A puzzle designed as visual material To algebraic theory, unexpectedly captivated the whole world. Already more than a decade away from higher mathematics people are passionately struggling with a complex and exciting task. "Magic cube" is an excellent tool for development logical thinking and memory. For those who first wondered how to solve a Rubik's cube, diagrams and comments will help maintain enthusiasm, and perhaps discover the world of speedcubing.

The six sides of the puzzle have specific colors and their order, patented by the inventor. Numerous fakes often give themselves away precisely because of their unusual colors or their position relative to each other. Educational diagrams and descriptions always use standard color schemes. It is quite easy for beginners to get confused in the explanations if they use a die with a different color scheme.

Colors of opposite faces: white - yellow, green - blue, red - orange.

Each side consists of several square elements. Based on their number, the types of Rubik's cubes are distinguished: 3*3*3 (the first classic version), 4*4*4 (the so-called “Rubik's Revenge”), 5*5*5 and so on.

The first model assembled by Ernő Rubik consisted of 27 wooden cubes, identically painted in six colors and stacked on top of each other. The inventor spent a month trying to group them so that the faces of a large cube were made up of squares of the same color. It took even more time to develop the mechanism that held all the elements together.

A modern Rubik's cube of a classic design consists of the following elements:

Centers are parts that are motionless relative to each other, fixed on the axes of rotation of the cube. They face the user with only one colored side. Actually, the six centers form mirror pairs in the color scheme.
Ribs are moving elements. The user sees two colored sides of each edge. The color combinations here are also standard.
Corners are eight movable elements located at the vertices of the cube. Each of them has three colored sides.
The fastening mechanism is a cross of three rigidly fixed axes. Exists Alternative option mechanism similar to a sphere. It is used in speed or multi-element cubes. The design of cubes with an even number of elements on the faces is especially complex - it is a system of interconnected click mechanisms, sometimes combined with a cross. There are magnetic mechanisms for professional speed cubes.

The game with a Rubik's cube is that, using a moving mechanism, the colored elements on the faces are rearranged and try to be assembled in the original order.

Puzzle fans compete to solve it against the clock. In addition to manual dexterity, this requires learning, remembering and bringing to automaticity hundreds of combinations of colored elements and actions with them. This unusual sport is called speedcubing.

Speedcuber tournaments are held regularly and records are updated. New horizons for achievements are constantly opening up. As part of the tournaments, competitions are held in assembling blindly, with one hand, with legs, and so on.

The newest hobby is playing solitaire games (patterns) on cubes.

In order to describe manipulations with a puzzle, record solution patterns, movements of elements relative to each other, and simply for ease of communication, a rotation language was created. It provides letter designations for each face and how it can be rotated.

The sides of the puzzle are indicated in capital letters.

In Russian-language manuals for solving a Rubik's cube, the initial letters of Russian names are used:

F – from “facade”;
T – from “rear”;
P – from “right”;
L – from “left”;
B – from “top”;
N – from “bottom”.

In the world community, the initial letters of the names of faces in English are used.

Designations accepted by the WCA (World Cube Association):

R – from right;
L – from left;
U – from up;
D – from down;
F – from front;
B – from back.

The central element is named the same as the face (R, D, F, and so on).

The edge is adjacent to two faces, its name consists of two letters (FR, UL, and so on).

The angle is accordingly described by three letters (for example, FRU).

The groups of elements that make up the middle layers between the faces also have their own names:

M (from middle) – between R and L.
S (from standing) – between F and B.
E (from equatorial) – between U and D.

The rotation of faces is described by the letters that name the faces and additional icons.

The apostrophe "'" indicates that the face or layer is rotated counterclockwise.
The number 2 indicates a repetition of the movement.

Possible actions with a face, for example, with the right one:

R – clockwise rotation;
R’ – counterclockwise rotation.
R2 – double rotation, no matter in which direction, since the edge has only four possible positions.

To determine which direction to turn the face, you need to imagine a watch dial on it and be guided by the movement of an imaginary hand.

Rotation of opposite faces “clockwise” is counter-rotating.

The movements of the middle layers are tied to the outer edges:

Layer M rotates in the same directions as L.
Layer S – like F.
Layer E - like D.

Another important designation of "w" is the simultaneous rotation of two adjacent layers. For example, Rw – simultaneous rotation of R and M.

Rotations of the entire cube are called interceptions. They are performed in three planes, that is, along three coordinate axes: X, Y, Z.

x and x’ are rotations along the X axis of the entire cube. The movements coincide with the rotations of the right side.
y and y’ – rotations of the cube along the Y axis. The movements coincide with the rotations of the top face.
z and z’ – rotation of the cube along the Z axis. The movement coincides with the rotation of the front face.
x2, y2, z2 – designations of double intercepts along the specified axis.

In addition to generally accepted designations, assembly manuals are full of slang, names of techniques, techniques, algorithms, patterns and figures on the cube, popular among speedcubers, and so on. No less in demand are schematic descriptions of algorithms that use only arrows. The more experience you gain in solving a puzzle, the easier it is to understand the descriptions and explanations; many things begin to be perceived intuitively.

The cap is colored elements collected on one side of the cube. Assembling a puzzle is the same as assembling all six hats.
Belt - colored elements adjacent to the hat. The hat can be assembled in such a way that the belt consists of scattered colored fragments, that is, the corner and rib elements are not in their places.
A cross is a figure on a hat made of five fragments of the same color. Assembly often begins with the construction of a cross. There are no clear guidelines here. This step allows the most flexibility and requires some thought. When the cross is ready, all that remains is to follow the memorized algorithms.
Flip - turning a corner or edge in one place relative to the center; this action requires the use of special algorithms.

Schemes for beginners will help you learn and save your nerves while solving a hopelessly confused cube, feel the logic of movements and work out the simplest algorithms.

Before performing any action, you need to inspect the cube. At competitions, 15 seconds are allotted for “pre-inspection”. During this time, you need to find elements of the same color that will be assembled into a “head” at the first stage. Traditionally, one starts with the white side, meaning most manuals assume that the U is white. “Multicolor” speedcubers can start the assembly from any side, mentally rebuilding all the ready-made algorithms.

Rubik's Cube 2x2

"Mini cube" consists of 8 corner elements. At the first stage, one layer of four corners is assembled. At the second stage, the remaining corners are placed in their places, but they can be turned upside down, that is, the colored elements will not be on their edges. All that remains is to turn them the right way.

The “bang-bang” algorithm allows you to move the corner element and orient it correctly. If you do this sequence of actions six times in a row, the cube will return to its original position. Thus, if a cube is mixed, you need to apply it 1 to 5 times to place the element correctly. Algorithm entry: RUR’U’.
When one layer is assembled, you need to turn the cube with the second layer up. Moving this layer in any direction, set one of the corners in its place. Next, an algorithm is applied that allows you to swap two adjacent elements - the right and left corners of the front face. The sequence of actions is as follows: URU’L’UR’U’LU.
When all the corners are in place, they are turned over (flip) using the “bang-bang” algorithm. At this stage it is important not to intercept the cube.

How to solve a 3x3 Rubik's cube

Construct a “white cross” by gathering 4 edges with white stickers around a white center.
Combine the colored centers of the sides R, L, U, D with the corresponding edges of the “white cross”.
Place the corners with white stickers in their places. Using the R'D'RD algorithm, repeated up to five times, the corners will be flipped into the correct position.
To place the edges of the middle layer in their places, you need to intercept the cube - y2. Select the rib without the yellow sticker. Align it with a center that matches the color of one of the sides. Using formulas, shift the edge to the middle layer: The edge is lowered with a shift to the left: U’L’ULUFU’F’. The edge descends with a shift to the right: URU’R’U’F’UF. If an element is in place but not rotated correctly, these algorithms are used again to move it to the third layer and reinstall it.
Without intercepting the cube, collect a yellow cross on the cap of the third layer, repeating the algorithm: FRUR’U’F’.
Align the edges of the last layer with the side centers correctly, as was done for the first cross. The two ribs will easily snap into place. The other two will have to be swapped. If they are opposite each other: RUR’URU2R’. If on adjacent sides: RUR’URU2R’U.
Place the corners of the last face in the correct positions. If none of them is in the correct place, apply the formula URU’L’UR’U’L. One of the elements will fit correctly. Grab the cube at this angle towards you; it will be the top right one on the front edge. Move the remaining corners counterclockwise URU'L'UR'U'L or, conversely, U'L'URU'LUR'. At this stage, all the collected areas will be rebuilt, it will seem that something has gone wrong. It is important to ensure that the cube does not turn over and the center of F does not move relative to the user. The combination of moves must be repeated up to 5 times.
The corner elements may need to be rotated, aligning the colored pieces with the rest of the edges correctly. To unfold (flip) them, the first formula is used: R’D’RD. It is important not to intercept the cube so that F and U do not change.

Rubik's Cube 4x4

Puzzles with more than three elements on an edge offer a much larger number of combinations.

The “even” options are especially difficult, since they do not have a rigidly fixed center, which helps to navigate the classic puzzle.

For 4*4*4, about 7.4*1045 element positions are possible. That's why it was called "Rubik's revenge" or Master Cube.

Additional designations for internal layers:

f – internal frontal;
b – internal rear;
r – inner right;
l – inner left.

Assembly options: layer by layer, from corners or reduction to the form 3*3*3. The last method is the most popular. First, four central elements are assembled on each face. Then the rib pairs are adjusted and, finally, the angles are set.

When assembling central elements, you need to remember which colors are opposed in pairs. Algorithm to swap elements from the middle quad: (Rr) U (Rr)’ U (Rr) U2 (Rr)’ U2.
When assembling the ribs, only the outer edges rotate. Algorithms: (Ll)’ U’ R U (Ll); (Ll)’ U’ R2 U (Ll); (Ll)' U' R' U (Ll); (Rr) U L U’ (Rr)’; (Rr) U L2 U’ (Rr)’; (Rr) U L’ U’ (Rr)’. In most cases, the ribs can be assembled intuitively. When there are only two edge elements left: (Dd) R F’ U R’ F (Dd)’ – to install them side by side, U F’ L F’ L’ F U’ – to swap them.
Next, the 3*3*3 cube formulas are used to rearrange and rotate the corners.

Complex cases that require a special solution are parities. Their formulas do not solve the problem, but knock out elements from deadlock, bringing the puzzle into a form solvable by standard algorithms.

Two adjacent edge elements in the wrong orientation: r2 B2 U2 l U2 r’ U2 r U2 F2 r F2 l’ B2 r2.
Opposing pairs of edge elements in the wrong orientation: r2 U2 r2 (Uu)2 r2 u2.
Pairs of edge elements at an angle to each other, in the wrong orientation: F’ U’ F r2 U2 r2 (Uu)2 r2 u2 F’ U F.
The corners of the last layer are out of place: r2 U2 r2 (Uu)2 r2 u2.

Quick assembly of a 5x5 puzzle

Assembly consists of bringing it to a classic look. First, 9 central fragments on each cap and three rib elements are assembled. The last stage is the placement of corners.

Additional designations:

u – inner upper edge;
d – inner bottom edge;
e – inner edge between the top and bottom;
(two faces in brackets) – simultaneous rotation.

The assembly of the central elements is simpler than in the previous case, since there are rigidly fixed color pairs.

At the first stage, difficulties may arise if you need to swap elements on adjacent faces. If they are separated by one edge element: (Rr) U (Rr)’ U (Rr) U2 (Rr)’. If they are on the inner central layers: (Rr)’ F’ (Ll)’ (Rr) U (Rr) U’ (Ll) (Rr)’.
The combination of edge elements is intuitive, it does not affect the assembled centers: (Ll)’ U L’ U’ (Ll); (Ll)’ U L2 U’ (Ll); (Rr) U' R U (Rr)'; (Rr) U' R2 U (Rr)'. The only difficulty is assembling the last two ribs.

Formulas for parities:

swap elements in layers u and d on the edges of one face: (Dd) R F’ U R’ F (Dd)’;
swap the edge elements located in the middle layer on one face: (Uu)2 (Rr)2 F2 u2 F2 (Rr)2 (Uu)2;
unfold these elements in their places, that is, flip: e R F’ U R’ F e’;
unfold the rib element of the middle layer in place: (Rr)2 B2 U2 (Ll) U2 (Rr)’ U2 (Rr) U2 F2 (Rr) F2 (Ll)’ B2 (Rr)2;
swap elements in the side layer on one face: (Ll)’ U2 (Ll)’ U2 F2 (Ll)’ F2 (Rr) U2 (Rr)’ U2 (Ll)2;
flip three edge elements simultaneously into place: F’ L’ F U’ or U F’ L.

The last task is to arrange the corners according to the principle of a classic cube.

The fastest way. Jessica Friedrich Method

Those who have already learned how to solve a puzzle in 1 - 2 minutes, that is, can really quickly solve a Rubik's cube, are approaching a fundamentally new understanding of the problem. Mechanical acceleration becomes impossible at a certain stage. Special algorithms and techniques are needed to reduce the time required to find solutions.

Layer-by-layer assembly of the classic version to speed up the process comes down to four tasks:

initial cross on one hat;
simultaneous assembly of the first and second layers;
last hat;
third layer belt.

The difficulty is that you have to learn and keep in your head all the time 119 formulas compiled by the author of the method, Jessica Friedrich. Groups of algorithms F2L, OLL, PLL for each stage describe all possible combinations of element arrangement, rotations and permutations necessary for working with edge-angle pairs.

The method allows you to solve the puzzle in less than 20 seconds.

How to Solve a Rubik's Cube with Your Eyes Closed

Special techniques have been developed to facilitate this task. One of the popular methods among speedcubers is the old Pochmann method.

The assembly is not done layer by layer, but by groups of elements: first all the edges, then the corners.

Edge RU is a buffer edge. Using special algorithms, the cube occupying this position is moved to its place. The element that replaced it in the RU position is moved again, and so on, until all the edges are in their places. The same is done with the corners. The peculiarity of blind assembly algorithms is that they allow you to move an element without mixing the rest.

During the blind assembly process, the cube is not turned over to avoid confusion.

Before starting to assemble, the cube is “remembered”. A chain is mentally created along which the elements will move. Each sticker is assigned its own letter of the alphabet. Speedcuber makes separate alphabets for edges and corners. A jumbled Rubik's cube is remembered as a sequence of letters. The top sticker on the buffer cube is the first letter, the sticker that occupies its rightful place is the second, and so on. For simplicity, sequences of letters form words, and words form sentences.

Who holds the record for the fastest Rubik's Cube?

Australian Felix Zemdegs twice updated the world record for solving the classic Rubik's cube in 2018. At the beginning of the year, best time 4.6 seconds, in May the puzzle was solved in 4.22 seconds.

The 22-year-old athlete holds several other current records from 2015 to 2017:

4x4x4 – 19.36 seconds;
5x5x5 – 38.52 seconds;
6x6x6 – 1:20.03 minutes;
7x7x7 – 2:06.73 minutes;
Megaminx – 34.60 seconds;
one hand – 6.88 seconds.

The robot's record, recorded in the Guinness Book of Records, is 0.637 seconds. There is already a working model that can solve a cube in 0.38 seconds. Its developers are Americans Ben Katz and Jared Di Carlo.

Date of: 2013-12-24 Editor: Zagumenny Vladislav

Mathematics of Rubik's cube- a set of mathematical methods for studying the properties of the Rubik's cube from an abstract mathematical point of view. Studies algorithms for solving a cube, evaluating algorithms for solving it, etc. Based on graph theory, group theory, computability theory, combinatorics.

There are many algorithms designed to transform a Rubik's cube from an arbitrary configuration to a final configuration (assembled, all faces are the same color). In 2010, it was strictly proven that to transfer a Rubik's cube from an arbitrary configuration to a solved configuration (often this process is called “assembling” or “solving”) no more than 20 rotations of the faces are sufficient. This number is the diameter of the Cayley graph of the Rubik's Cube group. An algorithm that solves a puzzle in the minimum possible number of moves is called God's algorithm.

Rubik's Cube God Algorithm

The history of the search for the Rubik's Cube God algorithm began no later than 1980, when a mailing list for Rubik's Cube enthusiasts was opened. Since then, mathematicians, programmers and just amateurs have sought to find God's algorithm - an algorithm that would allow one to practically solve the Rubik's Cube in a minimum number of moves. Related to this problem was the problem of determining the God number - the number of moves that is always sufficient to complete the puzzle.

In July 2010, Palo Alto programmer Thomas Rokicki, Darmstadt math teacher Herbert Kozemba, Kent State mathematician Morley Davidson and Google Inc. engineer. John Detridge proved that each Rubik's Cube configuration can be solved in no more than 20 moves. In this case, any rotation of the edge was considered one move. Thus, the number of God in the FTM metric turned out to be 20 moves. The amount of computation involved about 35 years of processor time donated by Google. Technical data on performance and number of computers are not disclosed; The duration of the calculations was several weeks.

Lower Bounds for God's Number

It is fairly easy to show that there are solvable configurations that cannot be solved in less than 17 moves in the FTM metric or 19 moves in the QTM metric.

This estimate can be improved by taking into account additional identities, for example, the commutativity of rotations of two opposite faces (L R = R L, L2 R = R L2, etc.) This approach allows us to obtain a lower bound for the God number of 18f or 21q.

"Superflip" - the first configuration discovered, located at a distance of 20f* from the initial This estimate remained the best known for many years. Moreover, it follows from a non-constructive proof, since it does not indicate specific example configuration requiring 18f or 21q for assembly.

One configuration for which a short solution could not be found was the so-called “superflip”, or “12-flip”. A "superflip" is a configuration in which all the corner and edge cubes are in place, but each edge cube is oriented in the opposite direction.

The vertex corresponding to a superflip in the Rubik's cube graph is a local maximum: any move from this configuration reduces the distance to the initial configuration. This gave reason to assume that the superflip is at the maximum distance from the initial configuration, that is, it is a global maximum.

In 1992, Dick T. Winter found a solution to the superflip in 20f. In 1995, Michael Reed proved the optimality of this solution, resulting in a lower bound for God's number of 20 FTM. That same year, Michael Reed discovered the "superflip" solution at 24q. The optimality of this solution was proven by Jerry Bryan.

In 1998, Michael Reed found a configuration whose optimal solution was 26q*. As of July 2013, this number is the best known lower estimate of God's number in the QTM metric.

Upper bounds for God's number

To obtain an upper bound for God's number, it is enough to specify any algorithm for solving a puzzle consisting of a finite number of moves.

The first upper bounds for God's number were based on "human" algorithms consisting of several stages. Adding the estimates from above for each stage made it possible to obtain a final estimate of the order of several tens or hundreds of moves.

The first specific upper bound was probably stated by David Singmaster in 1979. His solving algorithm made it possible to solve the Rubik's cube in no more than 277 moves. Singmaster later reported that Alvin Berlekamp, John Conway and Richard Guy. developed an assembly algorithm that requires no more than 160 moves. Shortly thereafter, Conway's Cambridge Cubists, who were compiling a list of combinations for one face, found a 94-move algorithm.

As is known, the number possible states Rubik's cube equals
43,252,003,274,489,856,000 (43 quintillion 252 quadrillion 3 trillion 274 billion 485 million 856 thousand). Where does this figure come from? And here's where it comes from:
(number of rib cube arrangements) x
x(number of placements of corner cubes) x
x (number of combinations of rotations of the edge cubes) x
x (number of combinations of rotations of corner cubes).

There are also central cubes, but they are always in their places, and their orientation (for a cube with a monotonous coloring of each face) can be neglected.

There are 12 edged cubes in a Rubik's cube. This means that the first cube can be placed in 12 places, the second cube in 11 places, the 3 cube in 10 places, the fourth in 9 places and so on until the last one. That is, the number of ALL arrangements of edge cubes is equal to
12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 479001600.
This is written as 12! (12-factorial).

Factorial of a number n (lat. factorialis - active, producing, multiplying; denoted by n!, pronounced en factorial) - the product of all natural numbers from 1 to n inclusive.

Similarly, we count the number of ALL arrangements of corner cubes. There are 8 of them, which means
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320.

Now let's count the number of ALL combinations of rotations of the rib cubes. Each of the 12 edge cubes can only have 2 orientations - 0 and 180 degrees, so 2 to the 12th power = 4096.

In the same way, we calculate the number of all orientations of the corner cubes: 3 to the 8th power = 6561.

It would seem that you can multiply the resulting 4 numbers, and everything is ready. But it's not that simple. So far, the figure will be much higher. Let's cut off the excess.

If the cubes are moved out of their correct position only by permissible rotations (and not by physically disassembling and reassembling the entire device or repainting the faces), then a situation cannot arise in which:

all the middle cubes are in their places and only one of them is turned incorrectly;
all the middle cubes are both standing and turned correctly, and all the corner cubes, except two, are standing (in any positions) in their places;
all the middle cubes are both standing and turned correctly, and all the corner cubes are standing in their places and only one of them is turned incorrectly.

For anyone interested in where such properties were derived, I recommend reading the article “Mathematics of the Magic Cube” by V. Dubrovsky in the magazine “Kvant” No. 8 for 1982, and the article “Hungarian Hinged Cube” in No. 12 for 1980 in the same magazine, authors - V. Zalgaller and S. Zalgaller. . If you have never been a mathematician, I don’t recommend reading it, because you will blow your mind. So, just take my word for it.

In accordance with the first property, only one edge cube cannot be rotated, which means we will not take its orientation into account either. Therefore, we divide 2 to the 12th power by 2, which is equal to 2 to the 11th power. We get 2048.

Based on the third property, according to which only one corner cube cannot be rotated incorrectly (which means its orientation can be ignored), we will adjust the calculation of all orientations of the corner cubes to the minimum required. That is, we divide by 3, or write 3 to the 7th power, which is equivalent. The result will be 2187.

Well, the last adjustment is based on the second property. It cuts off impossible permutations. That is, if we have already placed 6 of the 8 corner cubes in their places (in any orientation), then the last 2 will definitely fall into place each in its place. Remember how we calculated the placement of angles? (From 8 possible places for the first cube to one place for the last cube.) So, the multipliers for the last cubes can now be ignored. Let's divide 8! by 2, we get 20160.

So, now you understand what and where it came from in this formula, which means you can safely multiply the resulting numbers:
12! * 8!/2 * 2 11 * 3 7 = 12! * 8! * 2 10 * 3 7 .
You can still expand 12! and 8! to prime numbers, then we get
2 27 * 3 14 * 5 3 * 7 2 * 11 = 43252003274489856000.
Or simply multiply the pre-calculated 4 numbers:
479001600 * 20160 * 2048 * 2187 = 43252003274489856000.

Let's now calculate how many possible states a Rubik's cube will have, taking into account the rotations of the central cubes (middles). As you know, there are 6 of them (in a cube measuring 3x3x3) and each of them can be rotated by 0, 90, 180 and 270 (or minus 90) degrees, that is, have 4 possible positions. Therefore, the number of possible combinations of centers is 4 to the 6th power. But in a cube it is impossible to have a state where, when the cube is fully assembled, only one central cube is rotated 90 degrees (in any direction), therefore, for the last central cube out of six, we take into account only two positions - 0 and 180 degrees. We get
(4 6)/2=(2 2) 6 /2=2 12 /2=2 11 = 2048 possible combinations.

Now multiplying this number by the number of combinations of corners and edges known to us, we get:
2048 * 43252003274489856000 = 88580102706155225088000.

So, the number of combinations of a 3x3x3 Rubik's cube, taking into account the orientation of the central cubes, is
2 11 * 2 27 * 3 14 * 5 3 * 7 2 * 11 = 2 38 * 3 14 * 5 3 * 7 2 * 11=
=88,580,102,706,155,225,088,000 (88 sextillion 580 quintillion 102 quadrillion 706 trillion 155 billion 255 million 88 thousand).

IN Lately many cubes appeared with designs (or patterns) on the edges. If you purchased one of these for yourself, then you will definitely have a situation where the central cubes are incorrectly oriented. In order to solve such a cube, you need to know (in its place, of course).

Kiseleva Anastasia

Project Manager:

Malysheva Tatyana Pavlovna

Institution:

MBOU "Secondary School No. 3" Konakovo, Tver region.

I chose mathematics research paper on Rubik's Cube because I consider the Rubik's cube not just a toy, but a serious test for the thinking abilities and a manifestation of the perseverance of those who collect it. The Rubik's cube is a toy for the mind, a fascinating puzzle.

In his research work(project) in mathematics "Rubik's Cube - a children's toy or a complex mathematical simulator" I will try to study the Rubik's cube, understand its structure and learn how to assemble this fascinating puzzle.

In his research project(work) on mathematics on the topic "Rubik's Cube - a children's toy or a complex mathematical simulator" the author examines the history of the creation of the Rubik's Cube, the algorithm for assembling it, the varieties of the toy and its appearance now.

Introduction
1. Theoretical presentations
1.1. History of creation.
1.2. Assembly algorithm.
1.3. Varieties.
1.4. Rubik's cube now.
Conclusion
List of used literature
Application

Introduction

I chose this topic because I consider the Rubik's Cube not just a toy, but a serious test of the thinking abilities and a manifestation of the perseverance of those who solve it.

There are many modifications of this toy. It would be great to comprehend all its secrets.

Objective of the project: study the Rubik's cube, understand its structure.

Task: learn how to assemble a puzzle yourself.

1. Theoretical presentations

1.1. History of creation.

Erne Rubik is a Hungarian teacher of industrial design and architecture. While inventing a visual aid on three-dimensional object modeling for students, I received a toy.

Rubik tried various materials - wood, cardboard, paper, put numbers and symbols on the edges, but still gave preference to painting the sides in different colors.

There is a legend that the design of the mechanism was suggested to him by a pebble; he placed a cross in place of the central cube, around which the rest of the cubes rotated freely, without falling apart.

The puzzle was ready by 1974 and was successfully tested on students and friends of the inventor, and patented more than a year later by the inventor himself.

Mass production began at the end of 1977, when one of the Hungarian companies released a trial batch of new puzzles around Christmas. The toy did not leave the country. Fortunately, the puzzle accidentally caught the eye of entrepreneur Tibor Lakzi, who came to his homeland on business. He was interested in mathematics and took up its commercial promotion.

Tibor Lakzi: ”When I first saw Erno Rubik and offered him some money, it felt like alms. Rubik was dressed terribly and smoked cheap cigarettes. But I already knew that a genius stood before me. We'll sell millions of puzzles, I told him.”

The toy ended up at the Nuremberg Toy Fair, where it attracted the attention of the English game inventor Tom Cramer.

Until 1979, Lakzi and Kremer tried to interest large toy manufacturers in the cube, but they were afraid because of its complexity in manufacturing and assembly (it took the inventor himself a month to assemble the puzzle; initially he was not sure that he could find a way to solve it).

The first cubes were heavy and unsafe to use; they were refused to be exported to the West. In 1980, a lighter and safer version appeared, at which time the cube changed its name from the magic cube to the Rubik's cube. The toy has caught on, only in Hungary, Portugal and Germany the puzzle is still called the magic cube, and the Chinese, who rejected both versions of the name, call it the Hungarian cube.

Finally, in September 1979, after five days of negotiations, Ideal Toy Corporation, a major toy manufacturer, was interested in the toy, and a contract was signed to supply 1 million cubes to America.

American Larry Nichols patented his magnetic cube (a puzzle similar to the CD) at the same time as Rubik. However, his toy did not catch on and was rejected by game manufacturers. And a year later, the Japanese Terutochi Ichige managed to patent an exact copy of the Hungarian cube in Japan. But it was not the Nichols or Terutochi cube that conquered the world, but the Rubik’s cube.

In 1980, the cube made its international debut; it successfully visited toy fairs in London, Paris, New York, Nuremberg, and even in Hollywood, where it was represented by the Hungarian film star Gabor.

The cube won a prestigious award BATR Toy of the Year in 1980, and then in 1981. In England, a ceremony was held to present the cube to Prince Charles and Lady Diana, in honor of whose wedding a special edition was released. In 1982, an entry about the Rubik's Cube appeared in the Oxford Dictionary.

In its two debut years, more than 100 million branded cubes were sold worldwide. And there are also one and a half times more fakes; Taiwan, Costa Rica, Brazil, and Hong Kong have joined in their production.

Because of a colored plastic toy, the world was gripped by mass hysteria: in 1981, Patrick Bosser, a 12-year-old English schoolboy, published a book You Can Do The Cube with its technology for solving CR. It sold about one and a half million copies in seventeen reprints and topped the bestseller list of the year!

IN last years Interest in the Cube has faded somewhat. Rapid development computer games significantly shook the entire industry board games and puzzles.

Erno Rubik himself practically retired, selling his name to the American company Tom Kremer in 1985 Seven towns, Ltd.

1.3. Varieties.

Pocket Cube (2x2)

Rubik's Cube (3x3)

Rubik's Revenge (4x4)

Professor's cube (5x5)

Rubik's triamide
A puzzle in the form of a three-dimensional triangle (consists of 10 diamond-shaped figures connected to each other by four crystals).

Hungarian rings.
The prototype of the puzzle was invented at the end of the 19th century by William Churchill; Erno Rubik (rings intersecting at an angle) and Endre Pap (flat version) also presented their versions. In our country, the puzzle was called "Magic Rings". It consists of two rings connected in the shape of a figure eight, filled with multi-colored (2-4 colors) balls. The balls move freely in the rings. The player's task was to create continuous sequences of balls of each color.
A similar puzzle, produced in Germany, was called Magic 8 (Magic Eight).

Rubik's snake.
The puzzle can be given different shape, since it consists of 24 prisms connected in series with hinges.

Rubik's brainchild(other puzzles created by Rubik).

Irregular Rubik's Cube.
A cube-shaped puzzle, the segments of which are made in the form of various trapezoids, can be assembled into three-dimensional multi-colored figures of the most bizarre shapes.

Corn or Traffic Light.
Patented by Endre Pap in 1982, it has a cylindrical shape, consisting of rows of disks (usually 4 to 7) with cuts forming vertical grooves in which colored balls are placed. The disks rotate freely relative to each other, one ball is missing, which makes it possible to swap the others. Purpose of the game- arrange the balls so that they form vertical rows of the same color.

There are two versions of the puzzle - with six balls various colors and with balls, which, in addition to six primary colors, also differ in shade. The second version of the puzzle is more difficult, since it is necessary to build vertical rows in increasing shade intensity.

Cubes of other sizes.

Meson.
Triple meson (represents several ordinary RCs connected together in a certain way).

Square (based on the method of connection and the number of connected cubes, they are distinguished: double meson, triple meson, Siamese cube, quartet, T-meson, Q-meson, etc.).
To solve it, you need to bring all available faces to your color).

Exclusive cubes.

Catfish cube.
The predecessor of the CR, invented by the Swedish scientist and writer Piet Hein, according to legend, during a lecture on quantum mechanics. The puzzle consists of 7 individual parts, from which you need to fold a 3x3x3 cube. There are 240 in total in various ways her decisions.

Cubes based on board games.

1.4. Rubik's cube in our time.

The peak of the popularity of the CD has passed, but since 1991, for several years, Kremer has tirelessly revived consumer interest and resumed the production of cubes. Finally, he succeeded. In 1996, 300 thousand cubes were sold in the USA, and in 1997 another 100 thousand in the UK. Sales turnover is increasing every year: in 2006, 5 million puzzles were already sold, and sales of 9 million are expected in 2007. Looking at these figures, we can say with confidence that the return of the Rubik's cube has taken place.

The US National Science Foundation awarded Northwestern University a grant of $200,000 to research the Rubik's Cube. The bulk of these funds will be used to purchase information storage systems with a total capacity of 20 TB. The researchers are going to record as many different states of the Rubik's Cube as possible.

The methods developed in the course of solving combinatorial problems will find application in a number of areas in the future (in business, they will help to optimally place goods on supermarket shelves).

George Helm– one of the most passionate people about puzzles (photo above);
The cube itself is periodically exhibited in one or another museum around the world, but does not yet have its own museum, except for photographs of private collections on the Internet. Maybe in the future the puzzle will have its own full-fledged museum.

Conclusion

I learned about the history of the creation and structure of the Rubik's Cube, as well as about its varieties and other puzzles, similar and dissimilar to it, and mastered the assembly.

I completed the task I set for myself and I advise everyone not to stop in the face of difficulties, but to look for a solution, because it is not so difficult!

Application

Today there are a huge number of varieties and modifications of the Rubik's Cube.

How to solve a Rubik's Cube

In a nutshell: if you remember 7 simple formulas of no more than 8 rotations each, then you can easily learn how to solve a regular 3x3x3 cube in a couple of minutes. This algorithm will not be able to solve the cube in less than a minute or a minute and a half, but two to three minutes is easy!

Introduction

Like any cube, the puzzle has 8 corners, 12 edges and 6 faces: top, bottom, right, left, front and back. Typically, each of the nine squares on each face of the Cube is colored one of six colors, usually arranged in pairs opposite each other: white-yellow, blue-green, red-orange, forming 54 colored squares. Sometimes instead of solid colors they put on the edge of the Cube, then it becomes even more difficult to assemble.

In the assembled (“initial”) state, each face consists of squares of the same color, or all the pictures on the faces are correctly folded. After several turns the cube is “stirred”.

Solving a Cube means returning it from being stirred to its original state. This, in fact, is the main point of the puzzle. Many enthusiasts find pleasure in assembling "solitaire" - patterns .

ABC of the Cube

The classic Cube consists of 27 parts (3x3x3=27):

6 single color centerpieces (6 “centers”)

12 two-color side or rib elements (12 “ribs”)

8 three-color corner elements (8 “corners”)

1 internal element- cross

The cross (or ball, depending on the design) is located in the center of the Cube. The centers are attached to it and thereby fasten the remaining 20 elements, preventing the puzzle from falling apart.

Elements can be rotated in “layers” - groups of 9 pieces. Rotating the outer layer clockwise by 90° (if you look at this layer) is considered “straight” and will be designated capital letter, and a counterclockwise turn is “reverse” to a straight line - and we will denote it with a capital letter with an apostrophe “"”.

6 outer layers: Top, Bottom, Right, Left, Front (front layer), Rear (back layer). There are three more inner layers. In this assembly algorithm, we will not rotate them separately; we will only use rotations of the outer layers. In the world of speedcubers, it is customary to make the designation with Latin letters from the words Up, Down, Right, Left, Front, Back.

Turn designations:

clockwise (↷ )- V N P L F T ⇔U D R L F B

counterclockwise (↶ ) - V" N" P" L" F" T" ⇔U" D" R" L" F" B"

When assembling the Cube, we will sequentially rotate the layers. The sequence of turns is recorded from left to right one after another. If some rotation of a layer needs to be repeated twice, then a degree icon “2” is placed after it. For example, F 2 means that you need to turn the front twice, i.e. F 2 = FF or F "F" (whichever is more convenient). In Latin notation, instead of F 2, F2 is written. I will write formulas in two notations - Cyrillic And Latin, separating them with this sign ⇔.

To make it easier to read long sequences, they are divided into groups, which are separated from neighboring groups by dots. If a certain sequence of turns needs to be repeated, then it is enclosed in parentheses and the number of repetitions is written at the top right of the closing bracket. In Latin notation, a multiplier is used instead of an exponent. In square brackets I will indicate the number of such a sequence or, as they are usually called, “formulas”.

Now, knowing the conventional language of notation for rotation of the layers of the Cube, you can proceed directly to the assembly process.

Assembly

There are many ways to assemble the Cube. There are those that allow you to assemble a cube with a couple of formulas, but in a few hours. Others, on the contrary, by memorizing a couple of hundred formulas allow you to solve a cube in ten seconds.

Below I will describe the simplest (from my point of view) method, which is visual, easy to understand, requires memorizing only seven simple “formulas” and at the same time allows you to assemble the Cube in a couple of minutes. When I was 7 years old, I mastered this algorithm in a week and solved the cube in an average of 1.5-2 minutes, which amazed my friends and classmates. That’s why I call this assembly method “the simplest.” I will try to explain everything “on the fingers”, almost without pictures.

We will assemble the Cube in horizontal layers, first the first layer, then the second, then the third. We will divide the assembly process into several stages. There will be five of them in total and one additional one.

6/26 At the very beginning, the cube is disassembled (but the centers are always in place).

Assembly steps:

10/26 - cross of the first layer (“upper cross”)

14/26 - corners of the first layer

16/26 - second layer

22/26 - cross of the third layer (“lower cross”)

26/26 - corners of the third layer

26/26 - (additional stage) rotation of centers

To assemble the classic Cube you will need the following: "formulas":

FV"PV ⇔FU"RU- rotation of the edge of the upper cross

(P"N" · PN) 1-5 ⇔(R"D RD)1-5- "Z-switch"

VP · V"P" · V"F" · VF ⇔UR · U"R" · U"F" · UF- edge 2 layers down and to the right

V"L" · VL · VF · V"F" ⇔U"L" · UL · UF · U"F"- edge 2 layers down and to the left

FPV · P"V"F" ⇔FRU R"U"F"- rotation of the ribs of the lower cross

PV · P"V · PV" 2 · P"V ⇔RU · R"U · RU"2 · R"U- rearrangement of the ribs of the lower cross (“fish”)

V"P" · VL · V"P · VL" ⇔U"R" UL U"R UL"- rearrangement of corners 3 layers

The first two stages could not be described, because Assembling the first layer is quite easy "intuitively". But, nevertheless, I will try to describe everything thoroughly and on my fingers.

Stage 1 - cross of the first layer (“upper cross”)

Target this stage: correct location 4 upper ribs, together with the upper center, forming a “cross”.

So, the Cube is completely disassembled. Actually not completely. Distinctive feature The classic Cube is its design. Inside there is a cross (or ball) that rigidly connects the centers. The center determines the color of the entire face of the Cube. Therefore, 6 centers are always already in place! First, choose the top. Typically, assembly begins with a white top and green front. For non-standard coloring, choose what is more convenient. We hold the Cube so that the upper center (“top”) is white, and the front center (“front”) is green. The main thing when assembling is to remember what color is the top and what is the front, and when rotating the layers, do not accidentally turn the entire Cube and get lost.

Our goal is to find an edge with top and front colors and place it between them. At the very beginning, we look for a white-green edge and place it between the white top and the green front. Let's call the required element a “working cube” or RK.

So, let's start assembling. The top is white, the front is green. We look at the Cube from all sides, without letting go of it, without moving it in our hands and without rotating the layers. We are looking for RK. It can be located anywhere. Found. After this, the assembly process itself begins.

If the RK is in the first (upper) layer, then by double turning the outer vertical layer on which it is located, we “drive” it down to the third layer. We do the same if the RK is in the second layer, only in this case we drive it down not with a double, but with a single rotation.

It is advisable to drive it out so that the color of the paint turns out to be the color of the top down, then it will be easier to install it in place. When driving the RK down, you need to remember about the ribs that are already in place, and if some edge was affected, then you need to remember to return it later to its place by reverse rotation.

After the RC is on the third layer, we rotate the bottom and “adjust” the RC to the center of the front. If the RK is already on the third layer, then simply place it in front of us from below, rotating the bottom layer. After this, turn F 2 ⇔F2 We put RK in place.

Once the RK is in place, there can be two options: either it is rotated correctly or not. If it is turned correctly, then everything is OK. If it is turned incorrectly, then we turn it over using the formula FV"PV ⇔FU"RU. If the RK is “kicked out” correctly, i.e. color from top to bottom, then you practically won’t have to use this formula.

Let's move on to installing the next rib. Without changing the top, we change the front, i.e. turn the Cube towards you with the new side. And we repeat our algorithm again until all the remaining edges of the first layer are in place, forming a white cross on the top edge.

During the assembly process, it may turn out that the RC is already in place, or it can be put in place (without destroying what has already been assembled) without first being driven down, but “immediately”. Well, good! In this case, the cross will come together faster!

So, already 10 elements out of 26 are in place: 6 centers are always in place and we have just placed 4 edges.

Stage 2 - corners of the first layer

The goal of the second stage is to assemble the entire top layer, installing four corners in addition to the already assembled cross. In the case of the cross, we looked for the right edge and placed it in front at the top. Now our RK is not an edge, but a corner, and we will place it in the front at the top right. To do this, we will do the same as at the first stage: first we will find it, then we will “drive” it to the bottom layer, then we will place it in the front lower right, i.e. under the place we need, and after that we’ll drive it up.

There is one wonderful and simple formula. (P"N" · PN) ⇔(R"D" RD). It even has a “smart” name - . She must be remembered.

We are looking for an element with which we will work (RK). The top right corner should contain a corner that has the same colors as the centers of the top, front and right. We find him. If the RK is already in place and turned correctly, then by turning the entire Cube we change the front and look for a new RK.

If the RC is in the third layer, then rotate the bottom and adjust the RC to the place we need, i.e. front lower right.

Let's turn the Z-switch! If the corner is not in place, or is in place, but is rotated incorrectly, then turn the Z switch again, and so on until the RK is at the top in place and correctly rotated. Sometimes you need to turn the Z-switch up to 5 times.

If the RK is in the upper layer and is not in place, then we drive it out of there with any other one using the same Z-commutator. That is, we first turn the Cube so that the top remains white, and the RK, which needs to be kicked out, is located at the top right in front of us and turn the Z-commutator. After the RK has been “kicked out,” we again turn the Cube towards us with the desired front, rotate the bottom, place the already kicked out RK under the place we need and use the Z-commutator to drive it to the top. We turn the Z-switch until the cube is oriented correctly.

We apply this algorithm for the remaining corners. As a result, we get a fully assembled first layer of the Cube! 14 out of 26 cubes are still in place!

Let's admire this beauty for a while and turn the Cube over so that the collected layer is at the bottom. Why is this necessary? We will soon need to start assembling the second and third layers, and the first layer has already been assembled and is in the way on top, covering all the layers that interest us. Therefore, let’s turn them upside down to better see all the remaining and uncollected disgrace. Top and bottom changed places, right and left too, but the front and rear remained the same. The top is now yellow. Let's start assembling the second layer.

I want to warn you that with each step the Cube becomes more assembled, but when you twist the formulas, the already assembled sides are stirred. The main thing is not to panic! At the end of the formula (or sequence of formulas), the cube will be assembled again. If, of course, you follow the main rule - during the rotation process you cannot spin the entire Cube, so as not to accidentally get lost. Only separate layers, as written in the formula.

Stage 3 - second layer

So, the first layer is assembled, and it's at the bottom. We need to put 4 ribs of the 2nd layer. They can now be located both on the second and on the third (now upper) layer.

Select any edge on the top layer without the color of the top face (without yellow). Now it will be our RK. By rotating the top, we adjust the RC so that it matches the color of some side center. We rotate the Cube so that this center becomes the front.

Now there are two options: our working cube needs to be moved down to the second layer, either to the left or to the right.

There are two formulas for this:

down and right VP · V"P" · V"F" · VF ⇔UR · U"R" · U"F" · UF

down and left V"L" · VL · VF · V"F" ⇔U"L" · UL · UF · U"F"

If suddenly the RK is already in the second layer out of place, or in its place, but incorrectly rotated, then we “kick it out” with any other one, using one of these formulas, and then apply this algorithm again.

Be careful. The formulas are long, you can’t make mistakes, otherwise the Cube will “figure it out” and you’ll have to start assembling again. It's okay, even champions sometimes get confused during assembly.

As a result, after this stage we have two assembled layers - 19 out of 26 cubes are in place!

(If you want to slightly optimize the assembly of the first two layers, you can use this.)

Stage 4 - cross of the third layer (“lower cross”)

The goal of this stage is to assemble the cross of the last unassembled layer. Although the unassembled layer is now on top, the cross is called "bottom" because in its original state this layer was at the bottom.

First, we will unfold the edges so that they all face up in a color that matches the color of the top. If they are already all turned up so that at the top you get a single-color flat cross, we proceed to moving the edges. If the cubes are turned incorrectly, we will turn them over. There can be several cases of edge orientation:

A) all are turned incorrectly

B) two adjacent ones are incorrectly rotated

C) two opposite ones are turned incorrectly

(There cannot be other options! That is, it cannot be that there is only one edge left to turn over. If two layers of the cube are completed, and on the third there is an odd number of edges left to turn over, then you don’t have to worry about it any further, but.)

Let's remember the new formula: FPV · P"V"F" ⇔FRU R"U"F"

In case A) we twist the formula and get case B).

In case B) we turn the Cube so that two correctly rotated edges are on the left and behind, twist the formula and get case C).

In case B), we turn the Cube so that the correctly rotated edges are on the right and left, and, again, we twist the formula.

As a result, we get a “flat” cross of correctly oriented, but out of place edges. Now you need to make a correct volumetric cross from a flat cross, i.e. move the ribs.

Let's remember the new formula: PV · P"V · PV" 2 · P"V ⇔RU · R"U · RU"2 · R"U(“fish”)

We twist the top layer so that at least two edges fall into place (the colors of their sides coincide with the centers of the side faces). If everything falls into place, then the cross is assembled, we move on to the next stage. If not everything is in place, then there can be two cases: either two adjacent ones are in place, or two opposite ones are in place. If the opposite ones are in place, then we twist the formula and get the adjacent ones in place. If the neighboring ones are in place, then we turn the Cube so that they are on the right and behind. Let's twist the formula. After this, the ribs that were out of place will change places. The cross is assembled!

NB: a small note about the “fish”. This formula uses rotation AT 2 ⇔U"2, that is, we rotate the top counterclockwise twice. Basically, for the Rubik's Cube AT 2 ⇔U"2 = AT 2 ⇔U2, but it’s better to remember exactly AT 2 ⇔U"2, because this formula can be useful for assembling, for example, Megaminx. But in Megaminx AT 2 ⇔U"2 ≠ AT 2 ⇔U2, since one turn there is not 90°, but 72°, and AT 2 ⇔U"2 = AT 3 ⇔U3.

Stage 5 - corners of the third layer

All that remains is to install it in place, and then turn the four corners correctly.

Let's remember the formula: V"P" · VL · V"P · VL" ⇔U"R" UL U"R UL" .

Let's look at the corners. If they are all in place and all that remains is to turn them correctly, then look at the next paragraph. If not a single corner is in place, then twist the formula, and one of the corners will definitely fall into place. We are looking for a corner that stands still. We turn the Cube so that this corner is at the back right. Let's twist the formula. If the cubes do not fall into place, then twist the formula again. After this, all the corners should be in place, all you have to do is turn them correctly, and the Cube will be almost solved!

At this stage, it remains to either turn three cubes clockwise, or three counterclockwise, or one clockwise and one counterclockwise, or two clockwise and two counterclockwise. There can be no other options! Those. It cannot be that there is only one corner cube left to turn over. Or two, but both clockwise. Or two clockwise and one counterclockwise. Correct combinations: (- - -), (+ + +), (+ -), (+ - + -), (+ + - -) . If two layers are assembled correctly, the correct cross is assembled on the third layer and the wrong combination is obtained, then again you can no longer worry, but go get a screwdriver (read). If everything is correct, read on.

Let's remember our Z-commutator (P"N" · PN) ⇔R"D" RD. Rotate the Cube so that the incorrectly oriented corner is in the front right. Rotate the Z-switch (up to 5 times) until the angle turns correctly. Next, without changing the front, we rotate the top layer so that the front right is the next “wrong” corner, and again rotate the Z-commutator. And we do this until all the corners are turned. After this, we will rotate the top layer so that the colors of its edges match the already assembled first and second layers. All! If we had a regular six-color cube, then it is already solved! It remains to turn the Cube with its original top (which is now bottom) up to get the initial state.

All. The cube is complete!

I hope you find this guide useful!

Stage 6 - Rotation of centers

Why won't the cube assemble?!

Many people ask the question: “I do everything as written in the algorithm, but the cube still doesn’t fit. Why?" Usually an ambush awaits on the last layer. Two layers are easy to put together, but the third is not easy. Everything is stirred, you begin to reassemble, again two layers, and again when assembling the third, everything is stirred. Why might this be so?

There are two reasons - obvious and not so obvious:

Obvious. You are not following the algorithms exactly. It is enough to make one turn in the wrong direction or miss a turn for the entire Cube to get mixed up. On initial stages(when assembling the first and second layers) an incorrect turn is not very fatal, but when assembling the third layer, the slightest mistake leads to complete mixing of all assembled layers. But if you strictly follow the assembly algorithm described above, then everything should come together. The formulas are all time-tested, there are no errors in them.

Not very obvious. And most likely this is exactly the point. Chinese manufacturers make Cubes of varying quality - from professional championship cubes for quick assembly to those that fall apart in your hands at the very first spins. What do people usually do if the Cube falls apart? Yes, they put back the fallen cubes, and don’t worry about how they were oriented and in what place they stood. But you can’t do that! Or rather, it is possible, but the likelihood of solving a Rubik's Cube after this will be extremely small.

If the Cube fell apart (or, as speedcubers say, “gotten”) and was assembled incorrectly, then When assembling the third layer, problems will most likely arise. How to solve this problem? Take it apart again and put it back together correctly!

On a cube with two layers assembled, you need to carefully pry up the lid of the central cube of the third layer with a flat screwdriver or a knife, remove it, unscrew the screw with a small Phillips screwdriver, without losing the spring attached to the screw. Carefully pull out the corner and side cubes of the third layer and insert them correctly color to color. At the end, insert and screw the previously unscrewed central cube (do not tighten too much). Twist the third layer. If it turns tightly, loosen the screw; if it turns too easily, tighten it. It is necessary that all faces rotate with the same force. After this, close the lid on the central cube. All.

Without unscrewing, you can rotate any edge by 45°, pry one of the side cubes with your finger, knife or flat screwdriver and pull it out. You just need to do this carefully, because you can break the cross. Then, one by one, pull out the necessary cubes and insert them back into their places, now correctly oriented. After everything is assembled color by color, you will also need to insert (snap) the side cube that you pulled out at the beginning (or some other, but side cube, since inserting a corner cube definitely won’t work).

After this, the Cube can be mixed and calmly assembled using the above algorithm. And now he’ll definitely get it together! Unfortunately, you cannot do without such “barbaric” procedures with a knife and a screwdriver, since if, after falling apart, the Cube is folded incorrectly, it will not be possible to assemble it by rotation.

PS: if you can’t assemble even two layers, then first you need to make sure that at least the centers are in the right places. Perhaps someone rearranged the center caps. The standard coloring should have 6 colors, white opposite yellow, blue opposite green, red opposite orange. Usually the top is white, the bottom is yellow, the front is orange, the back is red, the right is green, the left is blue. But the relative position of the colors is absolutely determined by the corner cubes. For example, you can find a corner white-blue-red and see that the colors in it are arranged clockwise. This means that if there is white on top, then there should be blue on the right and red on the front.

PPS: if someone made a joke and not only rearranged the elements of the cube, but re-glued the stickers, then it is generally impossible to assemble the Cube, no matter how much you destroy it. No screwdriver will help here. You need to figure out which stickers were re-glued, and then re-glue them in their places.

Could it be even simpler?

Well, how much easier is it? This is one of the simplest algorithms. The main thing is to understand him. If you want to pick up a Rubik's Cube for the first time and immediately learn how to solve it in a couple of minutes, then it is better to put it aside and do something less intellectual. Any learning, including the simplest algorithm, requires time and practice, as well as brains and perseverance. As I said above, I mastered this algorithm myself in a week, when I was 7 years old, and I was on sick leave with a sore throat.

This algorithm may seem complicated to some because it contains many formulas. You can try using some other algorithm. For example, you can assemble a Cube using one single formula, for example the same Z-commutator. But collecting this way will take a long, long time. You can take another formula, for example, F · PV"P"V"·PVP"F"·PVP"V"·P"FPF", which swaps 2 side and 2 corner cubes in pairs. And using simple preparatory rotations, gradually collect cube, putting all the side cubes in place first, and then the corner ones.

There are a huge bunch of algorithms, but each of them must be approached with due attention, and each requires enough time to master.