Hummingbird and Cumbria Rubik's Cube. Simple rules for solving a Rubik's cube

The human intellect needs constant training no less than the body needs physical activity. The best way develop and expand the abilities of this mental quality - to solve crosswords and solve puzzles, the most famous of which, of course, is the Rubik's cube. However, not everyone manages to collect it. Knowledge of diagrams and formulas for solving the assembly of this intricate toy will help you cope with this task.

What is a puzzle toy

A mechanical cube made of plastic, the outer edges of which consist of small cubes. The size of the toy is determined by the number of small elements:

2 x 2;
3 x 3 (the original version of the Rubik's cube was exactly 3 x 3);
4 x 4;
5 x 5;
6 x 6;
7 x 7;
8 x 8;
9 x 9;
10 x 10;
11 x 11;
13 x 13;
17 x 17.

Any of the small cubes can rotate in three directions along axes represented in the form of protrusions of a fragment of one of the three cylinders of the large cube. This way the structure can rotate freely, but small parts do not fall out, but hold on to each other.

Each face of the toy includes 9 elements, painted in one of six colors, located opposite each other in pairs. The classic combination of shades is:

red opposite orange;
white is opposite yellow;
blue is opposite green.

However, modern versions can be painted in other combinations.

Today you can find Rubik's cubes of different colors and shapes.

This is interesting. The Rubik's cube even exists in a version for the blind. There, instead of color squares, there is a relief surface.

The goal of the puzzle is to arrange the small squares so that they form the edge of a large cube of the same color.

History of appearance

The idea of the creation belongs to the Hungarian architect Erna Rubik, who, in fact, did not create a toy, but a visual aid for his students. So in an interesting way The resourceful teacher planned to explain the theory of mathematical groups (algebraic structures). This happened in 1974, and a year later the invention was patented as a puzzle toy - future architects (and not only them) became so attached to the intricate and colorful manual.

The release of the first series of the puzzle was timed to coincide with the new year of 1978, but the toy came into the world thanks to entrepreneurs Tibor Lakzi and Tom Kremer.

This is interesting. Since its introduction, the Rubik's cube ("magic cube", "magic cube") has sold about 350 million copies worldwide, making the puzzle the number one most popular toy. Not to mention dozens computer games, based on this assembly principle.

The Rubik's Cube is an iconic toy for many generations

In the 80s, residents of the USSR became acquainted with the Rubik's cube, and in 1982, the first world championship in speed puzzle assembly - speedcubing - was organized in Hungary. Then best result was 22.95 seconds (for comparison: a new world record was set in 2017: 4.69 seconds).

This is interesting. Fans of solving colorful puzzles are so attached to the toy that speed-assembling competitions alone are not enough for them. Therefore in recent years Championships for solving puzzles with closed eyes, one hand, and feet appeared.

What are the formulas for the Rubik's cube

To assemble a magic cube means to arrange all the small parts so that you get a whole face of the same color, you need to use God's algorithm. This term refers to a set of minimum actions that will solve a puzzle that has a finite number of moves and combinations.

This is interesting. In addition to the Rubik's cube, God's algorithm is applied to such puzzles as Meffert's pyramid, Taken, Tower of Hanoi, etc.

Since the magic Rubik's cube was created as a mathematical tool, its assembly is laid out according to formulas.

Solving a Rubik's cube is based on the use of special formulas

Important Definitions

In order to learn to understand the schemes for solving a puzzle, you need to become familiar with the names of its parts.

An angle is a combination of three colors. In the 3 x 3 cube there will be 3 of them, in the 4 x 4 version there will be 4, etc. The toy has 12 corners.
An edge represents two colors. There are 8 of them in a cube.
The center contains one color. There are 6 of them in total.
The faces, as already mentioned, are simultaneously rotating puzzle elements. They are also called “layers” or “slices”.

Values in formulas

It should be noted that the assembly formulas are written in Latin - these are the diagrams that are widely presented in various manuals for working with the puzzle. But there are also Russified versions. The list below contains both options.

The front face (front or façade) is the front face, which is the color facing us [F] (or F - front).
The back face is the face that is centered away from us [B] (or B - back).
Right Face - the face that is on the right [P] (or R - right).
Left Face - the face that is on the left [L] (or L - left).
Bottom Face - the face that is at the bottom [H] (or D - down).
Top Face - the face that is at the top [B] (or U - up).

Photo gallery: parts of the Rubik's cube and their definitions

To explain the notation in the formulas, we use the Russian version - it will be clearer for beginners, but for those who want to switch to professional level speedcubing without an international notation system English can't get by.

This is interesting. International system designation adopted by the World Cube Association (WCA).

The central cubes are indicated in the formulas of one lowercase letter- f, t, p, l, v, n.
Angular - three letters according to the name of the edges, for example, fpv, flni, etc.
Capital letters F, T, P, L, V, N denote the elementary operations of rotating the corresponding face (layer, slice) of the cube 90° clockwise.
The designations F", T", P", L", V", N" correspond to the rotation of the faces by 90° counterclockwise.
The designations Ф 2, П 2, etc. indicate a double rotation of the corresponding face (Ф 2 = ФФ).
The letter C indicates the rotation of the middle layer. The subscript indicates which face should be viewed from in order to make this turn. For example, C P - from the right side, C N - from the bottom side, C "L - from the left side, counterclockwise, etc. It is clear that C N = C " B, C P = C " L and etc.
The letter O is a rotation (turn) of the entire cube around its axis. O F - from the side of the front edge clockwise, etc.

Recording the process (Ф "П") Н 2 (ПФ) means: rotate the front face counterclockwise by 90°, the same - the right edge, rotate the bottom edge twice (that is, 180°), rotate the right edge 90° along clockwise, rotate the front edge 90° clockwise.
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http://dedfoma.ru/kubikrubika/kak-sobrat-kubik-rubika-3x3x3.htm

It is important for beginners to learn to understand formulas

As a rule, the instructions for assembling a puzzle in classic colors recommend holding the puzzle with the yellow center facing up. This advice is especially important for beginners.

This is interesting. There are sites that visualize formulas. Moreover, the speed of the assembly process can be set independently. For example, alg.cubing.net

How to solve a Rubik's puzzle

There are two types of schemes:

for beginners;
for professionals.

Their difference is in the complexity of the formulas, as well as the speed of assembly. For beginners, of course, instructions appropriate to their level of puzzle proficiency will be more useful. But after practice, they too will be able to fold the toy in 2–3 minutes.

How to solve a standard 3 x 3 cube

Let's start by solving the classic 3 x 3 Rubik's cube using a 7-step diagram.

The classic version of the puzzle is the 3 x 3 Rubik's Cube

This is interesting. The reverse process used to solve certain misplaced cubes is the reverse sequence of the action described by the formula. That is, the formula must be read from right to left, and the layers must be rotated counterclockwise if direct movement was specified, and vice versa: direct if the opposite is described.

Step-by-step assembly instructions

We start by assembling the cross on the top edge. We lower the desired cube down by rotating the corresponding side face (P, T, L) and bring it to the front face using the operation H, N" or H 2. We finish the removal stage with a mirror rotation (reverse) of the same side face, restoring the original position of the affected rib cube of the upper layer. After this, we carry out operation a) or b) of the first stage. In case a) the cube has reached the front face so that the color of its front face coincides with the color of the front. In case b) the cube must not only be moved to the top, but also rotated. , so that it is correctly oriented, falling into place.
Collecting the top line cross
The required corner cube is found (having the colors of the faces F, B, L) and, using the same technique described for the first stage, is brought to the left corner of the selected front face (or yellow). There are three possible orientations for this cube. We compare our case with the figure and apply one of the operations of the second stage a, beat c. The dots on the diagram mark the place where the desired cube should go. We find the remaining three corner cubes on the cube and repeat the described technique to move them to their places on the top face. Result: the top layer has been selected. The first two stages cause almost no difficulties for anyone: you can quite easily monitor your actions, since all attention is paid to one layer, and what is done in the remaining two is not at all important.
Selecting the top layer
Our goal: to find the desired cube and first bring it down to the front face. If it is at the bottom, simply turn the bottom edge until it matches the color of the facade, and if it is in the middle layer, then you must first lower it down using any of operations a) or b), and then match it in color with the color of the facade edge and perform the third stage operation a) or b). Result: two layers are collected. The formulas given here are mirror ones in the full sense of the word. You can clearly see this if you place a mirror to the right or left of the cube (edge facing you) and do any of the formulas in the mirror: we will see the second formula. That is, operations with the front, bottom, top (not involved here), and back (also not involved) faces change their sign to the opposite: it was clockwise, it became counterclockwise, and vice versa. And the left side changes from the right, and, accordingly, changes the direction of rotation to the opposite.
We find the desired cube and bring it down to the front face
Operations that move the side cubes of one face without ultimately disturbing the order in the assembled layers lead to the goal. One of the processes that allows you to select all the side faces is shown in the figure. It also shows what happens to the other cubes of the face. By repeating the process, choosing another front face, you can put all four cubes in place. Result: The rib pieces are in place, but two of them, or even all four, may be oriented incorrectly. Important: before you start executing this formula, look at which cubes are already in place - they may be oriented incorrectly. If there is none or one, then we try to rotate the top face so that the two located on two adjacent side faces (fv+pv, pv+tv, tv+lv, lv+fv) fall into place, after which we orient the cube like this , as shown in the figure, and execute the formula given at this stage. If it is not possible to combine the parts belonging to adjacent faces by rotating the top face, then we perform the formula for any position of the cubes of the top face once and try again by rotating the top face to put in place 2 parts located on two adjacent side faces.
It is important to check the orientation of the cubes at this stage
We take into account that the unfolded cube must be on the right side; in the figure it is marked with arrows (pv cube). Figures a, b, and c show possible cases locations of incorrectly oriented cubes (marked with dots). Using the formula in case a), we perform an intermediate rotation B" to bring the second cube to the right side, and a final rotation B, which will return the top face to its original position, in case b) an intermediate rotation B 2 and the final one also B 2, and in case c) intermediate rotation B must be performed three times, after turning over each cube, and also completed with rotation B. Many people are confused by the fact that after the first part of the process (PS N) 4, the desired cube is unfolded as it should, but the order in the assembled layers is disrupted. confusing and makes some people throw the almost completed cube halfway. Having performed an intermediate turn, not paying attention to the “breakage” of the lower layers, we perform operations (PS N) 4 with the second cube (the second part of the process), and everything falls into place. Result: the cross is assembled.
The result of this stage will be an assembled cross
We put the corners of the last face into place using an 8-step process, convenient for memorizing - a straight line that rearranges three corner details in a clockwise direction, and the reverse, rearranging the three cubes in a counterclockwise direction. After the fifth stage, as a rule, at least one cube will sit in its place, albeit in the wrong direction. (If after the fifth stage none of the corner cubes are in their place, then we apply any of the two processes for any three cubes, after which exactly one cube will be in its place.). Result: All corner cubes are in place, but two (or maybe four) of them may be oriented incorrectly.
Corner cubes sit in place
We repeat the sequence of turns PF"P"F many times. We rotate the cube so that the cube we want to expand is in the upper right corner of the facade. An 8-turn process (2 x 4 turns) will turn it 1/3 turn clockwise. If the cube has not yet oriented itself, we repeat the 8-move move again (in the formula this is reflected by the index “N”). We do not pay attention to the fact that the lower layers will become disordered. The figure shows four cases of incorrectly oriented cubes (they are marked with dots). In case a) an intermediate turn B and a final turn B are required, in case b) - an intermediate and final turn B 2, in case c) - turn B is performed after turning each cube to the correct orientation, and the final turn B 2, in case d) - intermediate rotation B is also performed after turning each cube to the correct orientation, and the final one in this case will also be rotation B. Result: the last face is assembled.
Possible errors are shown by dots

Formulas for correcting the placement of cubes can be shown as follows.

Formulas for correcting incorrectly oriented cubes at the last stage

The essence of the Jessica Friedrich method

There are several ways to assemble the puzzle, but one of the most memorable is the one developed by Jessica Friedrich, a professor at the University of Binghamton (New York), who is developing techniques for hiding data in digital images. While still a teenager, Jessica became so interested in the cube that in 1982 she became the world champion in speedcubing and subsequently did not abandon her hobby, developing formulas for quickly assembling a “magic cube.” One of the most popular options for folding a cube is called CFOP - after the first letters of the four assembly steps.

Instructions:

We assemble a cross on the top face, which is made up of cubes on the edges of the bottom face. This stage is called Cross.
We assemble the bottom and middle layers, that is, the edge on which the cross is located, and the intermediate layer, consisting of four side parts. The name of this step is F2L (First two layers).
We assemble the remaining edge, not paying attention to the fact that not all the parts are in place. The stage is called OLL (Orient the last layer), which translates as “orientation of the last layer.”
The last level - PLL (Permute the last layer) - consists of the correct placement of the cubes of the top layer.

Video instructions for the Friedrich method

The method that was proposed by Jessica Friedrich was so liked by speedcubers that the most advanced amateurs are developing their own methods to speed up the assembly of each of the stages proposed by the author.

Video: speeding up the assembly of the cross

Video: assembling the first two layers

Video: working with the last layer

Video: last level of assembly by Friedrich

2 x 2

A 2 x 2 Rubik's cube or mini Rubik's cube is also folded in layers, starting from the bottom level.

Mini cube is a light version of the classic puzzle

Beginner's instructions for easy assembly

We assemble the bottom layer so that the colors of the last four cubes match, and the remaining two colors are the same as the colors of the adjacent parts.
Let's start organizing the top layer. Please note that on at this stage The goal is not to match the colors, but to put the cubes in their places. We start by determining the color of the top. Everything is simple here: this will be the color that did not appear in the bottom layer. Rotate any of the top cubes so that it gets to the position where the three colors of the element intersect. Having fixed the angle, we arrange the remaining elements. For this we use two formulas: one for changing diagonal cubes, the other for neighboring ones.
We complete the top layer. We carry out all operations in pairs: we rotate one corner, and then the other, but in the opposite direction (for example, the first one clockwise, the second one counterclockwise). You can work with three angles at once, but in this case there will be only one combination: either clockwise or counterclockwise. Between rotations of the corners, rotate the top edge so that the corner being worked is in the upper right corner. If we are working with three corners, then place the correctly oriented one at the back left.

Formulas for rotating angles:

(VFPV · P"V"F")² (5);
V²F·V²F"·V"F·V"F"(6);
VVF² · LFL² · VLV² (7).

To rotate three corners at once:

(FVPV"P"F"V")² (8);
FV·F"V·FV²·F"V² (9);
V²L"V"L²F"L"F²V"F" (10).

Photo gallery: 2 x 2 cube assembly

Video: Friedrich method for 2 x 2 cube

Collecting the most difficult versions of the cube

These include toys with a number of parts from 4 x 4 and up to 17 x 17.

Cube models with many elements usually have rounded corners for ease of manipulation with the toy

This is interesting. A 19 x 19 version is currently being developed.

It should be remembered that they were created on the basis of a 3 x 3 cube, therefore the assembly is built in two directions.

We assemble the center so that the elements of the 3 x 3 cube remain.
We work according to the diagrams for assembling the initial version of the toy (most often cubers use Jessica Friedrich’s method).

4 x 4

This version is called "Rubik's Revenge".

Instructions:

The assembly of models 5 x 5, 6 x 6 and 7 x 7 is similar to the previous one, only we take the center as a basis more cubes.

Video: solving a Rubik's cube 5 x 5

Working on solving a 6 x 6 puzzle

This cube is quite inconvenient to use: large number requires small parts special attention. Therefore, we will divide the video instructions into four parts: for each stage of assembly.

Video: how to assemble the center of a 6 x 6 cube, part 1

Video: pairing edge elements in a 6 x 6 cube, part 2

Video: pairing four elements in a 6 x 6 puzzle, part 3

Video: final solving of the Rubik's cube 6 x 6, part 4

Video: putting together a 7 x 7 puzzle

How to solve the pyramid puzzle

This puzzle is mistakenly considered a type of Rubik's cube. But in fact, Meffert’s toy, which is also called the “Japanese tetrahedron” or “Moldavian pyramid,” appeared several years earlier than the visual aid of the teacher-architect.

Meffert's pyramid is mistakenly called a Rubik's puzzle

To work with this puzzle, it is important to know its structure, because the operating mechanism plays a key role in assembly. The Japanese tetrahedron consists of:

four axis elements;
six ribs;
four corners.

Each axle part has small triangles facing three adjacent faces. That is, each element can be rotated without the threat of it falling out of the structure.

This is interesting. There are 75,582,720 options for the arrangement of pyramid elements. Unlike the Rubik's cube, it's not that big of a deal. Classic version puzzles number 43,252,003,489,856,000 possible options configurations.

Instructions and diagram

Video: a simple method for assembling the entire pyramid

Method for children

Using formulas and using methods to speed up the assembly will be too difficult for children just starting out with the puzzle. Therefore, the task of adults is to simplify the explanation as much as possible.

The Rubik's Cube is not only an opportunity to keep your child busy with a useful and interesting activity, but also a way to develop patience and perseverance.

This is interesting. It is better to start teaching children with the 3 x 3 model.

Instructions (3 x 3 cube):

Decide on the color of the top edge and take the toy so that the central cube desired color was at the top.
We assemble the top cross, but the second color of the middle layer was the same as the color of the side edges.
We set the corners of the top edge. Let's move on to the second layer.
We collect last layer, but we start by restoring the sequence of the first ones. Then we set the corners so that they coincide with the central details of the edges.
We check the location of the middle parts of the last face, changing their location if necessary.

Solving a Rubik's cube in any of its variations is a great workout for the mind, a way to relieve stress and distract yourself. Even a child can learn to solve a puzzle using age-appropriate explanations. Gradually, you can master more intricate assembly methods, improve your own time indicators, and then you’re not far from speedcubing competitions. The main thing is persistence and patience.

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So, you have already read the introductory part and are ready to start solving the Rubik's cube!

At this stage (step 1), the most important thing is to understand the principle of assembling the cube, select the starting side and assemble a cross on it.

Step 1: Gather a cross on the starting side

Start side- this is the side from which assembly begins. When the first layer is solved, it will be assembled and all the colors on it will match.

You can choose the starting side of any color. Sometimes when choosing the starting side (especially when collecting on minimum quantity rotations) before assembling, look at which color is more profitable to start with. In speed assembly, they usually always start with the same one, for example, always with white.

Usually, when I solve a Rubik's cube, I start solving it from the white side, I'm just used to it, and among speedcubers it is believed that with white it is most profitable to start, because white is the brightest color and is easier to find with your eyes on a disassembled cube. In fact, it doesn’t matter at all to you what color you start with; I would even recommend starting from different sides at first in order to focus on the method, and not on the colors.

So, choose the color of the starting side. The first time, let it be white so that you don’t get confused with the algorithms, since I will show all the pictures for the case when the initial side is white.

Find the side of the Rubik's Cube with the white center. This is where the white side will be.

As you can see in the original drawing, the final goal of this step is a assembled white cross with four side elements containing white. But not everything is so simple, you also need to the second color of each white side piece matched the color of the center of the sides.

There are people who can solve the cross themselves without a technique. Therefore, if you wish, try to assemble the cross yourself.

If you can't collect correct cross, try to assemble the wrong white cross first, without the side stickers matching the centers. Just a white cross.

Then all you have to do is swap either 2 adjacent or 2 opposite side elements. How to change them is written at the end of this page.
If you can’t assemble the cross even without a match, then read on...

Method of assembling the cross

You may ask why I didn’t just give instructions right away, but suggested that we try it ourselves first? The fact is that there is no such technique for collecting the cross! There is a very large degree of freedom; if you painstakingly install piece by piece, then you need to write a large methodology for this, and the assembly will be slow. If you were able to come up with the idea of the cross yourself, then, most likely, you yourself will develop for yourself in the future some kind of instruction in the subconscious that you will follow.

Cube solving champions solve the cross this way: they are given 15 seconds before assembly (preinspection time), during which they can examine the cube and choose the most advantageous start. During these 15 seconds, they calculate how they will assemble the cross. And when the assembly itself begins, it takes 1.5 - 2 seconds to complete the cross!

Therefore, I will not give a complete methodology, but simply various cases with their descriptions, and how to solve them:

The cross consists of 4 movable side elements that need to be assembled around a white center (the white center does not move). These elements on a shuffled cube can be anywhere, but in any case they are side elements, and you can easily find them (side elements containing white). Now I will give examples of how to different cases make sure they fall into place.

At this stage, we do not pay attention to other elements of the cube, namely the side ones without white color and any corner ones. You need to assemble exactly the white cross and for this we mentally divide the cube into 3 layers.

Before you start assembling the cross, look at the side where the white center is, it is possible that next to the white center there is already a side element with white, as in the picture.

In this case, we just need to rotate the top edge IN, so that the side color of the element matches the side center. The remaining options for the case when there is white are similar. Just turn the top until the color matches

If there are already two or more side elements with white on the initial side, then rotate the top until the side centers coincide with greatest number elements.

Now let's move on to typical cases. The important thing here is not to memorize cases, but to understand the logic of the process, then you will remember everything without effort.

Examples:

A: The element is in the first layer

Image	Algorithm	Explanation
	P' V P V'	The piece is unfolded correctly, but is out of place. First you need to understand where “his” place is. Its place is where the orange side center is. In our case, the piece needs to go to the back plane, since the orange one is located opposite the red center. Therefore, we make the algorithm P’ V P V’. The logic here is this: we lower this piece into the 2nd layer, then turn the top so that its place is exactly where the piece was, and return the piece to the top layer. Then we move the top layer back so that everything falls into place.
	P' V' F' V	The piece is turned incorrectly, that is, not white at the top, and it must be moved to another place (in our case, to the left plane. We do the same as in the previous case, lower this piece into the 2nd layer, then turn the top so that when returning the piece, already unfolded correctly, it is in its place and then we return the top to its original position.

B: the element is in the second layer

B: The element is in the third layer

Image	Algorithm	Explanation
	H2 Z2	The piece with white and green colors (the white is not visible, it is at the bottom) must be moved from the third layer to the first. In this case, when white is in the lower plane, moving it to the upper plane is very simple, you just need to do a double 180-degree rotation of the side plane in which it is located. But before that, we will first transfer it to where it will go exactly to its place. We rotate the lower plane 180 so that it is under its place, then the rear plane 180 degrees.
	1. N’ F’ P F 2. P V F’ V’	In this case, the white piece is more difficult to move to the top layer because it is not deployed correctly.

How to make a correct cross from an incorrect one (so that all the side colors coincide with the corresponding centers)

You have assembled a white cross and see that not all the colors on the sides match. Rotate the top side and see what matches. At least 2 colors must match. When you find that two colors match, but the other 2 do not, then, therefore, you need to swap the other 2 colors.

There are only 2 cases possible:

Having learned how to assemble a cross, take the cube apart again and try a couple more times to assemble the cross yourself in white or any other color, and then move on to.

Which you have taken apart and want to reassemble. You will solve the cube according to Mikhail Rostovikov's technique. This technique contains 15 formula-algorithms taken from the high-speed assembly technique. These formulas are designed for the assembly of the 3rd (last) layer. The technique is more advanced than most basic options, and having studied this method, you can quickly switch to Jessica Friedrich’s speed method.

Purpose of the assembly (solve the puzzle)

Before you start solving the cube, read this material very carefully. Further training will depend on how you understand it.

How is the cube made?

The cube is designed very cleverly and at first glance it seems that all its parts are somehow attached to each other. But this is not entirely true. Only the central elements of each side are fixed, the side elements (cubes) are held on them, and the corner cubes are held on the side elements, and the corner and side elements are not connected to anything.

Central elements (6 pieces)- elements located in the middle of each of the 6 faces. Notice that no matter how you rotate the cube, they never change their position relative to the other central elements. The center element determines the color of the side of the cube because it doesn't move. If the central element is yellow, then on this side of the cube there will be exactly the yellow side. The same goes for all other colors. When in my explanations I say “keep the cube with the yellow side up,” and you still haven’t solved it, this means you need to hold the cube with the yellow center up.

Corner elements (8 pieces)— elements standing at the corners of the cube. They have three faces, each face a different color, and they always remain corner elements regardless of rotation.

Lateral (rib, side) elements (12 pieces)— elements standing on the edge side of the cube. They have two colors and always remain side elements (cubes). There is no way you can put a corner cube in the place of a side cube or vice versa. Some people sometimes try to do this...

Also note that any stickers placed on the surface of the cube always remain on the surface. No color ever leaves the inside of the cube! The colors on any element taken always remain on their element. An element cannot be “split” into its components in any way. Maybe with a hammer...

Concept of formula, algorithm or sequence

An algorithm is any sequence of rotations that causes something to change in the position on the die. If you perform the same algorithm several times, then after a certain number of repetitions the cube will return to its original state.

Examples of algorithms (rotation formulas):

P V P’ V’
L V L V2
F' P V P'

Don't worry about the fact that you don't understand anything about these notes yet. I’ll explain in more detail below how to decipher the algorithms. We are now talking about algorithms, which can be longer (for example, 15-16 moves), or they can be short, even one movement of some edge is also an algorithm.

What is the “layer-by-layer assembly method”?

This is a technique where the process of solving a cube is divided into 3 main parts: first layer, second layer and third layer.

View of a Rubik's cube with the first layer assembled.

View of a Rubik's cube with the first and second layers assembled.

A view of a “Rubik’s cube” with three layers assembled - that is, the puzzle is solved, the cube is assembled.

Start side- the side from which the solution begins. This is the side that is completely assembled when the first layer is solved. In the picture where the 1st layer is assembled, it is white.

End side- the side opposite to the initial one - in our case, yellow.

Well, you already know the basic concepts. Now is the time to understand how to read spin language"Rubik's cube". This is important because without it you will not understand anything in the notes.

How to read the formulas of the Rubik's Cube rotation language?

The language of rotations is necessary in order to formulate on paper the movements of the faces of the cube, and at the same time make the recording as concise and clear as possible. The language is very simple and in three minutes you will already be able to “read” algorithms written in it and execute them.
Take the cube in your hand and hold it in front of you. Look at him, wink at him and say “Hello Rubik's cube! I’ll collect you!” So, the Rubik's cube has six sides, these sides are coded with one letter.

Sides of the "Rubik's cube" in Russian and English notation

Rotate side clockwise is encrypted simply as a letter designating this side.
P - rotate the right side of the Rubik's cube clockwise. B – rotate the top face clockwise. L – left side. H - clockwise rotation of the bottom edge of the cube, if you were looking at the cube from below. Z - turning the back face of the Rubik's cube clockwise, if you were looking at the cube from behind. Don't get confused!

The direction of rotation for any side of the Rubik's cube is determined as if you were looking at the desired side "in person"

Rotate side counterclockwise is encrypted as a letter designating this side and stroke.
P' - rotate the right side of the cube counterclockwise. B’ – rotate the top face counterclockwise. L’ – left side, etc.

Rotate a face 180 degrees- this is a rotation twice clockwise or two times counterclockwise (which is the same thing) - encrypted as a letter indicating the side and the number two.
P2 – turn 180 degrees right side, B2 – 180 degree rotation of the top side, H2 – 180 degree rotation of the bottom side.

Not clear? Beautiful pictures for explanation

P turning the right side of the Rubik's cube clockwise.

This was a short algorithm, but when executing a long algorithm (long formula), the main thing is to remember where each edge is located while executing the sequence. You can get confused very quickly, so here is probably the most important rule when solving a Rubik's cube:

When performing algorithms, do not twirl the cube in your hands, hold it straight in front of you

One subtlety - there is no connection between the colors of the sides and the letter indicating the side. If you hold the cube with the green side towards you, then the green side is in at the moment and there is a frontal one. Next time you need to apply a different algorithm, and you turn the cube with the white side, then the white side will become the front.

That's all, now we can move on to solving the Rubik's cube.

Do you know which toy deserves the title of the most sold in the world? No, not the beautiful Barbie or even the Lego constructor. The absolute leader in sales is considered to be a much more intellectual thing - a Rubik's cube. This year the colorful puzzler of Hungarian origin celebrates its forty-first birthday. Over four decades, millions tried to conquer it. And today we will tell you a way to solve a Rubik's cube using only two movements and one little secret.

In 1980, a mailing list for Rubik's Cube enthusiasts was opened. Since then, thousands of puzzle enthusiasts, including a staggering number of mathematicians, engineers and programmers, have joined forces to find "God's algorithm": a way to solve a cube in a minimum number of moves. In July 2010, Palo Alto programmer Thomas Rokicki, Darmstadt math teacher Herbert Kozemba, Kent University 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. A current record – 4.94 seconds. Well, the method described below does not guarantee a speedy solution. But why not test the theory in practice?

Just rotate the left side.

Now rotate the top edge.

Repeat these two combinations one after another. How many times? Until you collect it!

Video demonstration This method has already collected more than 14 million views. Of course, there were many dissatisfied people in the comments who were unable to solve the puzzle. Maybe they just didn't repeat the combination long enough?

Have you noticed how quickly the sides of the cube “fly” in the hands of professionals? It turns out there is a little trick here too. To speed up the process, you need to use...lubricant! Liquid silicone will do.

Rotate the faces of the cube to the position as in the photo.

How to solve a Rubik's cube?

Don't rush to put the puzzle on the far shelf. After reading the article, you will be able to understand how to independently go through all the stages of the “cubic” assembly.

Step-by-step diagram and method of assembling a 3x3 Rubik's cube for beginners and children

If you decide to reveal the secret of assembling a popular puzzle toy, then you should start by studying it internal device and how the puzzle functions. The cube is sold in stationery stores, supermarkets and shopping centers, on the shelves in the toy department.

But out of billions of combinations, it’s unlikely that an adult will be able to find the only solution to this 3D puzzle without devoting a lot of time to studying and assembling it, let alone children.
After watching enough videos about quickly solving a Rubik's cube, you might think that it's easy. But it's not that simple. So, the first and important step before starting to solve a puzzle is to parse it into individual elements.
The 3x3 Rubik's Cube is made in the form of a mechanical cube with sides of a strictly defined color.

Each face is structured identically and consists of:

central segments(one side includes one such segment), capable of rotating around an axis while remaining in “their” cell (in our example, these are the brown central squares on each side)
8 corner segments, the square parts of which are painted in three different colors (in the example, such segments are purple)
12 ribs, located between the corner segments and having two different colors(in the example these are pale blue squares)
Rubik's cube consists of 20 moving parts- these are edges and corners. Knowing how the 12 edges and 8 corner segments can move will help you understand how the puzzle works.

What happens if you rotate one face? The centers are static (do not move), the edges change positions, taking the place of other edges, and the corners move into the corner.

With each shift and rotation of the sides of the cube, the edge remains the edge, and the segment located in the center remains the center.

How to solve a Rubik's cube easily, quickly and correctly: formula, order of assembly, combinations

A completed Rubik's cube means that all the elements are in their “right” places. The reference points for the correct location of the squares are the centers fixed in one place.

The sides of the rib between the red and green centers are colored red-green. So, have solved rubik's cube next to the green central segment there will be green edge, and next to the red central segment is red.
The correct location of the three-color corner is between the centers painted with the corresponding colors.

Stage 1: Edge Assembly

Let's start assembling the Cube with one color. In our diagram it will be yellow. If you prefer to start with a different color, then simply repeat all the steps with the elements painted in that color.
Place the cube with the yellow central segment facing up. Then a white center will be placed on the opposite bottom side (standard Rubik's cubes have the same arrangement of colored segments, so the yellow center is always above the white one).
We set all the edges of the color we need around the central square. A yellow cross should form on the top side of the cube.
But this is done as follows:
the edge, as we have already said, is painted in three different colors, so its second color should correspond to the center that is closer.

Without understanding the structure of the cube, this stage will be difficult to understand. But if you take the time to train (without tips from those who have mastered speed assembly), then everything will work out.

Anyone who sets out to solve a tricky puzzle for the first time usually gives up his idea after folding the cross and one of the sides. They don't have the patience to move forward. But we will continue, because the puzzle is not solved yet!

So, the main thing for us now is not to give up and try to fold the cross on your own. It’s better to close the article at this time, but if the solution doesn’t come to you, then look at the examples below.
The diagram below will help you understand how to arrange squares of the same color in a cross. Repeat this step 4 times, because each color must be laid out crosswise.

Start of assembling the cross

How to lay out a cross:

Flip the puzzle over with the yellow center facing up (if you chose a different color, place the side with the center segment of your chosen color at the top). The white center will be at the bottom.
We are looking for edges on the underside that are colored yellow. Let's not forget that the two colors of each edge are important to us now.
Find the bottom edge, painted yellow, and scroll it so that the yellow square of the edge takes “its place” on the top edge.

Let's do the following:

The yellow center is pointing down.

Yellow “looks” down

The yellow center is facing forward.

Yellow “looks” forward

We place the edge between two intermediate layers.

IMPORTANT: The yellow top edge segment may be oriented incorrectly relative to the other segments, or in the wrong position relative to the nearest center segment.

To return such an element to the right place, you must move another element to its position.
The edge will then end up in one of the three positions described above. We install it in the “right” place.
We assemble each yellow edge in the same way as the diagram above until we get a cross on the top side of the cube.

Stage 2: continuing to assemble the top face:

After assembling the cross, we continue to assemble the upper side: we move the corners to their places one after another.
But even here you should collect, adhering to certain rules, and not as your heart desires. The color of each corner depends on the place allocated to it.

There are several ways to get through this stage. Assembling each corner is carried out in 4 steps:

Turn the cube over with the yellow side up. The white side should be on the bottom. We are looking for a corner on the white side, one square of which is yellow.

Yellow “looks” to the left

Scroll this “white” layer so that the yellow corner takes “its” place.

Yellow “looks” to the right

set the cube with a corner element painted yellow to the left
flip it over, pointing the yellow element to the right
turn again, pointing the yellow to the underside

IMPORTANT: if there is no yellow corner at the bottom, then it has moved to the top side, which means it has taken a “foreign” position. To return the yellow corner to its place, rotate any corner of the bottom side up. After this, the yellow corner will be at the bottom. Crank up to complete assembly top layer.

Stage 3: Assembling the second layer

We collect the edges of the second layer. We remember that the centers of the cube do not move and there is no need to move them to find the right place for them. We repeat the steps 4 times. After all, we have 4 edges:

Place the cube with the white layer facing up. The yellow one, which is below, has already been assembled.
We find an edge on the top edge, both sides of which are not white.
We turn the top so that the color of the edge found in the previous step is the same color as the center. We should end up with an inverted T.
To do this, repeat one of the steps below. You need to find a solution in which the edge took a position on the left or on the right: follow the example that suits you.

Here are the ways to assemble this part of the Rubik's cube:

We move the edge from the position where it stopped to the right side.

Move the edge to the left.

IMPORTANT: the absence of an edge, any side of which is not white, means that it has not taken “its” position in the middle layer.

We move the other edge so that it takes the position of the outermost element in the top layer that took the “foreign” position.
Now there is no white square on the top edge, which can be scrolled according to the scheme described above.
We repeat all the steps again 4 times, thus collecting 4 edges.

Stage 4: assembly of the second cross

We have collected 2 faces. Next, you need to carry out such manipulations, after which the 4 white edges of the upper edge form a cross. Let's focus exclusively on the extreme elements. We shouldn't be interested in angles right now.
The top layer may have four white edges, two white edges, or no white edges at all. There may be such a position: on the top face there are all 4 white edges. In this case, you can immediately move on to the next stage.
The version with two white ribs is assembled according to the diagram below. We pay attention to how these ribs are located - next to or opposite each other.

If the white edges are adjacent:

If the white edges are opposite:

White squares are missing in their places:

It is necessary to perform the above-described manipulations to obtain 2 squares on the top face.
Next, we fold a cross depending on how the white squares are arranged.

Stage 5: placement of the second cross

When the second cross is folded, we need to place the sides of the cross so that they become a continuation of the central elements of the faces that match in color.
Again, we focus solely on the white edges, not taking into account the color of the corner elements.
We need to rotate the top face so that the color of the two edges matches the color of the central squares of the corresponding faces.
If only one edge matches, you need to continue rotating.
Follow the examples above. Here everything depends on the lateral extreme elements: they are located sequentially or are on opposite sides.

If on adjacent edges:

If on opposite edges:

We should now have a correctly positioned second cross.

Stage 6: corners

Now we proceed to arranging the corner elements of the last layer. The orientation of the corner pieces is not important now. The main thing is to determine whether the corner element is in the correct position.
This is not difficult to determine: with a correctly positioned corner element, the colors of nearby centers coincide with the color of the 3 squares of the corner.

The following examples will help you understand when a corner element is positioned correctly:

If the 4 corners are in the correct position, then you can proceed to step 7.
If only one corner piece is placed correctly, or there is no correctly placed corner at all, then choose one of the appropriate examples to place all the corner pieces in “their” places.

If all three corner parts are not in their “right” places, here are the possible solutions:

Three corners in place (option a)

If there are no correctly positioned corner elements:

In the latter case, it is necessary to follow one of the examples described above so that at least one corner element takes the desired position.
After that, continue depending on how the elements are arranged.

Stage 7: Assembly

The corners have taken their positions, and we just have to do the last steps: solve the puzzle by rotating the corner elements of the last layer.
Now on a Rubik's cube there may be 2, 3 or 4 corner pieces of the last layer that are oriented incorrectly.

In a situation where 2 corner elements are oriented incorrectly, do the following:

Before rotating the faces of the cube, pay attention to several important points:

The first option for solving the puzzle may have sub-options. It all depends on which one is right for you. It is necessary to perform the first sequence of actions, and then act in accordance with the result obtained.

Option 1:

with two incorrectly oriented elements: it is necessary to rotate the “neighboring” corner clockwise.

Option 2-3:

with three incorrectly oriented corner elements, the Rubik's Cube is solved according to the first example to reach 2 incorrectly oriented corner elements. Further manipulations are carried out based on the results obtained.

Option 4:

in the absence of correctly oriented corner elements, it is necessary to proceed according to the first example described above, and then select the solution that corresponds to the result obtained.

Assembly option for all incorrectly oriented corners

Are you still following our instructions and everything is done correctly? Congratulations! Your Rubik's Cube has been solved! And you solved this puzzle yourself!