Cube in a cube formula for a cube. How to collect a Rubik's cube without breaking your head. Schemes with pictures for beginners and children. What is a puzzle toy

Hello!

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

Jigsaw 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.

Surely there are still fans of this puzzle. Or maybe someone, having read this article and wants to get acquainted with this one can already say an old puzzle toy.

Rubik's Cube (sometimes erroneously called the Rubik's Cube; was 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 architectural professor Ernö Rubik. From Wikipedia.

In the mid-70s of the last century, the 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 to put together a whole cube with identical sides in color, the task is rather complicated. Erne Rubik struggled for a month until he achieved a result. And so, on January 30, 1975, he received a patent for his invention under the name “Magic Cube”.

However, this name was preserved only in German, Portuguese, Chinese and, naturally, Hungarian. In all other countries, including ours, it is called the Rubik's Cube.

At one time, this puzzle was a bestseller. Worldwide was sold in 80-90 years. only more than 350 million pieces

  What is a 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 the format 3x3x3. This cube (3x3x3) looks like 26 small cubes with 54 colored faces, which make up one large cube.

The faces of the cube revolve around its three internal axes. By turning the edges, the colored squares are reordered in a variety of different ways. The task is to collect the colors of all faces equally.

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 all over the world, and not only that, set the goal of finding as many combinations as would be the smallest when assembling it.

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

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

By the way, along with popularity, as it happens, opponents appeared who proved (even with examples) that assembling a cube, especially speedy one, entails dislocations 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. So, for example, a participant from Russia won the European Championship in 2012. The average build time for him was 8.89 seconds.

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

  How to collect a 3x3 cube, a scheme 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 concepts and notation that are found on the diagrams.

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

The designations F ’, T’, P ’, L’, B ’, N’ indicate that the faces rotate 90 ° counterclockwise.

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

The designation C is the rotation of the middle layer. At the same time: 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 turn the facade face counterclockwise by 90 °, then the right side as well. Next, rotate the bottom face twice - this is 180 °. Then turn the right side 90 ° clockwise, and also rotate the facade face 90 ° clockwise.

In the diagrams, this is indicated as follows:

So, let's start the assembly steps.

At the first stage, it will be necessary to collect the cross of the first layer.

The desired cube is lowered down, turning the corresponding side face (P, T, L) and we bring it to the front face by turning H, H ’or H 2. We finish everything by reverse turning the same side face

In 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 necessary corner cube, which has the colors of the faces F, B, L. Using a similar method for the first stage, we display it in the left corner of the selected facade face.

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

As a result, we get the following figure:

In the third stage we will collect the second layer.

Find the desired cube and initially display it down on the facade face. If it is located below, then we do this by turning the bottom face to match the color of the facade.

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

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

What needs to be done here. We move the side cubes of one face that do not violate the already assembled order in the layers. Next, select another face and repeat the process.

Thus, we put in place all four dice. As a result, everything is in place, but two, or even all four, can be oriented incorrectly.

First of all, you need to see which cubes sitting in their places are incorrectly oriented. If not one or one, then we rotate the upper face so that the cubes located on adjacent faces fall into place.

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

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

The cube that we will deploy 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 where the cubes may not be oriented correctly (figures a, b and c).

Figure a). Here you will need to make a B ’turn to draw the second cube on the right side. Next, finish by turning B, which will return the upper face to its original position.

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

Figure c). turn B is performed three times after the flip of each cube, after which we also finish by turning B.

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

It should be simple. The angles of the last face are set as follows:

First, a direct turn, with which we rearrange the three corner cubes clockwise. Then the reverse, by 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 also shows four options when the cubes may not be oriented correctly. They are marked with dots.

Figure a) First, make turn B and end with turn B ’,

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

Figure c) the rotation of B must be performed after we deploy each cube correctly, and then we make the rotation of B2,

Figure d) first make a rotation 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 begins with a cross on the upper side. Collecting it is almost straightforward. Moreover, the arrangement of colors on the other sides of the cube can be ignored, but only for now.

Usually advised to start the assembly 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 upper elements of the mating sides must have the same color as the central elements located on the same faces. If something didn’t match somewhere, we try to follow this algorithm:

A. if two neighboring sides did not match in color: P, B, P ’, B, P, B 2, P’, B

B. if opposite sides differ: Ф 2, З 2, Н 2, Ф 2, З 2

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

For what’s on top - P, B 2, P ’, B’, P, B, P ’

To the left - Ф ’, В’, Ф

To the right - P, B, P ’

As a result, we get one fully assembled side, and the upper layers of adjacent sides and their center have the same color.

1. Now we have to collect the second layer. To do this, turn the assembled side up. Next, twist the bottom face 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 coincide with the colors of the neighboring sides, you must do the following:

A. Turn the cube to the left - N, L, N ’, L’, N ’, F’, N, F

B. Move the cube to the right - Н ’, П’, Н, П, Н, Ф, Н ’, Ф’

1. We collect the third layer. To begin with, turn the cube unassembled side up. If the selected color was yellow, then now we must make white up. Now we collect white cubes using these formulas:

A. White cube in the center + two opposite side - Ф, П, В, П ’, В’, Ф ’,

B. White cube in the center + two adjacent side - Ф, В, П, В ’, П’, Ф

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

1. We collect the remaining layer completely. The assembly diagram is shown below with two possible options. If you have failed any of the above, use any.

A. Colors match when shifting counterclockwise - P, B, P ’, B, P, B 2, P’,

B. The colors match when shifted clockwise - P, B 2, P ’, B’, P, B ’, P’,

1. At this stage we arrange the corner cubes. It will be a little harder to do. However, practice, and everything will work out.

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 face is on the side -

F ’, L, F, P’, F ’, L’, F, P

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

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

B. Counterclockwise - P ’, F, P’, B 2 ’, P, F’, P ’, B 2’, P 2

If necessary, change the corner cubes crosswise or angles that are opposite, you can use either of these two options.

As a result, the puzzle will be fully assembled.

  Video master class on a cube

And finally, a short video

Hello. If you decide to learn how to assemble a Rubik's 3x3 cube, then at one of the assembly stages it will be very difficult for you to do without formulas. Reading formulas for assembling a 3x3 cube is not at all difficult. Below you will find all the notation with which you can read the formula for the assembly of the cube.

The language of rotation of the sides of a 3x3 cube

Since the Rubik's Cube has 6 sides, we will have 6 main notations.

F - front - front side
  B - back - back side
  L - left - left side
  R - right - right side
  U - up - top side
  D - down - bottom side

If there is nothing after the letter, then turn this side clockwise once, as if we were looking at the face in the face.
  If there is a stroke штрих (stroke) after the letter, then you need to twist it once counterclockwise, as if we were looking at the face in the face.
  If after the letter there is a deuce 2, then the indicated side needs to be twisted 2 times (180 degrees).

Rotation of the main sides of a 3x3 cube with the notation in the pictures (for clarity)

In addition to the basic values, there are others, you need to study them if you want to learn complex formulas for speedcubers.

Letter + w:

Fw  - frontal along with the middle layer
Bw  - back with the middle layer
Lw  - left along with the middle layer
Rw  - right along with the middle layer
Uw  - upper along with the middle layer
Dw  - bottom with middle layer

Fw ’- frontal with the middle layer counterclockwise
  Bw ’- back with the middle layer counterclockwise
  Lw ’- left with the middle layer counterclockwise
  Rw ’- right along with the middle layer counterclockwise
  Uw ’- the top along with the middle layer counterclockwise
  Dw ’- bottom with the middle layer counterclockwise

Fw2 - frontal with the middle layer 180 degrees
  Bw2 - back with the middle layer at 180 degrees
  Lw2 - left with the middle layer 180 degrees
  Rw2 - right with the middle layer 180 degrees
  Uw2 - top with the middle layer 180 degrees
  Dw2 - lower with the middle layer 180 degrees

Note: Previously, such movements in a 3x3x3 cube were indicated in small letters (r, l, b, etc.). However, some time ago, due to confusion with the language of rotations of large cubes (there small letters indicate rotations of only the inner layers), the world association of the cube switched to the notation Rw, Lw, etc. Therefore, it is now correct to denote the movements of any external face together with the internal index w adjacent to it. Small letters remained only for the 4x4x4 cube and indicate the rotation of only one inner layer adjacent to the outer.

Rotations of the middle layers

M  - middle layer located between the left and right layers

S  - the middle layer located between the front and rear layers

E  - middle layer located between the upper and lower layers

Instructions "How to assemble a Rubik's Cube 3x3" with pictures for beginners. The easiest and simplest scheme, but it will require your attention and accuracy. This is the second (improved, more complete and convenient) edition of the instructions for assembling the Rubik's Cube, it takes into account the wishes of our readers.

Step 1. Collect the first side of the Rubik's Cube

This step describes in detail how to assemble one (first) side of the Rubik's Cube with the first belt. There are many possible options at this step, so it is difficult to describe them all. It is recommended not to memorize the formulas, but to understand their essence, then you can cope with any situation.

You can skip a step

If you can collect one side of the Rubik's cube and the upper belt (Fig. 1–1c) without formulas and outside help, go to.

1.1. Volumetric cross of the first side

On one side of the cube we assemble a cross whose colors correspond to the central squares of the other sides (Fig. 1–1b).

Action 1.  Find a suitable rib cube (Fig. 1-2) and rotate the front side so that this cube moves up (Fig. 1-3). Then go to step 2. Perform steps 1 and 2 as many times as necessary.

If the rotation “breaks” the already assembled cube, move the found cube to another plane (Fig. 1-4a, b). If the die is not already at the top, go to step 1 again.

If moving to another plane also “breaks” the already assembled cube, use the appropriate formula (Fig. 1–4c).

The figure (Fig. 1-4c) shows only one of the possible options - proceed by analogy.

Action 2.When the found cube is moved up, use one of the formulas.

1.2. Side and belt

To arrange the corner cubes and complete this step (Fig. 1–1c), you will need the following formulas.

To remove the wrong corner cube, use formulas.

If the cube "hid" at the bottom, then we move it to the lower belt, then to move it to its place using the formulas above.

Step 2. Assemble the second belt

The second belt is easily assembled using two formulas. Find a suitable cube in the third belt so that both colors fit (if you need to twist the third belt), and move it diagonally into the second belt using formulas.

Formula: (N’P’NP) (NFN’F ’)

Formula: (NLN’L ’) (N’F’NF)

If there is no suitable cube

If there is not a single suitable cube using the same formulas, move any cube from the third belt to the second - the desired cube will appear.

Step 3. Cross on the opposite side

Now you need to collect the cross on the opposite side of the Rubik's Cube. The cross is assembled without taking into account the colors of the third belt (Fig. 3–1). In other words, only the cross is assembled at this step, and the cross is consistent with the colors of the third belt already at the next step.

Your Rubik's Cube now has one of four combinations: a, b, c, d - see Fig. 3–2. The transition from one combination to another takes place in a single formula: Ф П В П "В" Ф ". You need to repeat this formula 1-3 times depending on what combination you have.

If the cross is already assembled (Fig. 3–2d), skip this step. If you have only one central square (Fig. 3–2a), then you need to repeat the formula 3 times. If the angle (Fig. 3–2b) - 2 times. If the line (Fig. 3–2c) - 1 time.

Formula: Ф П В П "В" Ф "

note

Before each execution of the formula, the Rubik's cube must be positioned exactly as shown in the figures.

Step 4. Agreed Cross

As a result of this step, we get a cross consistent with the colors of the belt (Fig. 4–2c).

Rotate the upper belt until the 2 colors of the cross coincide with the middle squares of the upper belt (Fig. 4–1). Only two combinations are possible: the colors coincided with the line Fig. 4–2a) or the colors coincided with the angle (Fig. 4–2b).

Formula when the line coincides: P V P "V P VV P"

We move the incorrectly placed cubes of the cross located opposite each other (two opposite ends of the cross).

After completing this formula, rotate the upper belt again until the 2 colors coincide with the middle squares of the upper belt (Fig. 4–1). Please note that even now the two ends of the cross will not fall into place, but the combination will change to “the colors coincided with the angle” (Fig. 4–2b).

The formula when the angle coincides: P V P "V P VV P" V

We swap the incorrectly placed cubes of the cross, located diagonally relative to each other (two adjacent cubes of the cross).

After completing this formula, the cross will be assembled and its lateral colors will coincide with the colors of the upper belt (Fig. 4–2c). If the result is not achieved, then repeat this step again, after properly orienting the cube.

Step 5. Arrange the corner cubes

Corner cubes are arranged in two formulas. After applying these formulas, the corner cubes will stand in their places (in their corners), but may not be rotated correctly. In Fig. 5–1, a black dot indicates a cube that is placed in its place (in its corner), but is not deployed correctly. The cubes unfold already at the next step.

Right Upright Formula: (P’F’L’F) (PF’LF)

Left Upright Formula: (Ф’Л’ФП ’) (Ф’ЛФП)

Step 6. Turning the corner cubes

The spread of all the corner cubes is performed by the simple formula P’N’PN, performed many times. Before you begin, carefully read the entire section to the end and make sure that you have no questions left.

note

After the start of the formula, the Rubik's cube will “collapse” and finally assemble, only after all the corner cubes are correctly deployed. In other words, all the corner cubes unfold in a single operation, which will require your attention and endurance.

Find the corner cube to be deployed (counterclockwise or clockwise - it doesn’t matter), see Fig. 6–1.

Take the Rubik's Cube, as shown in the figure below, and follow the formula.

note

1) The formula (out of 8 moves) must be performed 1 or 2 times until the corner cube flips to the correct position (Fig. 6–2b).

2) When the corner cube rotates to the correct position, the Rubik's cube “collapses” - do not worry, the Rubik's cube will assemble only when you are done with all the corners.

3) Do not change the position (do not turn over) the Rubik's cube in your hands until the end of this step.

When the first corner cube is already correctly positioned (Fig. 6–2b), rotate the top layer (Fig. 6–3a) so that the next corner cube moves to the upper right corner (Fig. 6–3b). If the next corner cube is already rotated correctly (does not require a turn), make another rotation of the top layer (Fig. 6–3a).

Again, follow the formula of 8 moves (1 or 2 times) and follow all the above recommendations. These steps must be repeated until all angles are deployed correctly — until the entire Rubik's Cube is assembled.

I wish you patience and success!

For children and adults sometimes the task may seem overwhelminghow to collect a 3x3 rubik's cube. The scheme with pictures for beginners in this business is one of the main assistants.

Also, to make everything clear and transparent, you can use the video instructions. We will actively use both of these aids in practice, so that you finally learned to solve the eternal puzzle with a rubik's cube.

You can collect a rubik's cube in different ways and methods. You can do this in 15 moves, in 7 moves, and even in as many as 20. For many years, all sorts of wiseacres have been struggling to find the optimal solution to this problem. After all, a rubik's cube is a mechanical puzzle that lends itself to a completely logical solution. You only need step-by-step instructions, as well as a small supply of logic and patience.

Before you start, directly, the build algorithm, you should   learn key concepts.

The name of the toy speaks for itself - the cube consists of 6 sides (faces), 12 edges, 8 corners. The faces of the cube consist of 9 small colored elements that can rotate simultaneously, but only clockwise and against it. Letters of the Russian alphabet face names will be denoted as:

F - facade;

T - rear;

P - right;

L - left;

B - top;

H - bottom.

In many descriptions and diagrams there are designations of the faces of the cube in English.

Next Rubik's Cube Secret  lies in the arrangement of small colored elements.

1. Central cubes  determine the color of the entire side of the rubik's cube. These cubes will be called by analogy with the name of the faces (Φ, T, P), etc.
2. Edge cubes immediately adjoin two faces, therefore, the name will be double (for example, FP, PV) - depending on the faces with which they interact.
3. Corner cubescontain 3 letters in the name at once, since they relate to three faces at the same time (FPV).

And one more mini-secret - when you study the patterns of rotation of faces, letters without any additions will mean clockwise rotation, and letters with an extra ‘are counterclockwise.

Having understood all these conventions, it will be much easier for you to fold the rubik's cube and you will do it right and quickly. Also, for a change you can learn to do.

How to assemble a 3x3 rubik's cube: the easiest way, assembly diagram

The easiest and most reliable way to assemble our rubik's cube begins with the lower cross. Collect a cross on the bottom of the cube and start the phased solution to the problem of how to collect a 3x3 rubik's cube: the easiest way, the diagram of which is right in front of you.

And, of course, the video tutorial with a detailed description of an experienced virtuoso will serve as the most understandable tool for building a cube.

3x3 rubik's cube assembly diagram for beginners in pictures

At the first stages of the practice of collecting a rubik's cube, we will use the same method of the cross, but this time we will have a cross of colored cubes on the upper edge. As you know, a high-speed assembly of a rubik's cube is waiting for you ahead, at this stage you must learn to correctly determine the location of the faces  and moving them in the plane of the cube.

Cube assembly methods are different, and now you have to learn how to collect a 3x3 rubik's cube: The beginner's scheme consists of 7 steps. At each of the steps for you are available pictures with a description of the assembly process. You may spend more time on this puzzle than anticipated, but you will solve the problem, which is not available to all the inhabitants of our planet! It’s worth it and sweat.

By the way, the last rubik's Cube World Recordthe speed was set in 4.73 seconds. And it belonged to an Australian student Felix Zemdegs, who defeated the previous record holder in just 0.01 seconds. We have nowhere to rush in this matter, so we carefully study the instructions and begin to collect the first layer.

The principle of assembling a rubik's cube from the initial cross  not so complicated. Here you need to properly study the location of the faces. And then - a matter of technology, as they say. We have already passed the basic concepts and rules for assembling a rubik's cube for dummies.

We are sure that the 3x3 rubik's cube assembly scheme for beginners in pictures helped you set your own record and in further attempts you will reduce the time to a minimum.

If all these steps and formulas seemed complicated and confusing to you, we suggest that you review the video, in which the whole process is shown in detail on the example of a virtual Rubik's Cube.

Formulas Rubik's Cube 3x3: calculate the moves

If you think that the previous methods for assembling the proverbial cube were intended exclusively for stupid ones, catch a few formulas.

Human intelligence needs constant training no less than the body in physical activity. The best way to develop, 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 succeeds in collecting it. To cope with this task will help knowledge of the schemes and formulas for solving the assembly of this intricate toy.

What is a puzzle toy

A mechanical cube made of plastic, the outer edges of which are composed 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 the axes, presented in the form of protrusions of a fragment of one of the three cylinders of a large cube. So the design has the ability to rotate freely, but at the same time small parts do not fall out, but hold on to each other.

Each facet 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 opposite yellow;
• blue opposite green.

However, modern versions can be painted in other combinations.

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

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

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

Appearance story

The idea of \u200b\u200bcreation belongs to the Hungarian architect Erna Rubik, who, in fact, did not create a toy, but a visual aid for his students. In such an interesting way, the resourceful teacher planned to explain the theory of mathematical groups (algebraic structures). This happened in 1974, and a year later the invention was patented as a puzzle toy - future architects (and not only them) were so stuck with their souls in an intricate and vivid manual.

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

It is interesting. Since the advent of the Rubik's Cube (“magic cube”, “magic cube”), about 350 million copies have been sold worldwide, which puts the puzzle in first place in popularity among toys. Not to mention dozens of computer games based on this assembly principle.

Rubik's Cube is an iconic toy for many generations

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

It is interesting. Fans of assembling a multi-colored puzzle are so attached to a toy that it turns out to be not enough for them alone to assemble for speed. Therefore, in recent years, championships have appeared on solving puzzles with closed eyes, one arm, and legs.

What are formulas for the Rubik's Cube

To assemble a magic cube means to compose all the small details so that an entire facet of one color is obtained, you need to use the algorithm of God. This term refers to a set of minimum actions that will allow you to solve a puzzle with a finite number of moves and combinations.

It is interesting. In addition to the Rubik's Cube, God’s algorithm is applied to puzzles such as the Meffert Pyramid, Taken, Tower of Hanoi and others.

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

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

Important Definitions

In order to learn to understand the schemes for solving the puzzle, you need to get acquainted with the names of its parts.

1. A corner is a combination of three colors. In the 3 x 3 cube there will be 3 of them, in the 4 x 4 version - 4, etc. The toy has 12 corners.
2. Ribs denote two colors. There are 8 pieces in a cube.
3. The center contains one color. There are 6 of them.
4. Facets, as already mentioned, are simultaneously rotating puzzle elements. They are also called “layers” or “slices”.

Formula Values

It should be noted that the assembly formulas are written in Latin - such schemes are widely represented in various manuals for working with the puzzle. But there are also Russified versions. Both options are listed below.

1. The frontal face (front or facade) is the front face, which is located in color to us [Ф] (or F - front).
2. The back face is the face that is centered on us [3] (or B - back).
3. The Right Face is the face that is on the right [P] (or R - right).
4. The Left Face is the face that is on the left [L] (or L - left).
5. The Lower Edge - the edge that is below [H] (or D - down).
6. The Upper Face is the face that is at the top [B] (or U - up).

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

To clarify the notation in the formulas, we use the Russian version - this will be more understandable for beginners, but for those who want to switch to the professional level of speedcubing, an international notation system in English is indispensable.

It is interesting. The international naming system is adopted by the World Cube Association (WCA).

1. The central cubes are indicated in the formulas by one lowercase letter - f, t, n, l, c, n.
2. Corner - in three letters according to the name of the faces, for example, FPV, flni, etc.
3. Uppercase letters Ф, Т, П, Л, В, Н are the elementary operations of turning the corresponding face (layer, slice) of the cube 90 ° clockwise.
4. The designations Ф ", Т", П ", Л", В ", Н" correspond to the rotation of the faces 90 ° counterclockwise.
5. The designations Ф 2, П 2, etc., indicate a double rotation of the corresponding face (Ф 2 \u003d ФФ).
6. The letter C indicates the rotation of the middle layer. The subscript indicates which side to look at to make this turn. For example, С П - from the right side, С Н - from the lower side, С "Л - from the left side, counterclockwise, etc. It is clear that С Н \u003d С" В, С П \u003d С "Л and etc.
7. The letter O is the rotation (revolution) of the entire cube around its axis. О Ф - from the side of the front face clockwise, etc.

The recording of the process (Ф "П") Н 2 (ПФ) means: rotate the front face counterclockwise by 90 °, the same as the right side, rotate the bottom face twice (that is, 180 °), rotate the right side 90 ° clockwise, rotate the façade face 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 the formulas

As a rule, in the instructions for assembling the puzzle in classic colors, it is recommended to keep the puzzle with the yellow center up. This tip is especially important for beginners.

It 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 puzzle

There are two types of circuits:

• for newbies;
• for professionals.

Their difference in the complexity of the formulas, as well as the speed of assembly. For beginners, of course, instructions corresponding to their level of knowledge of the puzzle will be more useful. But they, having trained, after a while will be able to fold the toy in 2-3 minutes.

How to assemble a standard 3 x 3 cube

Let's start by assembling a classic 3 x 3 Rubik's Cube using a 7-step scheme.

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

It is interesting. The inverse process used to solve one or another incorrectly located cubes is the reverse sequence of actions described by the formula. That is, the formula must be read from right to left, and rotate the layers counterclockwise if direct movement was indicated, and vice versa: direct if the opposite is described.

Step-by-step assembly instructions

1. We start with the assembly of the cross of the upper face. The desired cube is lowered down by turning the corresponding side face (P, T, L) and displayed on the front face with the operation H, H "or H 2. We complete the stage of deriving by mirror rotation (reverse) the same side face, restoring the original position of the affected rib cube of the upper After this, we carry out operation a) or b) of the first stage. In case a), the cube is on the facade face so that the color of its front face matches the color of the facade. In case b), the cube must not only be moved up, but also expanded so that it is correct with oriented, becoming in its place.

   Putting the cross of the upper line together

2. The desired corner cube is found (having the colors of the faces Ф, В, Л) and in the same manner as described for the first stage, it is displayed in the left corner of the selected facade face (or yellow). There can be three cases of orientation of this cube. Compare your case with the picture and apply one of the operations of the second stage a, beat c. Dots on the diagram indicate the place where the desired cube should become. We find the remaining three corner cubes on the cube and repeat the described technique to move them to their places on the upper face. Result: the top layer is matched.  The first two stages cause almost no difficulties for anyone: it’s pretty easy to follow your actions, since all attention is paid to one layer, and what is done in the remaining two is completely unimportant.

   We select the top layer

3. Our goal: to find the desired cube and first bring down to the front face. If it is at the bottom, simply by turning the bottom face to match the color of the facade, and if it is in the middle layer, you must first lower it down any of the operations a) or b), and then combine the color with the color of the facade and perform the operation of the third stage a) or b). Result: two layers are collected.The formulas given here are mirror in the full sense of the word. You can visually see this if you put a mirror to the right or left of the cube (edge \u200b\u200bto your side) 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 the rear (also not involved) faces change the 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

4. Operations that move the side cubes of one face, which do not ultimately disrupt the order in the assembled layers, lead to the goal. One of the processes that allows you to select all the side faces is given in the figure. It also shows what happens with other face cubes. Repeating the process, choosing another facade face, you can put in place all four cubes. Result: The rib parts are in place, but two of them, or even all four, may not be oriented correctly. Important: before proceeding with this formula, we look at which cubes are already in place - they may be incorrectly oriented. If none or one, then try to rotate the top face so that two located on two adjacent side faces (fv + pv, pv + tv, tv + lv, lv + fv) fall into place, after that we orient the cube so , as shown in the figure, and execute the formula given at this stage. If it is not possible to combine parts belonging to neighboring faces by rotating the upper face, then we fulfill the formula for any position of the cubes of the upper face once and try again by rotating the upper 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 point.

5. We take into account that the expandable cube should be on the right side, in the figure it is marked with arrows (PV cube). Figures a, b, and c show possible cases of the location 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 the final turn B, which will return the upper face to its original position, in case b) the intermediate turn B2 and also complete B2, and case c) an intermediate turn of B must be performed three times, after the flip of each cube and also completed by turning B. Many people are confused that after the first part of the process (PS H) 4, the desired cube unfolds as it should, but the order in the assembled layers is disturbed. confused and some stasis It makes it possible to throw an almost assembled cube halfway. Having completed an intermediate turn, not paying attention to the “breakdown” of the lower layers, we perform operations (PS Н) 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 step will be the assembled cross.

6. We set the corners of the last face in their place using an 8-way process that is convenient for memorizing - a straight line, rearranging three corner parts in a clockwise direction, and a reverse one, rearranging three cubes in a counterclockwise direction. After the fifth stage, as a rule, at least one dice sits in its place, albeit incorrectly oriented. (If, after the fifth stage, none of the corner cubes sat in their place, then we use either of the two processes for any three cubes, after which exactly one cubic will be in place.). Result: all the corner cubes took their places, but two of them (or maybe four) can be oriented incorrectly.

   Corner cubes sit in their places

7. Repeatedly repeat the sequence of turns PF "P" F. We turn the cube so that the cube we want to expand is in the upper right corner of the facade. The 8-way process (2 x 4 turns) will turn it 1/3 turn clockwise. If the cube has not yet been oriented, we repeat the 8-move again (in the formula this is reflected by the “N” index). We do not pay attention to the fact that the lower layers will become disordered. The figure shows four cases of the location of incorrectly oriented cubes (they are marked with dots). In case a) an intermediate turn B and a final B "are required, in case b) an intermediate and final turn B 2, in case c) a turn B is performed after each cube is turned to the correct orientation, and the final B 2, in case d) - an intermediate rotation B is also performed after the rotation of each cube to the correct orientation, and the rotation B will also be final in this case. Result: the last facet is collected.

   Possible errors are indicated by dots.

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

Formulas for fixing mis-oriented cubes in the last step

The essence of the Jessica Friedrich method

There are several ways to assemble the puzzle, but one of the most memorable is the option developed by Jessica Friedrich, a professor at the University of Binghamton, New York, who develops techniques for hiding data in digital images. While still a teenager, Jessica was so carried away with the cube that in 1982 she became the world champion in speedboarding and subsequently did not leave her hobby, developing formulas for the quick assembly of the “magic cube”. One of the most popular cube folding options is called CFOP, based on the first letters of the four assembly steps.

Instruction:

1. We collect the cross on the upper face, which is made up of cubes on the edges of the lower face. This stage is called Cross - cross.
2. We collect the lower 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) - the first two layers.
3. We collect the remaining face, not paying attention to the fact that not all the details are in place. The stage is called OLL (Orient the last layer), which translates as “orientation of the last layer”.
4. The last level - PLL (Permute the last layer) - consists in the correct arrangement of cubes of the upper layer.

Friedrich video tutorials

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

Video: cross assembly acceleration

Video: collect the first two layers

Video: working with the last layer

Video: Friedrich's latest build level

2 x 2

A 2 x 2 Rubik's Cube or a Rubik's mini-cube also folds in layers, starting from the lower level.

Mini Cube is a lite version of the classic puzzle

Easy Beginner's Guide

1. We collect the bottom layer so that the colors of the last four cubes coincide, and the remaining two colors are the same as the colors of the neighboring parts.
2. We begin to organize the top layer. Please note that at this stage, the goal is not to combine the colors, but to put the cubes in place. We start by determining the color of the top. Everything is simple here: it will be the color that did not appear in the lower layer. We rotate any of the upper cubes so that it falls into a position when the three colors of the element intersect. Having fixed the angle, we place the elements of the remaining ones. We use two formulas for this: one for changing the diagonal cubes, the other for the neighboring ones.
3. Finish the top layer. We carry out all operations in pairs: we rotate one corner, and then another, but in the opposite direction (for example, the first is clockwise, the second is against). You can work with three angles at once, but in this case there will be only one combination: either clockwise or counterclockwise. Between the rotations of the corners, we rotate the upper face so that the worked-out corner is in the upper right corner. If we work with three angles, then we set the correctly oriented of them from the back to the left.

Formulas for rotating angles:

• (VFPV · P "V" F ") ² (5);
• В²Ф · В²Ф "· В" Ф · В "Ф" (6);
• FVF² · LFL² · VLV² (7).

To rotate three angles at once:

• (FVPV "P" F "V") ² (8);
• ФВ · Ф "В · ФВ² · Ф" В² (9);
• В²Л "В" Л²Ф "Л" Ф²В "Ф" (10).

Photo gallery: 2 x 2 cube assembly

Video: Friedrich method for 2 x 2 cube

We collect the most difficult versions of the cube

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

Cube models with many elements usually have rounded corners for the convenience of manipulating a toy