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Today our article is dedicated to all puzzle lovers. Solving problems, crosswords, puzzles, riddles, etc. has always attracted people from young to old. And this is not only a fun pastime, but also benefits for the mind, the development of logical thinking.

Puzzles can be either drawn in any edition or made in the form of objects, often toys. One of these is the famous Rubik's Cube in the 20th century.

There are probably still fans of this puzzle. Or maybe someone, after reading this article, will want to get acquainted with this already, one might say, an old puzzle toy.

Rubik's Cube (sometimes mistakenly Rubik's cube; originally known as the "magic cube", Hungarian bűvös kocka) is a mechanical puzzle invented in 1974 (and patented in 1975) by the Hungarian sculptor and architecture teacher Ernö Rubik. From Wikipedia.

In the mid-70s of the last century, Hungarian teacher Erne Rubik, in order to somehow help his students learn some mathematical features and understand three-dimensional objects more clearly, made several wooden cubes and painted them in six colors.

Then it turned out that putting them together into a whole cube with sides of the same color is a rather difficult task. Erne Rubik fought for a month until he achieved the result. And so, on January 30, 1975, he received a patent for his invention called "Magic Cube".

However, this name has survived only in German, Portuguese, Chinese and, of course, Hungarian. In all other countries, including ours, it is called the Rubik's Cube.

This puzzle was a hit at the time. It was sold worldwide in the 80-90s. only, more than 350 million pieces

What is Rubik's Cube

What is this puzzle? Outwardly, it is a plastic cube. Now it comes in various sizes, with 4x4x4 being considered popular. Initially, it was made in 3x3x3 format. This cube (3x3x3) looks like 26 small cubes with 54 colored faces, which make up one large cube.

The faces of a cube rotate around its three internal axes. By rotating the edges, the colored squares are reordered in many different ways. The task is to collect the colors of all faces in the same way.

There are a lot of different combinations. For example, a 3x3x3 cube has the following number of combinations:

(8! × 38−1) × (12! × 212−1) / 2 \u003d 43 252 003 274 489 856 000.

As soon as this puzzle gained popularity, mathematicians around the world, and not only, set a goal to find the number of combinations that would be the smallest when assembling it.

In 2010, several mathematicians from all over the world proved that each configuration of this puzzle can be solved in no more than 20 moves. Any turn of the face is considered a turn.

Fans of the cube did not just collect it, but began to organize competitions in speedy puzzle solving. Such people began to be called speedcubers. The result is not counted for a single assembly, but as an average of five attempts.

By the way, along with popularity, as it happens, opponents appeared who proved (even with examples) that the assembly of a cube, especially a high-speed one, entails dislocation of the hands.

But, be that as it may, the cube not only did not turn away from itself, but attracted more and more people. And the competitions were held both in a separate city and in the country, and international. For example, a participant from Russia won at the 2012 European Championship. The average assembly time was 8.89 seconds.

The cube became so popular that other modifications in shape began to appear. For example, a snake, a pyramid, various tetrahedrons, etc.

How to solve a 3x3 cube, diagram with pictures for beginners

So. Let's proceed to a simple option for assembling a 3x3x3 cube. It consists of seven stages. But first, about some of the concepts and designations that are found in the diagrams.

F, T, P, L, V, N - designations of the sides of the cube: front, rear, right, left, top, bottom. In this case, which side is the facade, rear, etc. depends on you and on the scheme on which these symbols are applied.

The designations F ', T', P ', L', V ', N' speak of turning the edges 90 ° counterclockwise.

The designations Ф 2, П 2, etc. indicate a double rotation of the face: Ф 2 \u003d ФФ, which means to rotate the front face twice.

Designation C - rotation of the middle layer. In this case: С П - from the side of the right side, С Н - from the side of the bottom, С'Л - from the side of the left, counterclockwise, etc.

For example, such a record (Ф 'П') Н 2 (ПФ) means that you must first rotate the front face counterclockwise by 90 °, then the right face as well. Next, rotate the bottom edge twice - this is 180 °. Then rotate the right edge 90 ° clockwise, and also rotate the front edge 90 ° clockwise.

In the diagrams, this is indicated as follows:

So, let's start the assembly steps.

At the first stage, you will need to collect the cross of the first layer.

We lower the required cube downward by turning the corresponding side face (P, T, L) and bring it to the front face by turning H, H 'or H 2. We finish everything by turning back the same side face

On the diagram, it looks like this:

At the second stage, we arrange the corner cubes of the first layer

Here we need to find the required corner cube, which has the colors of the faces F, B, L. In a similar way for the first stage, we bring it to the left corner of the selected front face.

On the diagram, the dots show the place where you need to place the desired cube. For the other three corner cubes, repeat the same operation.

As a result, we get the following figure:

At the third stage, we will collect the second layer.

We find the required cube and initially bring it down to the front face. If it is located at the bottom, then we do this by rotating the bottom edge until it matches the color of the facade.

If it is located in the middle belt, then we lower it down using the formula a) or b). Further, we combine the color with the color of the front edge and again do a) or b). As a result, we will have already assembled two layers.

We pass to the fourth stage. Here we will collect the third layer and the cross.

Things to do here. Move the side cubes of one face, which do not break the already assembled order in the layers. Next, select another face and repeat the process.

This will put all four dice in place. As a result, everything is in its place, but two, or even all four, may be oriented incorrectly.

First of all, you need to see which cubes sitting in their places are incorrectly oriented. If there is none or one, then we rotate the top face so that the cubes on the adjacent faces fall into place.

Here we apply such turns fv + pv, pv + tv, tv + lv, lv + fv. Further, we orient the cube as in the figure and already apply the formula written in the same place.

We pass to the fifth stage. Here we expand the side cubes of the third layer.

The cube that we will unfold should be located on the right side. In the figure, it is marked with arrows. The dots in the same place mark all possible cases when the cubes may be oriented incorrectly (Figures a, b and c).

Figure a). Here you will need to turn B 'to bring the second cube to the right side. Next, finish by turning B, which will return the top face to its original position.

Figure b). Here we do as in case a), only we turn B 2 and finish in the same way B 2

Figure c). Turn B is performed three times after the flip of each cube, after which we also end with turn B.

We proceed to the sixth stage, placing the corner cubes of the third layer.

It should be simple here. We set the corners of the last face according to the following scheme:

First, a straight turn, with which we rearrange the three corner cubes clockwise. Then the reverse one, with which we rearrange the three cubes already counterclockwise.

And finally, the last stage, during which we orient the corner cubes.

At this stage, the sequence of PF'P'F turns is repeated many times.

The figure below also shows four options where the cubes may be incorrectly oriented. They are marked with dots.

Figure a) first turn B and end with turn B ',

Figure b) here we start with B 2 and end with it.

Figure c) turn B must be performed after turning each cube correctly, and then making turn B2,

Figure d) we first make a turn B, which is also performed after we correctly orient each cube. We also finish by turning B.

As a result, everything is collected

Assembly diagram for children

This scheme is also divided into several stages.

1. The assembly starts with a cross on the top side. It is almost easy to assemble it. Moreover, you can ignore the arrangement of the colors of the other sides of the cube, but only for now.

It is usually advised to start assembling with yellow. But you can choose any.

1. We continue to collect the cross. Here it is necessary to take into account that all the top elements of the mating sides must have the same color as the central elements located on the same faces. If something does not match somewhere, we try to follow this algorithm:

A. if two adjacent sides do not match in color: P, V, P ', V, P, V 2, P', V

B. if opposite sides differ: F 2, Z 2, N 2, F 2, Z 2

1. At this stage, we place the corner cubes. Thus, we will collect one side completely. Let's examine these corner cubes and see that the cubes of the color that we have chosen as a basis, in particular yellow, are in three versions: top, left or right. For each we apply the appropriate combination:

For what is on top - P, V 2, P ', V', P, V, P '

For that on the left - F ', V', F

For the one on the right - P, V, P '

The result is one fully assembled side, and the top layers of adjacent sides and their center are the same color.

1. Now we have to collect the second layer. To do this, turn the assembled side up. Next, twist the bottom edge so that the color of the side element matches the color of the side, forming the letter "T". In order to move the side cube from the bottom layer to the middle one and at the same time its two colors must match the colors of the adjacent sides, you must do the following:

A. Rotate the cube to the left - N, L, N ', L', N ', F', N, F

B. Move the cube to the right - N ', P', N, P, N, F, N ', F'

1. We collect the third layer. Let's start by turning the cube with the unassembled side up. If the selected color was yellow, then now we need to make the top white. Now we collect white cubes according to these formulas:

A. White cube in the center + two opposite sides - Ф, П, В, П ', В', Ф ',

B. White cube in the center + two adjacent sides - F, V, P, V ', P', F

C. Only one white cube in the center - we use any combination, or A, or B

1. Collect the remaining layer completely. An assembly diagram with two possible options is shown below. If you have not succeeded in any of the above, use any.

A. Colors match when rearranged counterclockwise - P, V, P ', V, P, V 2, P',

B. Colors match when rearranged clockwise - P, V 2, P ', V', P, V ', P',

1. At this stage, we place the corner cubes. This will be somewhat more difficult. However, practice and you will succeed.

A. The side cube with the color of the top face is on the front side -

P ', F', L, F, P, F ', L', F

B. The side cube with the color of the top edge is on the side -

F ', L, F, P', F ', L', F, P

1. Last thing. Here you need to turn the corners correctly. Again, we need two options:

A. Clockwise - P 2, B 2 ', P, F, P', B 2 ', P, F', P

B. Counterclockwise - P ', F, P', V 2 ', P, F', P ', V 2', P 2

If you need to change the corner cubes in a crisscross pattern or the angles that are opposite, you can use either of these two options.

As a result, the puzzle will be completely assembled.

Video master class on the cube

And finally, a short video

The famous puzzle, consisting of several colored sectors combined into one cube, appeared in 1974. A Hungarian sculptor and teacher decided to create a study guide to explain group theory to students. Today this toy is considered the best-selling toy in the whole world.

But, success came to this puzzle only when the German entrepreneur Tibor Lakzi drew attention to it. He, together with the inventor of games Tom Kremer, arranged not only the release of cubes, but also organized the promotion of this puzzle to the masses. It is thanks to them that competitions in high-speed assembly of Rubik's cubes appeared.

By the way, people who are engaged in such an assembly of this puzzle are called speedcobers ("speed" - speed). It is not difficult to guess that the high-speed assembly of the "magic" cube is called speedcubing.

Rubik's cube structure and rotation names

In order to learn how to assemble this puzzle, you need to understand its structure and find out the correct name for certain actions with it. The latter is important if you are going to find instructions for building a cube on the Internet. Yes, and in our article we will call all the action with this puzzle, according to the well-established expressions.

A standard Rubik's cube has three sides. Each of which consists of three parts. Today there are also 5x5x5 cubes. The classic cube has 12 edges and 8 corners. It is dyed in 6 colors. Inside this puzzle there is a cross, around which the sides move.

At the end of the cross, a square with one of six colors is rigidly located. Around it, you need to collect the rest of the squares of the same color. Moreover, the puzzle is considered complete if its color is collected on all six sides of the cube.

IMPORTANT: In the original puzzle, yellow is always opposite white, orange is red, and green is blue. And if you disassemble the puzzle, and then put it down incorrectly, then this can lead to the fact that they will never be able to assemble it.

In addition to the centers of the cube, the corners are the constant components of this puzzle. Each of the eight corners has three colors. And no matter how you change the position of the colors in this puzzle, the composition of the colors of the corners in it will not change.

IMPORTANT: Rubik's Cube is collected by placing the corner and middle sectors in accordance with the colors of the central sectors.

Now that we understand the construction of this puzzle, it's time to move on to the names of the sides and rotations and their designations in the specialized literature.

In the process of solving the Rubik's cube, it may be necessary not only to move the sides, but also to change the position of this object in space. Experts call these movements interceptions. This is shown schematically as follows:

IMPORTANT: If only a letter is indicated in the cube assembly algorithm you have found, then we change the position of the side clockwise. If after the letter there is an apostrophe "’ ", then rotate the side counterclockwise. If after the letter the number "2" is indicated, then this means that the side must be rotated twice. For example, D2 ′ - rotate the bottom side counterclockwise two times.

Simple and easy way to assemble: Instructions for children and beginners

The most detailed assembly instructions for beginners are as follows:

• In the first stage of the assembly of this popular puzzle, we start with the correct cross. That is, from the fact that on each side of the cube there will be the same color of edges and centers.
• To do this, find a white center and white edges and collect crosses according to the diagram below:

• After the above steps, we must receive the cross. Of course, the cross will not be correct the first time, and you need to slightly transform the resulting version. If executed correctly, it will be enough to simply swap the ribs with each other.
• This algorithm is called "bang bang" and is shown in the diagram below:

• We proceed to the next step of the puzzle assembly. Find a white corner on the bottom layer and place a red corner above it. This can be done in different ways, depending on the position of the red and white corners. We use the bang bang method described above.

• As a result, we should get the following:

• We begin to collect the second layer. To do this, find four edges without yellow and place them between the centers of the second layer. Then spin the cube until the center color matches the face element color.
• As with the assembly of the previous layer, you may need one of several options to achieve this goal:

• After we have successfully completed the previous step, we move on to assembling the yellow cross. Sometimes, he "gathers" himself. But this happens very rarely. Most often, the cube at this stage has three options for the arrangement of colors:

So, the yellow cross is complete. Further action in solving this puzzle comes down to seven options. Each of them is shown below:

In the next step, we need to collect the corners of the top layer. Take one of the corners and put it in place using the U, U 'and U2 motions. In this case, one must take into account. So that the colors of the corner are identical to the colors on the layers below. Keep the white cube towards you when using this step.

Next build step

• The final stage of the cube assembly is the assembly of the edges of the top layer. If you did all of the above correctly, then four situations can arise. They are solved very simply:

The fastest way. Jessica Friedrich's method

This puzzle assembly method was developed by Jessica Friedrich in 1981. It is conceptually no different from most known methods. But, it focuses on assembly speed. Thanks to this, the number of assembly steps was reduced from seven to four. To master this method, you need to master "only" 119 algorithms.

IMPORTANT: This technique is not suitable for beginners. It should be studied when your cube assembly speed becomes less than 2 minutes.

1. At the first stage, you need to collect a cross with side faces. In specialized literature, this stage is called "Cross" (from the English. Cross - cross).

2. At the second stage, you need to collect two layers of the puzzle at once. They call him "F2L" (from the English First 2 Layers - the first two layers). To achieve the result, the following algorithms may be required:

3. Now you need to collect the top layer completely. You shouldn't pay attention to the sides. The name of the OLL stage (from the English Orientation of the Last Layer - the orientation of the last layer). To assemble, you need to learn 57 algorithms:

4. The final stage of the cube assembly. PLL (from the English Permutation of the Last Layer - arrangement of the elements of the last layer in places). Its assembly can be done using the following algorithms:

Rubik's cube assembly scheme 3x3 in 15 moves

Since 1982, when the competition for the high-speed assembly of the Rubik's cube appeared, many fans of this puzzle began to develop algorithms that will help to correctly arrange the cube sectors with a minimum of moves. Today, the minimum number of moves in this puzzle is called "God's Algorithm" and is 20 moves.

Therefore, it is impossible to collect a Rubik's cube in 15 moves. Moreover, a few years ago, an 18-move algorithm for the assembly of this puzzle was developed. But, it can not be used from all positions of the cube, therefore, it was rejected as the fastest.

In 2010, scientists from Google created a program with which they calculated the fastest algorithm for solving a Rubik's cube. He confirmed that the minimum number of steps is 20. Later, from the parts of the popular construction set, the Lego Mindstorm EV3 robot was created, which is able to assemble a Rubik's cube from any position in 3.253 seconds. He uses in his "work" a 20-step "Algorithm of God"... And if someone tells you that there is a 15-step cube assembly scheme, don't believe him. Even the power of Google is "not enough" to find it.

How easy it is to solve the Rubik's cube: Video

Side designations and language of rotations in Russian letters

First of all, let's agree on a notation system. The faces of the cube are indicated by letters F, T, P, L, V, N - with the initial letters of the words facade, rear, right, left, top, bottom. Which face of the cube is considered a front - blue, green, etc. - depends on you and on the resulting situation. During the assembly process, you will have to take one or another facet, which is convenient for this case, for the facade. The central cubes determine the color of the edge, that is, we can say that even in a completely confused cube, the central cubes have already been selected and 8 cubes of the same color remain to each of them. The central cubes are designated by one letter: f, t, n, l, w, n.

Edge cubes (there are 12 of them) belong to two faces and are designated by two letters, for example fp, pv, fn etc.

Corner cubes - in three letters according to the names of the faces, for example, fpv, fln etc.

Capital letters F, T, P, L, V, N elementary operations of rotation of the corresponding face (layer, slice) of the cube by 90 ° clockwise are indicated. Designations F ", T", P ", L", V ", N" correspond to the rotation of the faces 90 ° counterclockwise. Designations F 2, P 2 etc., talk about a double rotation of the corresponding face ( Ф 2 \u003d ФФ).

By letter WITH indicate the rotation of the middle layer. The subscript indicates which side to look from to make this turn. for example S P - from the right side, S N - from the bottom, S "L - from the left side, counterclockwise, etc. It is clear that C H \u003d C "B, S P \u003d S "L etc. Letter ABOUT - rotation (rotation) of the entire cube around its axis. About f - from the side of the front edge clockwise, etc.

Process recording (F "P") N 2 (PF) means: rotate the front face counterclockwise by 90 °, the same - the right face, rotate the bottom face twice (that is, by 180 °), rotate the right face 90 ° clockwise, rotate the front face 90 ° clockwise.

Along with the letter notation of processes, the matrix form of notation is also used, where elementary operations are depicted by a drawing of a facade face with corresponding arrows indicating the directions of rotations of the corresponding face.

The layered algorithm for solving the Rubik's cube is far from the only one. There are other methods, which are discussed on other pages of this section.

To be continued...

How to solve the Rubik's Cube

In a nutshell: if you memorize 7 simple formulas no more than 8 rotations each, then you can safely learn how to collect an ordinary 3x3x3 cube in a couple of minutes. Faster than a minute and a half, this algorithm will not be able to solve the cube, but two or three minutes is easy!

Introduction

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

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

To collect the Cube is to return it from the stirred one to its original state. This, in fact, is the main point of the puzzle. Many enthusiasts find it a pleasure to build "solitaire" - patterns .

Cube ABC

The classic Cube consists of 27 parts (3x3x3 \u003d 27):

6 single-color central elements (6 "centers")

12 two-color side or rib elements (12 "ribs")

8 three-color corners (8 "corners")

1 inner element - crosspiece

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

Elements can rotate "in layers" - in groups of 9 pieces. Rotation of the outer layer clockwise by 90 ° (if you look at this layer) is considered "direct" and will be denoted by a capital letter, and counterclockwise rotation - "reverse" to the direct one - and will be denoted by a capital letter with an apostrophe "" ".

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

Turn symbols:

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

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

When assembling the Cube, we will successively rotate the layers. The sequence of turns is recorded from left to right one after another. If a rotation of a layer needs to be repeated two times, then an icon of degree “2” is placed after it. For example, Ф 2 means that it is necessary to turn the front twice, i.e. Ф 2 \u003d ФФ or Ф "Ф" (whichever is more convenient). In Latin notation, F2 is written instead of Ф 2. I will write formulas in two notations - cyrillic and latinseparating them with this sign ⇔.

For the convenience of reading long sequences, they are divided into groups, which are separated from neighboring groups by dots. If you need to repeat some sequence of turns, then it is enclosed in parentheses and the number of repetitions is written at the top right of the closing parenthesis. In Latin notation, a multiplier is used instead of an exponent. In square brackets, I will indicate the number of such a sequence or, as they are usually called, "formulas".

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

Assembly

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

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

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

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

Assembly steps:

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

14/26 - corners of the first layer

16/26 - second layer

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

26/26 - corners of the third layer

26/26 - (additional stage) center rotation

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

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

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

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

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

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

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

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

The first two stages could not have been described, since assembling the first layer is quite easy "intuitively". But, nevertheless, I will try to describe everything thoroughly and on the fingers.

Stage 1 - the cross of the first layer ("upper cross")

The purpose of this stage: the correct location of the 4 upper ribs, together with the upper center of the "cross".

So, the Cube is completely disassembled. In fact, not completely. A distinctive feature of the classic Cube is its design. Inside there is a cross (or ball) that rigidly connects the centers. The center determines the color of the entire face of the Cube. Therefore, 6 centers always already stand in their places! First, select the top. Usually the assembly starts with a white top and a green front. For non-standard colors, choose whichever is more convenient. Hold the Cube so that the top center ("top") is white and the front center ("front") is green. The main thing when assembling is to remember which color is the top and which is the front, and when rotating the layers, do not accidentally rotate the whole Cube and do not get lost.

Our goal is to find a rib with top and front colors and place it in between. At the very beginning, look for a white-green edge and place it between the white top and the green front. Let's call the element we are looking for "working cube" or RK.

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

If the RC is in the first (top) layer, then by double rotation of the outer vertical layer on which it is located, we "drive" it down to the third layer. We act similarly if the RC is in the second layer, only in this case we drive it down not with a double, but with a single rotation.

It is advisable to drive out so that the RC turns out to be the color of the top down, then it will be easier to install it in place. When driving the RC down, you need to remember about the edges that are already in place, and if some edge has been touched, then you must not forget to return it to its place later by reverse rotation.

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

After the RC is in place, there are two options: either it is correctly rotated or not. If it is rotated correctly, then everything is OK. If it is turned incorrectly, then we turn it over with the formula FV "PV ⇔FU "RU ... If the RK is "kicked out" correctly, i.e. color of the top down, then this formula will hardly have to be applied.

We proceed to the installation of the next edge. Without changing the top, we change the front, i.e. we turn the Cube to ourselves with a new side. And again we repeat our algorithm until all the remaining edges of the first layer are in place, forming a white cross on the upper face.

During the assembly process, it may turn out that the RC is already in place or it can be put in place (without destroying the already assembled one) without first driving it down, but "immediately". Well, good! In this case, the cross will be collected faster!

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

Stage 2 - corners of the first layer

The goal of the second stage is to collect the entire top layer, adding four corners to the already assembled cross. In the case of the cross, we looked for the desired edge and put it in front at the top. Now our RC is not an edge, but an angle, and we will place it in the front top right. To do this, we will act in the same way as in the first stage: first we will find it, then we will "expel" it to the bottom layer, then we will put it in the front, bottom right, ie. under the place we need, and then we will drive it up.

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

We are looking for an element with which we will work (RC). In the upper right near corner, there should be a corner that has the same colors as the centers of the top, front and right. We find it. If the RC is already in place and correctly rotated, then by turning the entire Cube we change the front and look for a new RC.

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

We spin the Z-switch! If the corner does not snap into place, or stands up, but is incorrectly turned, then turn the Z switch again, and so on until the RC is in place at the top and correctly rotated. Sometimes you need to turn the Z-switch up to 5 times.

If the RC is in the upper layer and is not in place, then we expel it from there by any other using the same Z-switch. That is, first we turn the Cube so that the top remains white, and the RC that needs to be kicked out is in the upper right in front of us and turn the Z-switch. After the RC is "driven out", we again turn the Cube towards us with the necessary front, rotate the bottom, put the already driven RC under the place we need and with the Z-switch drive it up. We rotate the Z-switch until the cube is oriented properly.

We apply this algorithm to the remaining corners. The result is a fully assembled first Cube layer! 14 out of 26 cubes are standing still!

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

I want to warn you, with each step the Cube takes on a more collected look, but when you twist the formulas, the already assembled sides are stirred. The main thing is not to panic! At the end of the formula (or sequence of formulas), the cube will be reassembled. If, of course, the main rule is observed - during the rotation, you cannot twist the whole Cube, so as not to accidentally get lost. Only individual layers as written in the formula.

Stage 3 - second layer

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

Select any edge on the top layer without the color of the top edge (no yellow). Now it will be our RK. Rotating the top, we adjust the RC so that it matches in color with some lateral center. We turn the Cube so that this center becomes the front.

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

There are two formulas for this:

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

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

If suddenly the RC is already in the second layer out of place, or on its own, but incorrectly rotated, then we "expel" it by any other using one of these formulas, and then we apply this algorithm again.

Be careful. The formulas are long, you cannot make mistakes, otherwise the Cube will "figure it out" and you will have to start the assembly again. It's okay, even champions sometimes get confused when assembling.

In total, after this stage, we have two collected layers - 19 out of 26 cubes are in place!

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

Stage 4 - the cross of the third layer ("lower cross")

The goal of this stage is to collect the cross of the last unassembled layer. Although the unassembled layer is now at the top, the cross is called the “bottom” because it was originally at the bottom.

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

A) everything is wrongly turned

B) two adjacent ones are incorrectly rotated

B) two opposite ones are incorrectly turned

(There can be no other options! That is, it cannot be so that there is only one edge left to flip. If two layers of the cube are collected, and on the third there is an odd number of edges left to flip, then you can no longer steam, but.)

We remember the new formula: FPV · P "V" F " ⇔FRU · R "U" F "

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

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

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

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

We remember the new formula: PV · P "V · PV" 2 · P "V ⇔RU · R "U · RU" 2 · R "U ("Fish").

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

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

Stage 5 - corners of the third layer

It remains to put in place, and then turn the four corners correctly.

Remember the formula: V "P" · VL · V "P · VL" ⇔U "R" · UL · U "R · UL" .

We look at the corners. If they are all in place and it remains only to rotate them correctly, then look at the next paragraph. If none of the corners is standing still, then we twist the formula, and one of the corners will exactly fit into place. We are looking for a corner that stands still. Rotate the Cube so that this corner is at the back right. We twist the formula. If at the same time the cubes do not fall into place, then we turn the formula again. After that, all the corners should be in their places, it remains to turn them correctly, and the Cube will be almost assembled!

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

Remembering our Z-switch (P "N" · PN) ⇔R "D" · RD ... Rotate the Cube so that the incorrectly oriented corner is in the front right. We twist the Z-switch (up to 5 times) until the corner turns correctly. Further, without changing the front, we rotate the top layer so that the next “wrong” angle appears in front to the right, and again we rotate the Z-switch. And we do this until all the corners unfold. After that, rotate the top layer so that the colors of its edges coincide with the already assembled first and second layers. Everything! If we had a regular six-color cube, then it is already assembled! It remains to rotate the Cube with its original top (which is now bottom) upwards to get its original state.

Everything. The cube is complete!

Hope you find this guide useful!

Stage 6 - Rotation of the centers

Why isn't the cube going ?!

Many people ask the question: “I do everything as written in the algorithm, but the cube is still not assembled. Why?" Usually the ambush is waiting on the last layer. Two layers are easy to assemble, but the third is not. Everything is stirred, you begin to reassemble, again two layers, and again when assembling the third, everything is stirred. Why can this be so?

There are two reasons - obvious and not so:

Obvious... You don't follow the algorithms exactly. It is enough to make one turn in the wrong direction or skip a turn to move the whole Cube. At the initial stages (when assembling the first and second layers), incorrect rotation is not very fatal, but when assembling the third layer, the slightest mistake leads to complete mixing of all assembled layers. But if you follow the above assembly algorithm exactly, then everything should come together. All formulas are time-tested, there are no errors in them.

Not very obvious... And most likely this is the case. Chinese manufacturers make Cubes of different quality - from professional championship cubes for high-speed assembly to falling apart in the hands at the very first spins. What do people usually do if a Cube falls apart? Yes, they put back the fallen out cubes, and do not worry about how they were oriented and where they stood. And you can't do that! Rather, it is possible, but the likelihood after that to collect the Rubik's Cube will be extremely small.

If the Cube falls apart (or, as the speedcubers say, “pomp”), and it was collected incorrectly, then when assembling the third layer, problems are likely to arise... How to solve this problem? Break it up again and assemble it correctly!

On a cube with two layers assembled, you need to gently pry the lid of the central cube of the third layer with a flat screwdriver or a knife, remove it, unscrew the screw with a small Phillips screwdriver, while not losing the spring put on the screw. Gently pull out the corner and side cubes of the third layer and insert them in the correct color to color. At the end, insert and screw on the previously unscrewed central cube (do not tighten too much). Twirl the third layer. If it turns tight, loosen the screw, if too light, tighten it. It is necessary that all edges rotate with the same effort. Then close the center cube with the lid. Everything.

You can turn any edge by 45 ° without unscrewing it, pry one of the side cubes with your finger, knife or flat screwdriver and pull it out. Only this must be done carefully, because you can break the crosspiece. Then, in turn, pull out the required cubes and insert them back into their places, already correctly oriented. After everything has been assembled color to color, you will also need to insert (click) the side cube, which was pulled out at the beginning (or some other, but side one, because the corner cube will definitely not work).

After that, the cube can be mixed and easily assembled using the above algorithm. And now he will definitely get together! Unfortunately, one cannot do without such "barbaric" procedures with a knife and a screwdriver, since if the Cube was folded incorrectly after falling apart, it will not be possible to collect it by rotations.

PS: if it is not possible to collect even two layers, then first you need to make sure that at least the centers are in the right places. Perhaps someone rearranged the center caps. A standard paint job should have 6 colors, white opposite yellow, blue opposite green, red opposite orange. Usually the top is white, the bottom is yellow, the front is orange, the rear is red, the right is green, and the left is blue. But absolutely exactly the mutual arrangement of colors is determined by the corner cubes. For example, you can find angular white-blue-red and see that the colors are in clockwise direction. So, if the top is white, then the right should be blue, and the front should be red.

PPS: if someone was joking, and not just rearranged the elements of the cube, but re-glued the stickers, then collecting the Cube is generally unrealistic, no matter how much you ruin it. No screwdriver will help here. It is necessary to calculate which stickers were re-glued, and then re-glue them into place.

Is it even easier?

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

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

There are a huge pile of algorithms, but each of them needs to be approached with due attention, and each takes a lot of time to master.

The date: 2012-11-20 Editor: Zagumenny Vladislav

Stage 1. Getting acquainted with the Rubik's cube.
Rubik's Cube Part Names:
Rib parts or ribs - parts with two colors. In total, the cube has 12 edge parts located in the middle of the edges.

Corner parts or cornersAre pieces with three colors. In total, the cube has 8 corner pieces located in the corners.

Central parts or simply centers - parts with one color. In total, the cube has 6 central parts located in the center of each face. The center pieces do not move and represent the colors of their edges.
Centers always opposite to each other:

White is the opposite of yellow.
- Orange is the opposite of red.
- Green is the opposite of blue.

Each side of the cube is indicated by a Latin letter

R - right side - the right side of the die
L - left side - left side of the cube
U - top side - the top side of the cube
D - bottom side - the bottom side of the cube
F - front face - front side of the cube
B - back side - the back side of the cube.
Comment:the letter “i” after the letter of the face means backward movement or counterclockwise movement when looking directly at the face.

Very important
When performing the movements below, keep the cube fully turned with one side towards you, as shown in the picture. The dark gray in the pictures means that the actual color of these parts does not matter. Every move is one fourth of a full turn 360 degrees.

Stage 2. Putting together the white cross.

Task:Keeping your cube so that the white center is on the top (U), you must assemble the white cross as shown in the picture below. Much of this stage is achieved by trial and error, but there are still a few clues.

Hints:
Be sure to remember that you need to collect the parts of the white cross in the following order - blue, orange, green, red.
Notice how the edges in the picture above match the top white center and the side red or blue center. This way you can simply determine that the edges are in the correct places.
Keeping the white center on the top face, move the blue-white edge to the bottom face (D). Next, rotate the bottom edge until the blue-white edge is just below the blue center. Now take the cube so that the blue center and white-blue edges are on the right edge (R).
Rotate the right side (R) until the blue-white edge is on the top (U) face above the blue center.
If your cube looks like the picture below, then take the cube so that the orange center is on the right edge, and assemble the side with the orange center in the same way.
If your cube looks like the image below, then follow the sequence below, making sure the blue center is on the right (R) face.

The remaining parts of the white cross are collected in the same way.

Congratulations!
If your cube has a white cross the same as in the picture, then you can go to stage 3!

Stage 3. Collecting the white corners.

Task:take the cube so that the white cross is on the top (U). Now you have to collect the white corners and get a cube like in the picture below.

Hints:
The corners will have one white edge and 2 other colors.
If the corner is already on the bottom edge, rotate the bottom edge until the corner is directly below where it should be. After that, your cube may look like one of the 3 three pictures below.

Repeat the entire process for all four corners.
If the corner is located on the top face, then move it to the bottom face by following the sequence:

Now rotate the bottom face until the corner is just below its place on the top face.

Congratulations!
If your white layer looks like the picture below, then you have completed one third of the cube and you can go to stage 4.

Stage 4. Assembling the middle layer.
Task: Take the cube so that the completely assembled white layer is on the bottom edge. Now you need to assemble the middle layer by placing the side ribs in their places.

Hints:
Pay attention to the vertical blue stripe (it can also be red, orange, green) - this is critical.
Collect such a vertical strip by rotating the top face until the color of the edge on the top face without yellow matches the color of the center of the face. The color of the upper part of the edge on the upper face determines the direction of movement of the edge, that is, in which direction this part should move.
1) If you move the edge in the same direction as in the picture, then follow the sequence of pictures below.

2) If you move the edge in the same direction as in the picture, then follow the sequence of pictures below.

Repeat these steps until all the side ribs are in place.
Comment: if one of the edges is already in place, but not oriented correctly, do one of the above sequences and it will appear on the top layer. After that, follow the appropriate sequence of actions to place the edge back in its place in the middle layer.

Congratulations!
If the bottom two layers on your cube look the same as in the picture below, you can proceed to stage 5... You have passed two thirds of the way!

Stage 5. We collect the top layer. We get a yellow cross.
Task: compare the state of the yellow edge of your cube with the templates below. Then follow the appropriate sequence.
Hint:the yellow parts on the top face should not yet match the color of the side faces.
Step one: Collect the yellow cross.

Switch to step two and start collecting the corners of the yellow edge.

Follow these steps:

Option 3.

Option 4.

Step two: Make all the corners of the top face yellow.

Take a look at the top face and match the state of the cube with the options below.
If there is not a single yellow corner on the upper yellow facet, then you must take the cube so that the yellow facet of one of the corners is on the left side of the cube. See drawing.

If the yellow face has one corner, follow the sequence below.

Option 3.If there is not a single yellow corner on the top yellow face, and there is also no corner that could be used in option 1(that is, all corners have faces on the right). Then take the cube as shown in the picture below. The yellow part of the corner should be on the front edge of the cube.

Follow the sequence below 1, 2 or 3 times to get a fully assembled yellow facet. After each sequence, re-compare the state of your die with the options described above.

Congratulations!

If your cube looks like the picture, you can go to stage 6!

Stage 6. Putting the yellow corners in place.