. The colors on the sides match the center pieces.


Building the middle tier Top
Step 3:
In the middle horizontal plane only the side edge pieces with the colors blue / orange, blue / red, green / orange, green / red are missing. They are each classified from below.
The cube is held so that white is on top. The lower cube level is rotated in such a way that one of the edge pieces blue / orange or blue / red moves to the front (bottom center) and points to the front with the blue surface. Then there are two options 3a) and 3b).
 

3a) Edge piece to the right

3b) Edge piece to the left
If the blue area happens to be pointing downwards, you start with a different color.
If there are pieces of edge in the middle level, one of the sequence of moves shown above brings the stone down and then classifies it correctly.
Result: The upper and middle levels are now complete.


Building the last level Top
To build the last level, the cube is turned upside down for the sake of clarity (white facing down).

Step 4: Swap edges
One of the four edge pieces yellow / blue, yellow / orange, yellow / green, yellow / red is turned to the matching color of the cube side (yellow may still be on the side for the time being). If the other edge pieces are not yet in the right place, they can be exchanged using the front left corner. You may have to repeat the sequence of moves.

Step 5: Tilt edges
If all the edge pieces are in the right place, they can still be tilted so that yellow is on the side. You are now being turned in on yourself. The cube is held in such a way that the edge piece to be tilted is on the top right. Eight moves follow.
The cube may now look confused. Keep going! The next edge piece to be tilted is brought to the top right by turning the upper cube level (do not turn the entire cube). The eight moves shown follow again.
Result: Now a yellow cross has been created. It is turned so that the edge pieces on the side match the color of the center of the cube.

Step 6: Swap corners
First, the four remaining corner pieces should be brought into place. Your colored areas do not have to be right yet.
If all four corner pieces are in the right place, the following operation is not necessary.
If all four corner pieces are wrong after alignment, the following 22 moves are necessary:

If all four corner pieces are still wrong after this operation, the sequence of moves is repeated. The previously selected front side must remain in front.
After this operation, a corner piece is right. The cube is now held in such a way that this corner is at the back on the left. The sequence of moves follows again.
Result: The four corner pieces are correctly positioned.

Note on the 6th step
Soon after it was released, a simple version for swapping the corners in the last layer that I'm including here was revealed. Instead of a sequence of 22 cumbersome moves in SPIEGEL, you only need 8.

I pass this sequence of moves on with reservation.

7th step: Corner pieces are tilted.
The corner pieces are now brought into the correct position. The cube is held in such a way that a corner piece to be tilted is at the top right in the front. Eight moves follow:

If, after this operation, the processed corner piece is not yet on top, the eight moves are repeated.
To tilt the next corner piece, the upper level (not the whole cube) is rotated so that the corner piece to be tilted comes to the front right again. This is followed by eight or two eight moves as described above.
When all four corners are tilted so that yellow is on top, there is only one last step left to do: rotate the upper level so that the sides of the cube become one color. MADE!


Planned chaos Top
Can you twist a cube so that each color appears at least once on each side of the cube? One can. During the rotations, "middle white above" and "middle blue front" (5).


Disassembling the cube Top
You can also arrange the cube by disassembling it and putting it back together again to fit.
There are some brands that have a screw under the colored square of a center piece. You have to solve it and then you can dismantle the cube.
Most brands can only be dismantled with light force. Turn the top level about 45 degrees and carefully lift it with a screwdriver or spoon handle. In the inclined position of the upper level, you can then detach an edge piece and then the adjacent corner pieces.

Very clever people carefully remove the color squares and stick the cube appropriately ;-).


Judge with the stopwatch Top
Whoever is able to arrange the cube sees the next challenge:
How can you straighten the cube as quickly as possible?
Professional cube rotators always require fewer than 90 moves in total. These cube rotators know a lot of moves in order to react quickly and appropriately to the respective situation. You do not proceed stubbornly step by step, but keep an eye on many dice at the same time.
The cube is also made easily rotatable with silicone oil.

In "The new Guiness Book of Records 1986" you can find the keyword "Würfelitis":
On June 5th, 1982 Min Thai (16), USA, won the Rubik's Cube Championship in Budapest. Winning time 22.95s.


Judging with as few moves as possible Top
Most prefer a way to order the dice, in which one gets by with as few moves as possible (not moves). If you want to straighten the dice without looking at a template, you have to learn the sequence of moves by heart.
In this regard, the SPIEGEL solution is a good method.
With a little practice you can solve the first level by improvising. 2c) can be traced back to 2a) or 2b) and is omitted. For the last two levels you only need sequence of moves with eight or fewer moves. Nevertheless, you usually need between 120 and 180 moves in total, as certain sequences of moves can often be repeated. If you are unlucky, you need "turning corners" around 75 moves for the last step.
After all, with the SPIEGEL method you can straighten the cube in 2 to 3 minutes.


Some math Top
In the book (3) by Trajber, a mathematical theory about the cube is developed.
The moving squares of the cube are numbered from 1 to 48 (48 = 6x9-6). A move or a sequence of moves leads to a new order of the numbers 1 to 48. This rearrangement can be understood as a permutation. But the permutations form a finite group. So the study of the cube can be shifted to the study of a group. It is complicated, especially since not all permutations occur as moves or move sequences.
One of the most interesting results is the transfer of the order of a group element to the cube. This means that when you repeat a sequence of moves you return to the starting position after a certain number of repetitions ("order").
For example, if you want to practice the sequence of moves of the SPIEGEL solution, you proceed as follows:

You start from the ordered cube and repeat a sequence of moves over and over again. After n repetitions you get back to the ordered cube. (n can be found in the second column.)

Theoretically there are 54! / (9! * 9! * 9! * 9! * 9! * 9!) = 1.10 * 10 ^ 38 combinations of the 54 squares for a 3x3x3 cube.
The Rubik's Cube has "only" 8! * 3 ^ 8 * 12! * 2 ^ 12 = 519.024.039.293.878.272.000 = 5.19 * 10 ^ 20 combinations if you take it apart and put it back together.
The twelfth part, i.e. 43,252,003,274,489,856,000 combinations, can be reached by turning.


template Top
Finding out patterns is a broad field of activity.
Here is an example that can be expanded. (Each arrow indicates a quarter turn.)

After another 6 quarter turns of the cube with the diagonal pattern you get back to the ordered cube. So the order of this sequence of moves is 2.



Variations
...If you don't start with the ordered cube, but start with variants as shown on the left, you get new patterns.

 
If the levels are rotated in a different way, other patterns result.

You get 12 patterns:


Rolling cube Top
A variant of the cube is the rolling cube. It is also called octagon or devil's barrel.

It is created from a cube if you cut off the four vertical edges. In this way, ten surfaces are created that are colored differently. It has the mechanics of the Rubik's Cube and is solved according to the same rules.
Those who have mastered the cube will have no difficulty in arranging them. However, you have to set a certain color distribution for the first level, as can be seen on the right, for example. You only notice at the last level whether it is correct.

Rubik's cube


Rubik's Cube on the Internet Top

German

Michael Jasmund
Rubik's Cube (solution, game, models)

Lars Petrus
Solve Rubik's Rubik's Cube for a while

Oliver Reimann
Instructions for the Rubik's Cube

Record club Saxonia
Rubik's Cube

Ronald Bieber
Rubik's Cube

Mirror knowledge
Shout hurray! Throw a round!
The mirror edition 4/1981 from January 19th, 1981 is now (Feb2008) released for private use! :-)

Sigrun Dewess
Arrange Rubik's Cube

Urs Manser
Rubik's Cube (solution)

Wikipedia
Rubik's Cube


English

Georges HELM
Collection of Rubik's cubes and related puzzles

Jaap Scherphuis
Rubik's Cube 3x3x3, barrel / octagon

Jessica Fridrich
My speed cubing page

Lars Petrus
Solving Rubik's Cube for speed

Nader (naderc)
CV Rubik - Computer sees Rubik's cube and solves it (The Spiegel solution as a video)

Rubik on-line
Ernö Rubik's Official Homepage.

Stefan Pochmann
Stefan Pochmann's Cube Corner

Wikipedia
Rubik's Cube


credentials Top
(1) DER SPIEGEL No. 4/1981
(2) Josef Trajber: The Cube, Niedernhausen / Ts. 1981 (Falkenverlag 0565)
(3) Josef Trajber: The cube for advanced learners, Niedernhausen / Ts. 1981 (Falkenverlag 0590)
(4) Tom Werneck: The Rubik's Cube, Munich 1982 (Heyne 4831)
(5) Tom Werneck: The magic cube for experts, Munich 1982 (Heyne 4834)
(6) Kurt Endl: Rubik's Riddle of the Century, Giessen 1981
(7) Alexander H. Frey, Jr and David Singmaster: Handbook of Cubik Math, Hillside New Jersey 1982 [ISBN 0-89490-060-9]


Feedback: Email address on my main page

This page is also available in German.

URL of my homepage:
http://www.mathematische-basteleien.de/

© 1999 Jürgen Köller

Top