How to assemble a cube in a cube. How to solve a Rubik's cube using the layer-by-layer method

Probably, the Rubik's cube no longer needs an introduction, but not everyone knows how to handle it. Although, judging by the number of requests, there are a lot of people who want to learn how to collect it. And so, we bring to your attention one of the many schemes for assembling the famous Rubik's cube.

We will depict the rotations of the faces using arrows in a 3 by 3 square, representing the front face of the cube.

is. 0. Arrow and letter designations for rotations of five faces (we won’t need the back face). For example, the letter F indicates a rotation of the front (Facade) face by 90° clockwise, F’ - its rotation by 90° counterclockwise. Ф2 - its rotation by 180°. In this and the following pictures, the unshaded faces of the cubes are faces whose color we do not want to fix in this picture.
Each assembly stage is specified by drawings that show the initial cubic position, which are rearranged at this stage, the sequence of rotations of this stage and the appearance of the cube after its completion.
Let's agree that when assembling, the edge with the blue central square will always be the top one. The central square of the opposite face is different in different copies of the cube; For definiteness, we will consider it green. So, as a result of assembly, the top edge of the cube should become blue, the bottom - green. The front face during assembly can be any of the other four (side) faces.
If you have spun the cube even a little, you realized that the central cubes of all faces can immediately be considered standing in their place (since their relative position is rigidly established by the design of the cube), and for each of the other cubes there is a very definite final position: each face of the cube must be adjacent (along the side or top) to the central square of the same color.
We will assemble the cube layer by layer - first the bottom layer (the first two steps), then the middle layer (the third step) and, finally, the top layer (the last four steps).
So let's begin! First step. Lower cross: install the lower rib cups. Select some edge cube with a green side that is not in its final position, and by rotating the side face in which it is located, move it to the top face. Let the second side of the selected cube be yellow; by turning the cube, make a face with the yellow neutral square on the front and by turning the top face, bring the cube to one of two initial positions (picture below). Proceed according to the picture - the selected cube will be in the desired position. By installing each next rib cube, you cannot spoil what has already been achieved (think about how to do this!).

Rice. 1. First step: installation of the lower rib cube.
In the future, in all drawings we will also depict the front face as yellow (that is, with a yellow central square, the right one as orange. But, of course, at each step, bringing the cube to the initial position of the corresponding picture, you yourself will have to figure out which face to take behind the front.

Rice. 2. Second step: installing the bottom corner cube.
Second step. Bottom corners: set the bottom corners of the cube (Fig. 2). Select a corner cube with a green edge located in the top layer, and by rotating the top edge, place it exactly above its place in the bottom layer. In this case, the selected cube will take one of the three initial positions in Figure 2. Proceed according to the figure - the selected cube will be in the desired position. If there are no corner cubes with a green edge left in the top layer, but in the bottom layer some corner cube is not in its final position, rotate the cube so that the cube is “front-right-bottom” and do any of the operations in Figure 2 - it will end up in the top layer.

Rice. 3. Third step: assembling the middle layer of the Rubik's Cube.
Third step. Middle layer: install the middle rib cubes (Fig. 3). Select some rib cube without blue edges located in the top layer. By turning the top face, bring the cube to one of the two initial positions of Figure 3. Proceed according to the figure - the selected cube will be in the desired position.
If there are no edge cubes left in the top layer without blue edges, but any of the middle edge cubes are not in their final position, rotate the cube so that this cube is "front-right" and advance any of the operations of Figure 3 - it will be in the top layer.

Rice. 4. Fourth step: orienting the top two rib cubes. The red arrows show how they are rearranged, which is not important for us at this stage.
Fourth step. Orientation of the upper rib cubes: install the upper rib cubes with the blue edges facing up (Fig. 4). Incorrectly turned and there can only be two or four dice - so it is enough to be able to turn over any pair. Depending on whether you want to turn over a pair of adjacent or a pair of opposite cubes, perform one of the two operations in Figure 4 - the selected cubes will turn over. (At the same time, they will also be rearranged.)

Rice. 5. Fifth step. Rearranging the top three rib cubes.
Fifth step. Rearranging the upper rib cubes: we place the upper rib cubes in their places without turning them over (Fig. 5). If one of them is already in the correct position, and the other three need to be rearranged in a clockwise direction (case A), place the cube in the original position of Figure 5 and act according to the figure - the cubes will be placed in their place. Otherwise, rotate the top face so that any two of its edge cubes fit correctly. (This is always possible. Why?) If the other two do not stand up correctly, then we proceed further depending on whether the “correct” cubes are adjacent (case B or opposite (case C). In case B, rotate the top face another 90° counterclockwise - you get case A. In case B, proceed according to Figure 5, taking any side face of the cube as the front; after that, turning the top face 90° in the desired direction, we again arrive at A. (By the way, case B occurs in 5 times less often than case B - prove it!)

Rice. 6. Sixth step. Orientation of the top three cubes. (When choosing the starting position of the cube, the red arrows are ignored).
There's not much left. Sixth step. Orienting the top cubes: place the top corner cubes with the blue edges facing up (Fig. 6). After the fifth step, two, three or all four cubes may be incorrectly rotated. In the case of three “wrong” cubes, place the cube in one of the two original positions of Figure 6 and act according to the drawing - the cube will rotate. At the same time, they will also be rearranged). If you need to turn over two or four cubes, place the cube so that the upper left corner of the front face is blue and perform the T' operation for the case of two cubes or T for four. After this, perform operation T, taking the corresponding side face of the cube as the front one.

Rice. 7. Seventh step: installation of the three upper corner cubes.
And finally. Seventh step. Rearranging the upper corner cubes: we place the upper corner cubes in their places without turning them over (Fig. 7).
After the sixth step, either all the upper corner cubes will stand correctly, or one of them will stand correctly, and the other three must be rearranged cyclically, or they will all stand incorrectly. In the first case, everything is fine - the Rubik cube is completed. In the second case, depending on whether you need to rearrange the incorrect cubes counterclockwise or clockwise, perform one of the two operations in Figure 7 - the cubes will be placed in their places. In the third case, perform any of the operations in Figure 7, taking any side face of the cube as the front one - one corner cube will stand correctly, and we will get the previous case).
All. You can breathe a sigh of relief - the Rubik's cube has been solved!

So, you have chosen and bought your first one. It's time to learn how to assemble it.

You can either learn how to assemble it directly from this page. So, how to solve a 3x3 Rubik's cube? Let's get started!

3x3 cube design

The 3x3 Rubik's Cube has six different colored sides and consists of 26 elements that are fastened together and move freely among themselves.

Cube elements are divided into three types

What does a 3x3 Rubik's Cube consist of?

Fig.1 basic elements of a Rubik's cube

Fig.2 The crosspiece is the internal mechanism for attaching the Rubik's cube.

To solve a Rubik's cube you need to know the formulas for assembling it. Therefore, first of all you need to learn the language of rotations.

The language of rotations. What do the letters mean in the formulas for solving a Rubik's cube?

Main

The cube has a top, a bottom, a right, a left. When rotating, keep the cube in one position relative to you, and simply rotate the desired side. REMEMBER THIS!
The centers of the cube do not move anywhere, they always remain in their places relative to each other, because they are fastened together by a cross (Fig. 2).

Rubik's cube formulas are written with letters that indicate the rotation of a certain side of the cube 90° clockwise. If there is an apostrophe (’) next to the letter, the side is rotated counterclockwise. The number before the letter indicates the number of turns.

We remind you: when you rotate the sides, the cube itself remains motionless, you simply rotate the desired side.

Practice rotating the desired sides of the cube clockwise and counterclockwise. Let your fingers remember the movement, and your mind – what and where to rotate if there is a certain letter in the formula. This will make it a lot easier for you to learn assembly algorithms.

As a respite, we recommend that you learn about the differences between professional speed cubes and beginner cubes. And is it worth it for a beginner to immediately invest in the purchase of an expensive sports cube? Briefly, our opinion: on the one hand, it’s damn nice to twirl the cosmically mobile MoYu Hualong in your hands, for example. An elite cube can be a great motivation for speed building. On the other hand: beginners may not notice the difference between a budget cube and a sports one, if the budget cube is good and fast, but we don’t keep others :)

Stage one - assembling the first (bottom) layer of the Rubik's Cube.

Assembling the cross

Assembling the cross is the first step in assembling the first (bottom) layer. Take the cube at your convenience and study the position of the centers. Remember the color of the bottom and top. In our case it is blue. Until the end of the first assembly stage, keep the blue center at the bottom and the green at the top.

Your task when assembling the cross: one by one, find four on the cube ribs With blue color and move them down to blue center so that they second rib colors coincided with colors of the lateral centers. The picture shows ribs with a blue color that have become at the bottom, and their second colors yellow And red matched the colors of the side centers - this is correct.

In order to assemble a cross, you do not need special algorithms, but for example, let’s look at situations that may occur and test your understanding of simple algorithms.

Attention! As soon as you have started to perform an algorithm not an algorithm for assembling a cube, do not twirl the cube itself in your hands until you complete the combination. The centers of different colors must maintain their position. For example, yellow is in front of you, blue is below, red is to the right.

Assembling corners

So, the cross is assembled. We move on to assembling the corners - the final stage of assembling the first layer. Take the cube with the cross facing down. Please note colors of the three centers, between which there should be corner, find it on the cube. In our case we are looking for blue-yellow-red corner. There is only one in the cube.

We put the corner in the top layer above the place where it should go down and do the URU’R’ algorithm. If the corner is in its place and the colors from the centers match, then we move on to the next corner. If not, then we repeat the algorithm until it becomes as we need.

Interesting fact: if the cube is solved and we repeat this algorithm (URU’R’) six times, then the cube will get confused and then solve.Let's see what happens to our corner after each algorithm. All of the options below may be available to you during assembly.

Stage two - assembling the second (middle) layer of the Rubik's cube

Hold the cube with the blue side facing down and the green center facing up.

In order to assemble the second layer, we need only one algorithm, but before executing it, we need to prepare the cube - bring it to one of the two possible situations shown below. Find in the top layer any edge who has no green. Rotate the top layer (movements U or U') so that the side color of the edge matches any of the side centers. Now take the cube so that the coinciding center is facing at you, and blue, as before, remained at the bottom. In our example we found yellow – red edge. Lateral rib color – yellow. Rotate the top layer and align the edge with the yellow center. You may also have an option when you combine red edge with a red center, and yellow the rib color remains on the top side.

We take the cube with the yellow or red center towards us and get one of three possible cases.

THIRD CASE

The rib is already in place, but twisted. We need to “replace” it with any edge with a green color from the top layer, then we again bring it to the two cases that are indicated above and solve it.

The third stage of assembly is assembling the top layer of the cube

We are approaching the last stage - assembling the 3rd (top) layer of Rubik. First, we need to arrange the edges on the top layer so that they form a green cross. After assembling the first two layers, on the top layer you will get one of the four cases shown in the pictures. Find the one you have and perform the algorithm FRUR'U'F' to make a cross. You can start with a “dot” and consistently come to a “cross”.

Important! Before each start of the algorithm, hold the cube in your hands exactly as shown in the pictures!

So, at the top we have a cross.

We combine the side colors of the ribs with the side centers.

By rotating the top face (U or U’) trying to combine side ribs colors With lateral centers. All four colors must match (yellow, orange, white, red). If four do not match, then put the layer so that they match at least two ribs.

If you don't find two matching edges, then run the algorithm R U R’ U R 2U R’ U and look for the ribs again.

So, on the top layer we have a cross assembled and the ribs are correctly placed.

We put the corners in place.

Check that the corners of the top layer are in place; the corners may be twisted. But the main thing is that they have the same colors as the centers between which they stand. If so, then skip this step and move on to the next one.

If the corners need to be placed correctly, then take the cube in your hands so that there is a corner on your right that is in its place and perform the algorithm without changing the position of the cube: U R U’ L’ U R’ U’ L

If there is not a single corner that stays in its place, then do the algorithm given above from any position and the corner will appear.

The cube is almost complete, all that remains is to twist the corners.

You may have two, three or four twisted corners. Corners are twisted by a simple algorithm R' D' R D R' D' R D,

Important!!! This algorithm only works for one corner, which is located to your right. The secret is that when the corner becomes correct, you need to turn the top edge (U or U’) and substitute the next corner that needs to be twisted in its place. We can repeat the algorithm from 2 to 5 times and it will seem to you that the cube is confused, don’t worry, it will come together. The main thing is not to let go of the cube, not to twist it in your hands until you have completed the entire sequence of algorithms.

Let's consider the most complex case with four twisted corners:

Congratulations!

Now you know exactly how to solve a Rubik's cube! Disassemble and assemble your cube according to these instructions until you remember all the algorithms!

And then a huge world of mechanical puzzles will open before you, the assembly formulas of which are based on the formulas of a 3x3 cube!

So, you got acquainted with the 3x3x3 Rubik's Cube puzzle and you liked it. But you don’t yet know how to learn to solve a cube, or even better, to solve it faster. Especially for you, beginner puzzle lovers, I am making this instruction, which will not only help you learn how to solve the Rubik's Cube, but also do it in less than 1 minute (in the future, we plan to create instructions for those who want to solve the cube in less than 30 seconds).

Let's start with the fact that here you can, this is especially true for those who want to solve the cube quickly, but the old cube does not allow this for technical reasons =)..

The most common method for solving a 3x3x3 cube is Jessica Friedrich's method. This technique breaks down solving a Rubik's cube into 4 stages. And at the initial level of assembly (at a speed of up to 1 minute), there are not so many formulas to learn. I will try to make instructions that will be clear and contain all the necessary information.

First, briefly about the assembly stages.

Stages of solving a Rubik's cube

1. We collect the cross. The task of this stage is to place 4 cubes in their places around the white center (many people use white as the main color when assembling, you can use any).

2. In Jessica Friedrich’s method, at the second stage, the first 2 layers are assembled immediately ( F2L – first two layers). But for a beginner puzzle assembler this will be quite difficult, so we will look at how to do this step in 2 steps, simplifying the task a little.

3. Assembling the yellow side of the cube ( OLL – orientation of the Last Layer). At this stage we collect the yellow side of the cube. Assembly of this stage, even by advanced speedcubers, is not always accomplished using one formula. We'll look at how to assemble the yellow side in a few steps.

4. The last stage of assembling the cube is called Permutation of the Last Layer (PLL). At this stage, it is necessary to place the corner and edge cubes correctly in the last third layer of the puzzle.

Well, now let's move from theory to practice.

So, let's start assembling the cube. For ease of learning, please remember that the cube must be kept with the white center down and the yellow center up!

Assembling the cube begins with a cross on the main side, usually white. In this instruction, white will be the main one.. This stage is carried out completely intuitively, there are no formulas here, but there are typical situations that are worth remembering to speed up the assembly.

Important! We are not just collecting a white cross on the white side. Each edge cube has two colors, and it must match two centers, white and one of the other four colors (in the photo you can see how the orange-white and green-white edge coincide with the orange and green centers).

1. Check the side with the white center for the presence of white edges. If they exist, then simply by rotating the bottom layer of the cube you can match this edge with the second center. Let's see how to do this in the video below. Let me remind you that you need to solve the cube with the white center down!

2. If you have already completed the first step of this step, turn your gaze to the top of the cube (the side with the yellow center). If there are white rib cubes near the yellow center, then it is easy enough to install them in the desired place on the main side (with a white center). To do this, you need to rotate only the top layer to match this edge with the second center (orange, red, green or blue), while turning the side on which the center coincides and the edge to face you. After the edge coincides with the additional center, you need to rotate the front edge twice so that the white color is not at the top of the cube, but at the bottom (where the white center is). Let's see a visual application in the video below.

3. All other situations are solved by lifting the cube with the white side up (the side with the yellow center) and turning it down towards the white center as in point 2. Below is a video with visual examples.

I propose to assemble the first two layers in two steps. After assembling the white cross, our task is to install four corner cubes in their places, followed by four more edge cubes.

Like assembling the cross, this can all be done purely intuitively.

Installing corner cubes in the first (bottom) layer

To make the information easier to understand, I will demonstrate how to install corner cubes.

To install the corner cubes in their places, you need to learn one technique, which is called “bang-bang” among speedcubers. The formula for this technique looks like this R U R' U'. read here.

In the video, I looked at 4 situations that arise during the installation of corner cubes.

The corner cube faces the white side to the right (we hold the cube with the white center down). We perform the U’F’UF form

The corner cube faces the white side to the left (we hold the cube with its white center down). We perform the URU’R’ form.

The corner cube faces up with its white edge (we hold the cube with its white center down). We perform the form R U R’ U’ R U R’ U’ R U R’ U’ (three bang-bang) The corner cube is in its place, but upside down (we hold the cube with the white center down). We perform the shape R U R’ U’ (one bang-bang), after which the corner cube will be on top (on the side with the yellow center). From this position we perform one of the formulas described above.

Once all the corners are in place, the cube should look like this:

Installation of rib cubes

After you have placed all the corner cubes in the bottom layer, our task is to install the edge cubes into place. After this, the F2L stage will be completed.

The installation of rib cubes is carried out using one formula and its mirror execution. Before executing the formula, the main thing is to install the rib cube in the right place; this is done by rotating the top layer.

The rib cube must be installed so that the color of the side face matches the color of the central cube of the middle layer.

1. If after this the rib cube is located to the left of its place, we perform the formula URUR’ U’F’U’F.

2. If the rib cube is to the right of its place, then we perform the mirror formula U’L’U’L UFUF’.

3. There are cases when the rib cubes are not in their places, or in their places, but upside down. The above formulas will help raise the rib cube to the top layer, after which you can easily install it in the right place.

After assembling the first two layers, you need to assemble the side with the yellow center, this stage is called OLL. At the same time, our task is simply to assemble the yellow side; at this stage it is not at all necessary that all the cubes be in their places.

We look at the video on how to install rib cubes when assembling the first two layers

1. Corner

Once you've completed the first two layers, the yellow side of the cube might look like this:

But in practice, during the assembly process, other combinations may appear. Let's look at how to get out of all these situations using universal formulas.

Our task is to make a corner from yellow cubes. After assembling the first two layers, you can see completely different combinations of yellow cubes at the top, but most often we get either a corner or nothing. By nothing we mean that neither a corner nor a cross nor a fish fell out. The images show several possible combinations that may exist before assembling the corner.

The corner is very easy to assemble. We carry out the formula: F RUR’U’ F. After completing the formula, you will receive one of the many combinations that are possible when assembling an OLL that contains a corner. Let's move on to the next step.

2. Cross

The cross can be assembled using one formula, but only at the stage of the assembled corner. There can be many combinations based on the corner, but to assemble the cross you only need to know one formula. So, before assembling, you need to take the cube so that the corner vectors look: one towards you, the other to the left (in fact, as in the picture above). Next we perform the formula: RU BU’B’ R’. As a result, you will get one of the combinations based on the cross:

After this, you can proceed to assembling the fish.

3. Fish

We need the fish combination in order to use one formula to collect the entire yellow side. In fact, after assembling the cross, the same formula will help you make a fish, and after the fish, completely OLL.

For this operation there is a universal formula that will help us - RU'-RU-RU-RU'-R'U'-R2 (mirror version on the left: L'U-L'U'-L'U'-L'U- LU-L2). In the video I tell you in what cases which formula to use.

2. Arrangement of corner cubes

In the video I show how to arrange the corner cubes in the two most common cases.

Formula for case one (the formula should be performed from the position shown in the video): R'U2RDR'U2RDR'U2RDDR'U2R

Formula for case 2 (the formula should be performed from the position shown in the video): R'U2RD2R'U2RD'R'U2RD'R'U2R

These formulas are easier to learn intuitively than simply memorize.

How to entertain yourself when you have a free minute, but nothing to do? Solving all kinds of puzzles is a great option!

The most popular puzzle in the history of mankind is rightfully considered the famous Rubik's Cube, invented back in 1975 and named after its inventor. After his birth, he “took over the whole world” with lightning speed. Everyone at least tried to solve a Rubik's cube, but not everyone was able to do it.

How to solve a Rubik's cube? Without outside help, it is quite difficult to do this absolutely independently; this is far from a child’s task. You need to know the algorithm for solving a Rubik's cube.

By the way, it has been proven that for any initial situation, a cube of size 3x3x3 can be completely assembled in no more than 20 moves (turns). The number 20 is therefore also called the number of God, and the algorithm that solves the cube in the minimum number of moves is called the algorithm of God.

If you have long wanted to learn how to solve a Rubik's cube, then this post is just for you. Let's get this task over with once and for all and have a little celebration for ourselves. Having done this, you can safely put a plus sign on the list of your achievements and then show off in front of your friends who do not know how to do this. So, we present to your attention an algorithm for solving a Rubik's cube.

The pictures show diagrams of actions, following which we will eventually be able to arrange the colors on the sides of the cube.

First, let's understand the notation that is used in the diagrams, and which we will operate in the process of studying the algorithm for solving a Rubik's cube of the classic size 3x3x3.

Side designations:

F - frontal (front)
Z - back
L - left
P - right
IN - top
N - lower

Now let's deal with names of turns, which we will apply to the above-described parties.

A letter without any prefixes indicates a rotation of the indicated side by a quarter of a full turn (90 degrees) clockwise(For example, " F"means we turn the front side a quarter turn clockwise, i.e. one shift).

Letter with " ’ " means turning the indicated side a quarter full turn (90 degrees) counterclockwise. Thus, the inscription “ F'" means that we must turn the front side a quarter of a full turn counterclockwise.

Letter with " ’ ’ " means that we turn the indicated side in any direction half a turn(180 degrees)

Let's fix: inscription L ’ ’ PF' means that we first turn the left face half a turn, then make a quarter turn of the right face clockwise, and complete the combination with a quarter turn of the front face counterclockwise.

Arrangement of flowers.

Select the bottom color, it will remain bottom throughout the cube assembly process. Instead of the gray color, which is shown in the diagrams of the algorithm for solving a Rubik's cube, there can be any color, it doesn't matter. The place where we moved the part we need will be shown in black. Let's look at the first drawing.

Let's move on directly to the assembly and the answer to the question “How to solve a Rubik's cube?”

Step #1.

You need to assemble a cross on the bottom side of the cube, so that all the middle side squares correspond to the middle of the side faces (look at the diagram). Unfortunately, there is no ready-made algorithm here. You'll have to tinker a little and use your brain.

Step #2.

The second step will be to assemble the bottom layer. We need to put the bottom corner cubes in place. Everything here is much simpler than in step 1 - there are ready-made turn patterns.

If the corner is in the lower layer, but is incorrectly oriented, then it must first be lifted up, rotated the way we need it and put in its rightful place. We look at the picture and apply the techniques given there. Each turn corresponds to a formula, which we dealt with a little higher.

Step #3.

The bottom layer is assembled. Let's move on to the second, middle layer. We place the 4 side cubes of the second layer in their rightful places. If the side cube is in its place, but not turned correctly, then you can turn it over by following these steps - look at the diagram.

Two layers are assembled. There is a final push left, but you shouldn’t relax ahead of time.

Step #4.

The task is to turn the middle cubes of the top layer over with the color we need facing up. It doesn’t matter whether they are in their place or not, at this step it is not so important. Using one of the proposed action schemes, we turn the sides of the upper side with the desired color facing up.

Step #5.

On the top face there is a cross of the desired color, but as you can understand from the previous paragraph, the side cubes of the top face may not be in their places. The task of step 5 is to put them in their place.

There are 4 options, each of which has its own effective algorithm of action. We apply them and install the sides in place. The cross on the upper edge can be considered fully assembled.

Step #6.

Let's continue to figure out how to solve a Rubik's cube? And we have almost reached the finish line.

We install the corners of the top edge in their places, but they can be turned upside down.

In this case " in its place" means that the corner contains the colors of all the central squares of those faces at the junction of which it is located.

Here are three rotation formulas that correspond to three options for moving the corner cubes. We remind you that the corners may be oriented incorrectly, but they should fall into place.

Step #7.

Friends, we have reached the finish line! There is one last step left in solving the Rubik's cube.

The corner cubes are in place, but some may be oriented incorrectly. They need to be turned over. To do this, you should perform the operations prescribed in the diagram of step No. 7 in pairs (look at the figure above).

Did it work? Well, of course it worked! In just 7 steps, we have solved the puzzle that has kept millions of people awake and still unable to sleep.

Naturally, at one time you did not remember all the steps and formulas for turns and movements. Here you just need to practice and get better at it.

The main thing is that you now know exactly the answer to the question “ How to solve a Rubik's cube»?

The human intellect needs constant training no less than the body needs physical activity. The best way to develop and expand the abilities of this quality of the psyche is 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. The resourceful teacher planned to explain the theory of mathematical groups (algebraic structures) in such an interesting way. 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 of 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 the 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 have appeared in solving puzzles with closed eyes, one hand, and feet.

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 edge (front or façade) is the front edge, 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 move to the professional level of speedcubing, they cannot do without an international notation system in English.

This is interesting. The international notation system is adopted by the World Cube Association (WCA).

The central cubes are designated in the formulas by 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 indicate the elementary operations of rotating the corresponding face (layer, slice) of a 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 can be 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 do not cause any difficulties for almost 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 the 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 of arrangement 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 in place using an 8-step process that is easy to remember - forward, rearranging the three corner pieces in a clockwise direction, and 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 face 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 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 the 5 x 5, 6 x 6 and 7 x 7 models is similar to the previous one, only we take a larger number of cubes as the basis for the center.

Video: solving a Rubik's cube 5 x 5

Working on solving a 6 x 6 puzzle

This cube is quite inconvenient to work with: a large number of small parts require 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. The classic version of the puzzle has 43,252,003,489,856,000 possible 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):

We decide on the color of the top edge and take the toy so that the central cube of the desired color is 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 assemble the last layer, but 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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