In 1975, the sculptor Erne Rubik patented his invention under the name “Magic Cube”. For over 40 years, all rights to the puzzle belong to the company of Tom Inner's close friend, the inventor, called Seven Towns Ltd. The English company controls the production and sale of the cube around the world. In Hungary, Germany, Portugal and China, the puzzle has retained its original name, in other countries the toy is called the Rubik's Cube.
Varieties of puzzles
The classic Rubik's Cube measures 3 by 3 squares. Over time, came up with a huge number of shapes and sizes for toys. No one will surprise anyone with a puzzle in the form of a pyramid or a 17x17 cube size. However, humanity never rests on its laurels.
Obviously, there is no assembly scheme for the beginners of this cube. The process of assembling and solving the puzzle may take years. Recently, interest in the cube is growing not only in Asia and Europe, but also where the toy was not very popular, for example, in the USA. One of the fans of the Rubik's Cube shot a video assembly of the puzzle 17 on 17. The total length of the video is 7.5 hours, the shooting was carried out during the week.
Growing demand creates supply. Sometimes the models sold are incredible and it is not always clear how they will look when assembled. Each country has its favorite varieties of toys.
What is speedcubing?
Fans of the game organize real competitions in cube assembly speed. Special speed puzzles are on sale. The rotation mechanism of such Rubik's cubes is very high-quality, and the turns of faces and rows can be made with the movement of one finger.
The World Cube Association (WCA) is a non-profit organization supporting the speedcubing movement. The WCA regularly hosts competitions around the world. In almost all countries there are representatives of the organization. Anyone can become a participant in a speedcubing event, you just need to register on the site and meet the assembly standards. The most popular discipline in such competitions is the high-speed assembly of the Rubik's Cube 3x3. The norm for participation is 3 minutes, but even if a person cannot solve the problem in the allotted time, he will still be allowed to attend the event. You can sign up for any discipline, but you need to come with your puzzle.
The 3x3 Rubik's Cube assembly record belongs to the Sub1 robot, created by engineer Albert Beer. The machine is able to solve the puzzle in a split second, while a person will need 4.7 seconds to achieve it (achievement of Mats Valka 2016). As you can see, the participants in the speedcubing movement have someone to look up to.
What are the algorithms for assembling a Rubik's Cube 3x3?
There are many ways to solve a well-known puzzle. Variants of 3x3 Rubik's cube assembly schemes have been developed for both beginners and advanced people with complicated schemes: 4x4, 6x6 and even 17x17.
The 3x3 puzzle option is considered a favorite classic for most fans. Therefore, there are much more instructions on how to assemble a 3x3 Rubik's cube than any other.
What should the puzzle look like?
You can assemble a toy according to the scheme only from a previously prepared position. If the patterns on the faces of the cube are not located correctly, then it will not work for the beginners to solve it using the 3x3 rubik's cube assembly algorithm. There is a set of such positions for different solutions.
The figure shows a “white cross” or simply “cross” - the starting point of the easiest way to assemble a 3x3 Rubik's cube. It is recommended to disassemble and fold the toy correctly.
Designations of schemes and methods of rotation of the cube
Before you begin to disassemble the formulas of the Rubik's Cube 3x3, it is worth learning the notation used in speedcubing. All puzzle movements are indicated by capital letters. The absence of an apostrophe above the symbol means that the rotation is carried out clockwise, if there is a sign, then it should be rotated in the opposite direction.
The first letters of English (or Russian) words denoting movements are considered generally accepted:
- front - F or - rotation of the front side;
- back - B or T - rotation of the back side;
- left - L or L - rotation of the left row;
- right - R or P - rotation of the right row;
- up - U or B - rotation of the upper row;
- down -D or H - rotation of the bottom row.
Pointers can also be used to change the position of the cube in space - the interception movement. Everything is simple here, too, from the school course of geometry, the coordinate axes X, Y and Z are known to everyone. The X movement means that the cube must be rotated by the F face to the place of the U face, when Y - F is shifted, it should be replaced by L, and when Z is rotated - F moves to R.
The following group of notations is rarely used; it is used in drawing up patterns of patterns:
- M - the rotation of the middle row, between the right (R / P) and left (L / L);
- S - rotation of the middle row, between the front (F / F) and the rear (B / T);
- E - rotation of the middle row, between the upper (U / B) and lower (D / H).
Why collect patterns on the faces of the cube?
At meetings on speedcubing compete not only in solving the puzzle, but also in the ability to make various patterns on a 3x3 Rubik's Cube. They do this in order to quickly and easily assemble the cube in the desired position.
There are a huge number of schemes for assembling a variety of patterns: "dots", "chess", "dots with chess", "zigzag", "meson", "cube in a cube in a cube" and many others. There are more than 46 of them for the classic puzzle alone. Speedcubing masters consider it shameful to disassemble the toy. Also, drawing patterns on a 3x3 Rubik's Cube is a great way to train and improve skills.
The figure depicts options for various puzzle patterns. The following are some more formulas for assembling the most interesting drawings from the cross position:
- chess - M 2 E 2 S 2 ;
- zigzag - (PLFT) 3;
- four z - (PLFT) 3 V 2 H 2 ;
- Plummer's Cross - TF 2 N'P 2 FNT'FN'VF'N'L 2 FN 2 V ';
- cube in a cube in a cube - V'L 2 F 2 N'L'NV 2 PV'P'V 2 P 2 PF'L'VP.
3x3 Rubik's Cube Build Algorithm for Beginners
Although there are many ways to solve the puzzle, simple and understandable schemes for beginners are not so easy to find. With each passing step of the assembly, the formulas of a 3x3 Rubik's Cube become more complicated. It is necessary not only to change the pattern correctly, but also to preserve what has been done before. Below will be one of the options for how easy it is to assemble a 3x3 Rubik's Cube.
Conventionally, the whole process can be divided into the following stages:
- The assembly of the cross in the upper face of the cube.
- The correct preparation of the entire upper face.
- Work on the middle layers.
- Proper assembly of the ribs of the last row.
- Assembling the cross of the lower bound.
- Correct orientation of the corners of the last face of the cube.
Puzzle Solution - Preparatory Work
The first stage is the easiest. Beginners can try their hand and practice drawing cube patterns according to the instructions, but this process will take a lot of time.
You need to select the top face and the color that will be collected first. The 3x3 Rubik's Cube assembly algorithm for beginners is designed from the “cross” position. Make it easy, you need to select the central color, find 4 rib elements of the same shade and raise them to the selected face. The colored arrow in the picture indicates the part to be found. Variants of the location of the desired element may be different, depending on this, 2 sequences of actions A and B are described. The difficulty is to continue the cross on the sides of the cube. A closer look at the final form of the stage can be in the image above.
Puzzle solution - work on the middle row
At this stage, beginners need to find and assemble the corner elements of the upper facet of the Rubik's 3x3 cube assembly diagram. In the end result, the face with the cross and the top row of the puzzle must be completely solved.
The image shows three cases of a possible pattern of faces. Choosing one of the methods A, B or C, you need to collect all 4 corners of the cube. By memorizing rotation algorithms and practicing them, skills and mastery of puzzle assembly are acquired. It is pointless to consider formulas and represent the process, it is much easier to take a cube and try all the methods in practice.
The third stage seems simple, but it is only an appearance. To solve it, two situations of patterns are described and, accordingly, two rotation formulas are composed. Applying them, it is worth remembering the preservation of previously achieved results. Masters constantly keep 3-4 last rotations in their memory in order to return the cube to its original state in case of failure.
To solve the puzzle, you need to rotate it along the coordinate axis in the search for the necessary elements and work with them. Such movements are rarely displayed in formulas, only in special cases. It is recommended to start assembling the rib faces from the elements of the lower rows, after such rotations all the necessary cubes will go down from the middle to the lower row.
Puzzle Solution - Making the Second Cross
At the fourth stage, the toy is turned upside down. Solving the last facet is the most difficult part of the Rubik's 3x3 cube assembly algorithm for beginners. The rotation formulas are long and complex, their implementation will require special care. The purpose of the action is to position the rib elements in their places for further drawing up the cross. The orientation of the rib parts may be incorrect. The formula for the movements of the cube is only one, and it should be applied until the goal of the stage is achieved.
The rotation of the fifth stage is aimed at the rotation of the elements on the right side. Its peculiarity lies in the fact that the same rotation formula is used for all three patterns in the figure, the only difference is in the orientation of the cube itself.
Formulas for the movements of the 5th stage are as follows:
- (PS N ) 4 V (PS N ) 4 B '- option "A";
- (PS N ) 4 V '(PS N ) 4 V - option “B”;
- (PS N ) 4 V 2 (PS N ) 4 V 2 - option "B".
is the rotation of the middle row clockwise, and the exponent above the bracket is the number of repetitions of the actions in parentheses.
Puzzle Solution - Last Spins
At the sixth stage, as well as at the fourth, the necessary cubes are placed in their places, regardless of their orientation. The puzzle should be rotated so that the element, which is already in the right place, is located in the far left corner at the top of the cube. The options proposed for solving the formula mirror each other. Repeat the rotation is necessary until the desired result.
The seventh stage is the most solemn and the most difficult. When the cube rotates, violations in the already assembled rows are inevitable. It will be necessary to completely focus on the movements, otherwise the result of the assembly may be irrevocably ruined. As in the fifth stage, the sequence of movements is only one, but repeated 4 times. First, rotations are made to orient the element, then reverse to restore broken rows.
Do not forget about the recording of movements using signs of the English alphabet. The formulas for the movements of the faces and rows of the cube of this stage are as follows:
- (RF'R'F) 2 U (RF'R'F) 2 - option "a";
- (RF'R'F) 2 U ' (RF'R'F) 2 - option "b";
- (RF'R'F) 2 U 2 (RF'R'F) 2 - option "c".
B - rotation of the upper face by 90 degrees, B '- rotation of the same face counterclockwise, and B 2 - double rotation.
The complexity of the stage is in the correct assessment of the arrangement of elements and the choice of the necessary rotation option. It can be difficult for beginners to immediately correctly determine the pattern and compare it with the correct formula.
Rubik's cube and children
A tricky puzzle is interesting not only for adults, but also for children. Teenagers became world champions in assembling the Rubik's Cube. In 2015, Colin Burns, who at that time was only 15 years old, assembled the toy in 5.2 seconds.
A simple but exciting toy continues to interest the younger generation for the past 5 decades. Children's hobby often develops into a profession. There are mathematical methods for evaluating solutions to problems of the Rubik's Cube. This section of mathematics is used in the design and writing of decision algorithms for automated computers. Robots that are really looking for ways to build a cube, and do not perform a pre-driven motion algorithm, solve the puzzle in 3 seconds, for example, CubeStormer 3.