Methods for solving the Rubik's Cube
There are different methods for solving the Rubik's Cube . In July 2010 Tomas Rokicki together with Morley Davidson, John Dethridge and Herbert Kociemba proved the assumption that never more than 20 moves are necessary. If solving is done competitively, it is called speed cubing . There are various levels of difficulty from "one-handed" to "blindfolded". The "simple" solution can be done by experts in less than 10 seconds.
Terms
Each of these methods is based on certain common terms, which are explained below:
Center stones
The center stones are the small building blocks that only have one surface. With the standard cube there is such a stone in the middle of each side. There are therefore six center stones. Each center stone can be rotated, but the position of the center stones relative to one another cannot be changed. They cannot be pushed outwards. The center stones thus indicate which color the respective side will get later.
edge
Edges are called the cubies, which have two faces. You are always between two corners. There are exactly twelve edges on a 3 × 3 × 3 Rubik's Cube.
Corners
With corners we mean the cubies that have three faces and are located between three edges. There are a total of eight such corners on a Rubik's Cube.
Slots
Slots are specific areas that need to be solved. In the methods mentioned here, a slot means a pair, consisting of a corner stone and an edge stone that go down from the first level.
Algorithms
Each method has specific algorithms . This means that you determine certain sequences of moves for certain situations in order to achieve certain goals. There are solution methods with many, but also some with few algorithms.
Working level
A working level is a level that can be moved (more or less) freely without destroying something that has already been built. Towards the end of the solution process, sometimes earlier and sometimes later, depending on the method, these working levels become fewer and finally they disappear completely. A working plane is therefore not defined mechanically, but is defined depending on the method used.
Look ahead
The look ahead is a technique that is almost essential for solving a Rubik's Cube quickly, but also requires a lot of practice. While one step in the solution is being taken, the next step is already being planned, which reduces the time between the individual steps. This makes it possible to solve the cube practically without pauses.
The solution methods
First publications
The first solutions were developed by enthusiastic mathematicians in 1979 and published in specialist papers. Well-known representatives of these early Rubik's Cube enthusiasts were the mathematicians David Singmaster and John Horton Conway , who worked in England . Soon after the Rubik's Cube was available on the market in Germany, the first solutions were also published in German.
In November 1980, Max Konrad Koppe's solution method was published in the journal Bild der Wissenschaft . In contrast to later approaches, here the corners were brought into the correct position in front of the edges. After completing the first level (top), the corners of the bottom have been properly positioned. Then the finished page was tilted backwards. Now the two edges in the middle level (middle band) have been corrected, then the edges above and below have been swapped and rotated by different sequences of moves.
Since many readers seemed to find the solution in the November issue difficult, Bild der Wissenschaft published the solution method of the well-known mathematician John Horton Conway in December 1980 . The solution method was supplemented by mathematical considerations on the group structure of the cube. It was a detailed described and illustrated layer-by-layer method with which the cube could be solved easily. It was characterized by a systematic and easily comprehensible procedure using the following strategic steps:
- Loosen the bottom
- Loosen the middle horizontal washer
- Loosen the top:
- Positioning the curb stones
- Positioning the corner stones
- Orientation of the curb stones
- Orientation of the corner stones
In April 1981 a similar solution was published in Spiegel magazine , described with pictorial representations of the individual rotations. It was also a layer-by-layer method and differed from Conway's method in the order of the strategic steps.
Beginner method LBL (Layer by Layer)
overview
The beginner's method, also known as the beginner or layer-by-layer (LBL) method, is probably the best-known solution method for the Rubik's Cube today, but it cannot keep up with the more advanced methods. The layer-by-layer method was also the one described in the first German publications by Bild der Wissenschaft and Spiegel .
There are several variants of the layer-by-layer method, including an easy-to-understand method by Leyan Lo. The method consists of seven steps: first a white cross is formed, then the corners are filled in. Then the curb stones are filled in accordingly in order to create a cross on the last (mostly yellow) surface as the fourth, whereupon the positioning of the edges is corrected as a fifth step. The penultimate step is to position the corners to finally align them correctly.
system
- The cross : This first phase is solved intuitively, since this method is actually only used by newcomers to speedcubing.
- Filling in the corners : The same applies here as in the previous step. It is actually completely intuitive to solve, but due to the lack of experience of the users, there are a few algorithms available. At the end of this phase, the first (white) level is complete and the adjacent levels have a kind of small "T" in their respective colors.
- Filling in the edges : There are exactly two algorithms for this step. An intuitive implementation is not easy. At the end of this step, the slots are filled.
- Cross on the last level : A cross is created on the last level by repeatedly applying an algorithm.
- Position edges : The edges are also positioned with an algorithm that can be executed several times if necessary.
- The positioning of the corners is again possible using two algorithms.
- No new algorithm is required to rotate the corners - one that is already required for step 2 is used here several times until the cube is solved.
use
This method is recommended for beginners, but does not have enough potential to be of use at championships, where it is used by few speed cubers. Even experienced and practiced cubers find it difficult to achieve times below the 40-second limit, which makes the method uncompetitive for competitions.
Optimized train sequences
Deviating from the step-by-step solution described above for completing the second and third levels, advanced users use different sequences of moves depending on the position and position of the individual stones, so that further corrections of the stones are no longer necessary.
For example, if the initial situation is optimal, it is possible to completely solve the second level with just eight moves and the third level with only six moves.
However, this ideal case rarely occurs in practice. As a rule, a combination of at least two sequences of moves is required for both levels.
Fridrich method / CFOP
overview
The Fridrich Method, developed by Jessica Fridrich in the 1980s and first published on the internet in 1997, is the most popular advanced method for solving the Rubik's Cube.
This system provides to solve the cube in four steps: First, to construct the white cross, then the first two layers ( First two layers ) to solve, followed by orientation ( Orientation load layer ) and finally the correct arrangement of the last page ( Permutation last layer ). This is why the Fridrich method is also called CFOP (Cross, F2L, OLL, PLL).
With the help of the Fridrich method, the cube can also be solved in just three steps. For this purpose, the last level is completely solved with just a single algorithm. This technique is called 1LLL (one look last layer). It is only used very rarely, however, since algorithms are necessary to cover all the possibilities of the last level.
system
- The cross - the aim of this step is to form a white cross on the first (mostly white) side, i.e. the side with the white center stone, with the edge stones already in the correct position. This step is usually solved intuitively and laid out in the 15 seconds inspection time.
- F2L (from the English “First two layers” , the first two levels) describes the step in which the so-called slots are filled. This step is also largely done intuitively, but it can also be shortened for certain special cases with a few algorithms.
-
OLL (from the English "Orientation of the last layer" , orientation of the last page) means the step in which the colors of the last page are all aligned to this. After this step, the last, mostly yellow, side only consists of areas of the same color. There are 57 algorithms to learn for this.
A simpler alternative to this is the " 2-Look-OLL ", in which in two steps first the curb stones (3 algorithms, one of which consists of the other two) and then the corner stones (7 algorithms, one of which is the mirrored version another). -
PLL (from the English “Permutation of the last layer” , swapping the last side) stands for the last process in which the stones that form the last side (last layer) are swapped with each other in order to finally solve the cube. A total of 21 different algorithms are required for this. 6 of them are mirrored, one backwards and one mirrored and backwards, so only 13 have to be learned.
A simpler alternative to this is the " 2-Look PLL ", in which, in two steps, first the curb stones (4 algorithms, one algorithm is the mirrored version of another) and then the corner stones (3 algorithms, one algorithm is the mirrored one) Version of another).
use
The Fridrich Method is by far the most popular method. It is the most common method used in competitions and championships. The current world record holder for solving the 3 × 3 × 3 Rubik's Cube, Yusheng Du , also achieved an official record time of 3.47 seconds using the Fridrich method.
Roux method
overview
The Roux method developed by the Frenchman Gilles Roux is one of the most popular systems after the Fridrich method. The main difference is that with the Roux method fewer algorithms have to be mastered and the cube can be solved more intuitively. The steps into which the Roux method can be broken down are the construction of a 1 × 2 × 3 block on one side, in the second step the construction of a 1 × 2 × 3 block on the opposite side. After the four remaining corners have been solved, the remaining cubies are fitted.
system
- 1 × 2 × 3 block - within this step, the goal is to first correctly place an edge and then fill the two slots around it. This step can be solved almost completely intuitively.
- Another 1 × 2 × 3 block is constructed in the following step. This step can also be solved intuitively and also consists of placing an edge piece and then filling the two adjacent slots.
- The last four corners must now be moved to the correct position. This step is hardly intuitive and is carried out according to more or less rigid algorithms.
- The last step is quite extensive, because it is necessary to move ten Cubies to the right place with the correct direction. This step, which ultimately distinguishes the Roux method, is almost completely intuitive.
use
The Roux method is mainly used for those Speedcubers who find it difficult to learn algorithms by heart. The difference to some other methods of speed solving is that on average only around 50 pulls are required for solving. As a result, the cube can be solved more quickly. However, this is counteracted by the fact that the "look ahead" is more difficult, since positions that are not directly visible must also be observed. However, this method is the second most common method used in competitions.
Peter's method
Overview
The Petrus Method was developed by Lars Petrus. It stands out very clearly from the other methods in one aspect: With the Petrus Method, it is by no means necessary to complete a page first. Many other methods build such a page and must direct everything in their future steps towards restoring the first level. The Petrus method tries to avoid this, for a very long time two working levels are freely movable, with which (more or less) one can act freely.
The method consists of seven steps: First a 2 × 2 × 2 block is formed, this is then expanded to a 2 × 2 × 3 block. Then the edges are rotated in order to finish the last two levels. After positioning and rotating the corners, the positioning of the edges follows.
system
- In the 2 × 2 × 2 block , the first thing to do is to move four stones to the correct position and align them correctly. This step is solved intuitively.
- Few algorithms are available to expand to a 2 × 2 × 3 block , but they are not absolutely necessary.
- Next , you twist the edges . A cross must be formed on each of the two levels that are still freely movable.
- Only in this step do you move on to finishing the two levels , i.e. positioning two corners and three edges. Up until now there were two working levels.
- The positioning of the corners can be solved with algorithms, but can also be handled intuitively.
- The corners are then turned , also by algorithms. At the end of this step, the last layer is already monochrome.
- Finally, the edges are correctly positioned using algorithms. At the end of this turn the die is solved.
use
This method is also one of the most common solution methods for the Rubik's Cube. Lars Petrus personally won the Swedish championships with this method and in 1982 he reached 4th place in the world championship. With this method, times of less than 15 seconds can be achieved with a lot of practice.
Web links
- A German tutorial on the beginner's method
- A German tutorial on the Fridrich method
- A German tutorial on the Roux method
- A detailed English page of the Petrus Method
- Methods for one-handed and blind loosening, as well as methods for the pocket cube
Individual evidence
- ↑ God's Number is 20
- ^ The Diameter of the Rubik's Cube Group Is Twenty . In: SIAM J. Discrete Math. , 27 (2), pp. 1082-1105, doi: 10.1137 / 120867366
- ↑ Mathematical Cabinet: We unravel the Rubik's Cube . In: Bild der Wissenschaft 11/1980, pp. 174–177.
- ↑ Mathematical Cabinet: Darn it - Again . In: Bild der Wissenschaft 12/1980, p. 180ff.
- ↑ "Scream Hurray! Throw a round!" - Solution procedure for the "Rubik's Cube" . Der Spiegel 04/1981 from January 19, 1981
- ↑ Beginner's Method
- ↑ Fridrich method (English)
- ↑ Reconstruction of the 3 × 3 × 3 world record by Feliks Zemdegs
- ^ Peter's method