How to solve the Rubik's Cube

In a nutshell: if you remember 7 simple formulas with a length of no more than 8 rotations each, then you can safely learn how to solve a regular 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. Typically, each of the nine squares on each face of the Cube is colored one of six colors, usually arranged in pairs opposite each other: white-yellow, blue-green, red-orange, forming 54 colored squares. Sometimes, instead of solid colors, they put on the faces of the Cube, then it becomes even more difficult to collect 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 "stirs".

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

ABC Cube

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

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

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

8 tricolor corner pieces (8 "corners")

1 internal element - cross

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

Elements can be rotated in "layers" - groups of 9 pieces. Clockwise rotation of the outer layer 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), Rear (back layer). There are three more inner layers. In this assembly algorithm, we will not rotate them separately, we will use only 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 designations:

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

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

When assembling the Cube, we will sequentially rotate the layers. The sequence of turns is recorded from left to right one after the other. If some rotation of the layer needs to be repeated twice, then the degree icon “2” is placed after it. For example, Ф 2 means that you need to turn the front twice, i.e. F 2 \u003d FF or F "F" (as convenient). In Latin notation, instead of Ф 2, F2 is written. I will write formulas in two notations - Cyrillic and latin, separating them like this sign ⇔.

For the convenience of reading long sequences, they are divided into groups, which are separated from neighboring groups by dots. If it is required 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 bracket. In Latin notation, a multiplier is used instead of an exponent. In square brackets, I will indicate the number of such a sequence or, as they are usually called, “formulas”.

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

Assembly

There are many ways to build a Cube. There are those that allow you to assemble a cube with a couple of formulas, but in a few hours. Others - on the contrary, by memorizing a couple of hundred formulas, they allow you to collect 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 solve the Cube in a couple of minutes. When I was 7 years old, I mastered such an algorithm in a week and collected a cube in an average of 1.5-2 minutes, which amazed my friends and classmates. That's why I call this assembly method "the simplest". I will try to explain everything "on the fingers", almost without pictures.

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

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

Assembly steps:

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

14/26 - corners of the first layer

16/26 - second layer

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

26/26 - corners of the third layer

26/26 - (additional stage) rotation of centers

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

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

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

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

V"L" VL VF V"F" ⇔U"L" UL UF U"F"- edge 2 layers down and 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- permutation of the edges of the lower cross ("fish")

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

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

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

The purpose of this stage: the correct location of the 4 upper edges, which, together with the upper center, make up the “cross”.

So, the Cube is completely disassembled. Actually not completely. A distinctive feature of the classic Cube is its design. Inside there is a cross (or ball), which rigidly connects the centers. The center determines the color of the entire face of the Cube. Therefore, 6 centers are always already in their places! Let's start with the top. Usually the assembly starts with a white top and a green front. With non-standard coloring, 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 what color we have top and what is the front, and when rotating the layers, do not accidentally turn the whole Cube and not go astray.

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

So, let's start assembling. White top, green front. We look at the Cube from all sides, without releasing it, without turning it over in our hands and without rotating the layers. 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 (upper) layer, then by double-turning the outer vertical layer on which it is located, we “drive” it down to the third layer. We act similarly if the RK is in the second layer, only in this case we drive it down not with a double, but with a single rotation.

It is desirable to drive out so that the RK 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 was 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 RK is already on the third layer, then simply put it in front of you from below, rotating the bottom layer. After that, turning F 2 ⇔F2 put RK in place.

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

Let's move on to installing the next edge. Without changing the top, we change the front, i.e. turn the Cube to itself 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 gather faster!

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

Stage 2 - corners of the first layer

The goal of the second stage is to collect the entire top layer by installing four corners in addition to the already assembled cross. In the case of a 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 put it in front at the top right. To do this, we will proceed in the same way as in the first stage: first we will find it, then we will “drive” it to the bottom layer, then we will put it in front at the bottom right, i.e. under the place we need, and after that we will drive it upstairs.

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

We are looking for an element with which we will work (RC). In the upper right near corner 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 rotated correctly, 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 did not fall into place, or stood up, but turned incorrectly, then turn the Z switch again, and so on until the RK is at the top in place and correctly turned. Sometimes you need to twist the Z-switch up to 5 times.

If the RC is in the upper layer and not in place, then we drive it out of 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 we turn the Z-commutator. After the RC is “kicked out”, we again turn the Cube towards us with the desired front, rotate the bottom, put the already expelled RC under the place we need and drive it up with the Z-switch. We twist the Z-switch until the cube is oriented as it should.

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

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

I want to warn you, with each step the Cube takes on a more assembled 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 assembled again. Unless, of course, you follow the main rule - during the rotation you can not twist the entire Cube, so as not to accidentally go astray. Only separate 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 of the 2nd layer. They can now be located both on the second and on the third (now upper) layer.

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

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

There are two formulas for this:

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

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

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

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

As a result, 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 here.)

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

The purpose of this step 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 rotate the edges so that they are all facing up in the same color as the top. If they are already all turned up so that at the top we get a one-color flat cross, we move on to moving the edges. If the cubes are turned incorrectly, we will turn them over. There can be several cases of edge orientation:

A) all wrongly rotated

B) two adjacent ones are incorrectly rotated

C) two opposite ones are incorrectly rotated

(There can be no other options! That is, it cannot be that only one edge is left to turn over. If two layers of the cube are completed, and an odd number of edges are left to turn on the third, then you can stop worrying, but .)

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, twist the formula and get case C).

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

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

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 everyone fell into place, then the cross is assembled, proceed to the next stage. If not everything is in place, then there can be two cases: either two adjacent ones are in place, or two opposite ones are in place. If they are opposite in place, then we twist the formula and get neighboring ones in place. If there are neighboring ones, then we turn the Cube so that they are on the right and behind. We twist the formula. After that, the edges that were out of place will be swapped. Cross completed!

NB: a little note about the "fish". This formula uses rotation IN 2 ⇔U "2, that is, rotate the top counterclockwise two times. In principle, for the Rubik's Cube IN 2 ⇔U "2 = IN 2 ⇔U2, but it's better to remember 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 = AT 3 ⇔U3.

Stage 5 - corners of the third layer

It remains to install in place, and then correctly rotate the four corners.

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

Let's look at the corners. If they are all in place and it remains only to rotate them correctly, then we look at the next paragraph. If not a single corner stands still, then we twist the formula, while one of the corners will definitely fall into place. We are looking for a corner that stands still. Rotate the Cube so that this corner is on the back right. We twist the formula. If at the same time the cubes did not fall into place, then we twist the formula again. After that, all the corners should be in place, it remains to rotate them correctly, and the Cube will be almost completed!

At this stage, there are either three dice to turn 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 die left to flip. Or two, but both clockwise. Or two clockwise and one against. 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 not bathe further, 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 wrongly oriented corner is front right. Rotate the Z-commutator (up to 5 times) until the corner turns correctly. Next, without changing the front, we rotate the top layer so that the next “wrong” angle is in front on the right, and rotate the Z-commutator again. And so we do until all the corners turn around. After that, rotate the top layer so that the colors of its faces match the already assembled first and second layers. Everything! If we had an ordinary six-color cube, then it is already completed! It remains to turn the Cube with its original top (which is now on the bottom) up to get the original state.

Everything. Cube collected!

Hope you find this guide useful!

Stage 6 - Rotation of centers

Why is the cube not going?!

Many people ask the question: “I do everything as it is written in the algorithm, but the cube still does not collect. Why?" Usually the ambush waits on the last layer. Two layers are easy to assemble, but the third - well, no way. Everything is stirred, you start reassembling, 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 are not following the algorithms exactly. It is enough to make one turn in the wrong direction or skip some turn to stir the entire Cube. At the initial stages (when assembling the first and second layers), the wrong rotation is not very fatal, but when assembling the third layer, the slightest mistake leads to complete mixing of all the collected layers. But if you strictly follow the assembly algorithm described above, then everything should come together. The formulas are all time-tested, there are no errors in them.

Not very obvious. And that's probably the point. Chinese manufacturers make Dice of different quality - from professional champion dice for high-speed assembly to falling apart in the hands at the very first spins. What do people usually do if the Cube fell apart? Yes, they insert back the fallen out cubes, and do not worry about how they were oriented and in what place they stood. And you can't do that! Or rather, it is possible, but the probability after that to collect the Rubik's Cube will be extremely small.

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

On a cube with two layers assembled, you need to carefully pry off the cover of the central cube of the third layer with a flat screwdriver or a knife, remove it, unscrew the screw with a small Phillips screwdriver, without losing the spring on the screw. Carefully pull out the corner and side cubes of the third layer and insert them correctly color by color. At the end, insert and screw the previously unscrewed central cube (do not overtighten). Rotate the third layer. If it's tight, loosen the screw, if it's too easy, tighten it. It is necessary that all faces spin with the same effort. After that, close the lid of the central cube. Everything.

You can, without unscrewing, turn any face by 45 °, pry one of the onboard cubes with your finger, knife or flat screwdriver and pull it out. Just do it carefully, because you can break the cross. Then, in turn, pull out the necessary cubes and insert them back into their places already correctly oriented. After everything is assembled color to color, it will also be necessary to insert (snap) the onboard cube, which was pulled out at the beginning (or some other, but onboard, because the corner one will definitely not work).

After that, the Cube can be mixed and calmly assembled using the above algorithm. And now he's definitely coming! Unfortunately, one cannot do without such “barbaric” procedures with a knife and a screwdriver, because if the Cube was not folded correctly after falling apart, it will not work to assemble it with rotations.

PS: if you can't 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 caps of the centers. The standard coloring should have 6 colors, white opposite yellow, blue opposite green, red opposite orange. Usually white top, yellow bottom, orange front, red rear, green right, blue left. But absolutely exactly the mutual arrangement of colors is determined by the corner cubes. For example, you can find an angular white-blue-red and see that the colors in it are arranged clockwise. So, if the top is white, then the right should be blue, and the front red.

PPS: if someone joked, 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 break it apart. No screwdriver will help here. It is necessary to calculate which stickers were re-glued, and then re-stick them in their places.

Can it be even easier?

Well, where is it easier? This is one of the simplest algorithms. The main thing is to understand it. If you want to pick up a Rubik's Cube for the first time and learn how to solve it in a couple of minutes, then it's better to put it aside and do something less intellectual. 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 it has a lot of formulas. You can try to use some other algorithm. For example, you can assemble the Cube, really using one single formula, for example, the same Z-commutator. It just takes a long, long time to assemble in this way. You can take another formula, for example, F PW "P" V " PVP" F" PVP" V" P" FPF", which swaps pairs of 2 side and 2 corner cubes. And using simple preparatory rotations, gradually collect cube, setting in place first all the side cubes, and then the corner ones.

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

The famous puzzle, which consists of several colored sectors combined into one cube, appeared in 1974. The Hungarian sculptor and teacher decided to create a textbook to explain group theory to students. To date, this toy is considered the best-selling in the world.

But, success came to this puzzle only when the German entrepreneur Tibor Lakzi paid attention to it. He, together with the game inventor Tom Kremer, not only launched the production of cubes, but also organized the promotion of this puzzle to the masses. It was thanks to them that competitions in the speed assembly of Rubik's cubes appeared.

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

The structure of the Rubik's cube and the names of rotations

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 established expressions.

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

A square with one of six colors is rigidly located at the end of the cross. Around it, you need to collect the rest of the squares of the same color. Moreover, the puzzle is considered completed if all six sides of the cube have their own color.

IMPORTANT: In the original puzzle, yellow is always opposite white, orange is red, and green is blue. And if you take the puzzle apart and then put it together incorrectly, it can lead to the fact that it will never be able to be assembled.

In addition to the centers of the cube, the constant components of this puzzle are the corners. Each of the eight corners is made up of 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: The Rubik's Cube is assembled by placing the corner and middle sectors in accordance with the colors of the central sectors.

Now that we have understood the construction of this puzzle, it is time to move on to the names of the sides and rotations and their designation in specialized literature.

In the process of assembling a 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 intercepts. Schematically, this is shown as follows:

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

Easy and simple way to assemble: Instruction for kids and beginners

The most detailed assembly instruction for beginners is as follows:

• At the first stage of assembling 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, we find the white center and white edges and assemble the crosses according to the diagram below:

• After the above steps, we should get a 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 edges between themselves.
• This algorithm is called "bang-bang" and is shown in the diagram below:

• Let's move on to the next step of assembling the puzzle. Find the white corner on the bottom layer and put 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 color and place them between the centers of the second layer. Then we twist the cube until the color of the center matches the color of the face element.
• 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 "goes" 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 assembled. 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 with the U, U' and U2 movements. This must be taken into account. So that the colors of the corner are identical to the colors on the lower layers. When using this step, hold the white cube towards you.

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

The fastest way. The Jessica Friedrich Method

This puzzle assembly method was developed by Jessica Friedrich in 1981. It is conceptually the same as most known methods. But, it focuses on the speed of assembly. Due to this, the number of assembly stages 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. You need to study it when your cube assembly speed becomes less than 2 minutes.

1. At the first stage, you need to assemble a cross with side faces. In specialized literature, this stage is called Cross(from 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. Don't pay attention to the sides. The name of the stage is OLL (from the English Orientation of the Last Layer - 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 - the arrangement of the elements of the last layer in place). It can be assembled using the following algorithms:

Rubik's cube assembly scheme 3x3 in 15 moves

Since 1982, when the Rubik's cube speed contest appeared, many puzzle lovers began to develop algorithms that would help to correctly place the sectors of the cube 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 solve a Rubik's cube in 15 moves. Moreover, a few years ago, an 18-way algorithm for assembling this puzzle was developed. But, it can not be used from all positions of the cube, so it was also rejected as the fastest.

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

How easy it is to solve a Rubik's Cube: Video

The puzzle, invented as a visual aid to algebraic theory, unexpectedly captivated the whole world. For more than a decade, people far from higher mathematics have been passionately struggling with a complex and exciting task. "Magic Cube" is an excellent tool for developing logical thinking and memory. For those who first wondered how to solve the Rubik's Cube, diagrams and comments will help maintain enthusiasm, and perhaps discover the world of speedcubing.

The six faces of the puzzle have specific colors and their order, patented by the inventor. Numerous fakes often impersonate precisely unusual colors or their position relative to each other. Teaching charts and descriptions always use the standard color scheme. It's easy for beginners to get lost in the explanations if you use a die with a different color scheme.

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

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

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

The modern Rubik's cube of classical design consists of the following elements:

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

The game with the Rubik's Cube is that with the help of a movable mechanism, the colored elements on the faces are reordered and try to collect in the original order.

Puzzle fans compete to solve the puzzle against the clock. In addition to manual dexterity, for this it is necessary to study, remember and bring to automaticity hundreds of combinations of colored elements and actions with them. This unusual sport is called speedcubing.

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

The newest hobby is assembling solitaires (patterns) on a cube.

The structure of the Rubik's cube and the names of rotations

In order to describe the manipulations with the puzzle, write down the solution schemes, the movements of the elements relative to each other, and just for the convenience of communication, a language of rotations was created. It is a letter designation for each face and for ways to rotate it.

The sides of the puzzle are indicated by capital letters.

In Russian-language guides for assembling the Rubik's Cube, initial letters from Russian names are used:

• F - from the "facade";
• T - from "rear";
• P - from "right";
• L - from "left";
• B - from "top";
• N - from "bottom".

The world community uses the initial letters of the names of the faces in English.

Designations adopted by the WCA (World Cube Association):

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

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

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

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

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

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

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

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

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

• R - clockwise rotation;
• R' - counterclockwise rotation.
• R2 is a double turn, no matter in which direction, since the edge has only four possible positions.

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

The rotation of opposite faces "clockwise" turns out to be counter-clockwise.

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

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

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

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

• x and x' are rotations along the X axis of the entire cube. The movements coincide with the rotations of the right side.
• y and y' are rotations of the cube along the Y axis. The movements coincide with the rotations of the top face.
• z and z' - rotation of the cube along the Z axis. The movement coincides with the rotation of the front face.
• х2, y2, z2 – designations of double interceptions along the specified axis.

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

• Hat - colored elements collected on one side of the cube. Assembling the puzzle is the same as assembling all six hats.
• Belt - colored elements adjacent to the cap. The hat can be assembled in such a way that the belt consists of disparate colored fragments, that is, the corner and rib elements are out of place.
• The cross is a figure on a cap of five fragments of the same color. Assembly often begins with the construction of a cross. There is no clear direction here. This step allows for the greatest leeway and requires some thought. When the cross is ready, it remains to follow the learned algorithms.
• Flip - turning a corner or edge in one place relative to the center, this action requires the use of special algorithms.

Schemes and steps for assembling a puzzle for beginners

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

Before performing any action, it is necessary to inspect the cube. In competitions, 15 seconds are allotted for "inspection". During this time, you need to find elements of the same color, which will be collected in a "header" at the first stage. It is traditional to start on the white side, meaning most manuals assume the U is white. "Multicolor" speedcubers can start the assembly from any side, mentally rebuilding all the ready-made algorithms.

Rubik's Cube 2x2

"Mini cube" consists of 8 corner elements. At the first stage, one layer of four corners is assembled. At the second stage, the remaining corners are placed in their places, while they can be turned upside down, that is, the colored elements will not be on their faces. It remains to deploy them to the desired side.

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

How to solve a Rubik's Cube 3x3

1. Build a "white cross" by assembling 4 edges with white stickers around the white center.
2. Align the colored centers of the sides R, L, U, D with the appropriate edges of the "white cross".
3. Put the corners with white stickers in their places. With the R'D'RD algorithm repeated up to five times, the corners will flip to the correct position.
4. To put the edges of the middle layer in their place, you need to intercept the cube - y2. Select the edge without the yellow sticker. Align it with the center, matching in color with one of the sides. Using the formulas, shift the edge to the middle layer: The edge descends with an offset to the left: U'L'ULUFU'F'. The edge descends with an offset to the right: URU'R'U'F'UF. If the element is in place but not rotated correctly, these algorithms are used again to move it to the third layer and set it again.
5. Without intercepting the cube, collect the yellow cross on the cap of the third layer, repeating the algorithm: FRUR'U'F'.
6. Align the edges of the last layer with the side centers correctly, as was done for the first cross. The two ribs snap into place easily. The other two will have to be swapped. If they are opposite each other: RUR'URU2R'. If on adjacent sides: RUR'URU2R'U.
7. Arrange the corners of the last face in the correct positions. If none of them are in the right place, apply the URU'L'UR'U'L formula. One of the elements will fit correctly. Intercept the cube with this angle towards you, it will be the upper right on the front face. Move other corners counterclockwise URU'L'UR'U'L or vice versa U'L'URU'LUR'. At this stage, all the collected sections will be rebuilt, it will seem that something went wrong. It is important to ensure that the cube does not turn over and the center F does not move relative to the user. The combination of moves must be repeated up to 5 times.
8. The corner elements may need to be unfolded so that the color fragments align with the rest of the faces correctly. To unfold (flip) them, the first formula is used: R'D'RD. It is important not to intercept the die so that F and U do not change.

Rubik's Cube 4x4

Puzzles that have more than three elements in a line involve a much greater number of combinations.

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

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

Additional symbols for inner layers:

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

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

• When assembling the central elements, one must remember which colors are contrasted in pairs. Algorithm to swap elements from middle quadruple: (Rr) U (Rr)' U (Rr) U2 (Rr)' U2.
• When assembling edges, only the outer faces rotate. Algorithms: (Ll)’ U’ R U (Ll); (Ll)' U' R2 U (Ll); (Ll)' U' R' U (Ll); (Rr) U L U’ (Rr)’; (Rr) U L2 U’ (Rr)’; (Rr) U L' U' (Rr)'. In most cases, the edges can be assembled intuitively. When only two edge elements remain: (Dd) R F’ U R’ F (Dd)’ to set them side by side, U F’ L F’ L’ F U’ to swap them.
• Next, the 3 * 3 * 3 cube formulas are used to rearrange and rotate the corners.

Difficult cases that require a special solution are parities. Their formulas do not solve the problem, but knock out the elements from the impasse, bringing the puzzle into a form that can be solved by standard algorithms.

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

Quick assembly puzzle 5x5

The assembly consists in bringing to the classical form. First, 9 central fragments are assembled on each cap and three edge elements. The last stage is the arrangement of corners.

Additional designations:

• u is the inner top face;
• d is the inner bottom face;
• e - the inner edge between the upper and lower;
• (two faces in brackets) - simultaneous rotation.

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

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

Formulas for parities:

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

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

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

The assembly is carried out not in layers, but in groups of elements: first all the edges, then the corners.

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

In the process of blind assembly, the cube is not turned over so as not to get confused.

Before proceeding with the assembly, the cube is “remembered”. A chain is mentally created along which the elements will move. Each sticker is assigned its own letter of the alphabet. For ribs and for corners, the speedcuber makes up separate alphabets. A shuffled Rubik's Cube is remembered as a sequence of letters. The top sticker on the buffer cube is the first letter, the sticker that occupies its rightful place is the second, and so on. For simplicity, letters form words, and words form sentences.

The 22-year-old athlete holds several more current records 2015 - 2017:

• 4x4x4 - 19.36 seconds;
• 5x5x5 - 38.52 seconds;
• 6x6x6 - 1:20.03 minutes;
• 7x7x7 - 2:06.73 minutes;
• megaminx - 34.60 seconds;
• with one hand - 6.88 seconds.

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

Steps for assembling a 6x6 Rubik's Cube: We collect the centers (16 elements each) + We collect the edges (4 elements each) + We collect it as a 3x3 cube.
But first - the language of rotations, the designation of edges and turns.

L - rotation of the left side, The number 3 in front of the letter means the number of sides rotated simultaneously. For example - 3L, 3R, 3U, etc. Small letters indicate the inner faces of the cube. For example - r, l, u, b, f ...

The number 3 in front of the small letter means the rotation of one specified inner middle (third) face. For example - 3l, 3r, 3u, etc... Simultaneous rotation of two internal faces is indicated by the numbers 2-3 in front of the small letters denoting this face. For example - 2-3r, 2-3l...

" - a dash after the letter, means that the rotation is COUNTER-CLOCKWISE. For example - U", L", R"...

You need to rotate the face to face you in order to orient yourself in the direction of rotation - clockwise or counterclockwise. Further in the formulas, the designation R2, U2, F2 ... will also be used - this means turning the face 2 times, i.e. at 180.

Stage 1. Assembly of centers.

At the first stage, you need to collect the central (sixteen elements) on each side of the 6x6 cube (Fig. 1). The center is 16 elements of the same color in the middle of each face. If you rotate only the outer faces (Fig. 2), you will not disturb the position of the central elements of the cube. Rotate the outer edges to position the center elements you want to swap. Apply a formula to swap elements. In this case, the previously collected elements of the other centers will not be violated.

By rotating the outer faces, we achieve the correct positioning of the elements from the center of the cube before applying the appropriate formula. And don't forget that the centers in a 6x6 cube are not strictly fixed! They need to be placed focusing on the corner elements, according to their colors, and you need to do this from the very beginning.

3r U" 2L" U 3r" U" 2L		2R U" 3l" U 2R" U" 3l
2R U 2R" U 2R U2 2R"		3r U 3r" U 3r U2 3r"
3r U 3l" U" 3r" U 3l

The first four centers are easy and interesting to assemble, for this it is not at all necessary to know the formulas, it is enough to understand the basic principles.

Also, the entire first stage of assembly can be viewed on the video.

Stage 2. Assembly of ribs.

At the second stage, you need to collect four edge elements of the cube. The starting positions before applying the formulas are given in the figures. Crosses show edge pairs that have not yet been joined and will be affected during the application of the formula. Applying formulas does not affect all other previously collected edges and centers. Everywhere in the figures it is considered that yellow is the front (front face), red is the top. You may have a different location of the centers - it does not matter.

The result to be reached in the second stage.

rU L"U"r"		3r U L" U" 3r"
3l" U L" U" 3l		l"U L"U"l

It is important to understand the idea of ​​this stage. All formulas consist of 5 steps. Step 1 is always to rotate the edges (right or left) so that the 2 edge elements fit together. Step 2 is always the turn of the top. Where to turn the top depends on which side there is an unassembled edge that you will substitute for the docked one in step 1. In the pictures and in these formulas, this edge is on the left, but it can also be on the right. Step 3 is always a rotation of one right or left face so that instead of a joined edge, a non-joined edge is substituted. Steps 4 and 5 are the reverse of steps 2 and 1 to return the cube to its original state. So - they docked, put aside, set up the unassembled, returned it back.
For a better demonstration, watch the video.

This article provides a step-by-step instruction for beginners, with which you can solve the Rubik's cube using the layer-by-layer method. Compared to other methods, this method is quite simple, because you will not need to remember many sequential actions. Mastering the layering method will help you later on smoothly transition to Jessica Friedrich's quick assembly method, which allows you to solve a cube in less than 20 seconds in competition. In order to conquer this insidious Erno Rubik's puzzle, you will need patience and diligence. Good luck!

Steps

Part 1

Familiarize yourself with the three types of elements. There are three main types of elements in the Rubik's Cube, the definition of which depends on their location in the cube.

• Central the elements are located in the center of the cube on each of its sides, surrounded by the other eight elements. Each such element cannot be moved, and it has only one color.
• corner elements are located at the corners of the cube. Each element has three different colors.
• Side the elements are located between the corner elements. Each such element has two different colors.
• Note. Elements of one type cannot become elements of another. The corner element will always be in the corner of the cube.

Learn to distinguish the six sides of the cube. Each side of the Rubik's cube has its own color, which is determined by its central element. So, for example, the side that has a red element in the center will be the "red side" even if there are no other red elements nearby. However, sometimes it is better to name the sides based on their position relative to the side you are currently looking at. Here are some terms that will be used in this guide:

• F(Front) - Raise the cube to eye level. Directly in front of you will be the front side.
• W(Back) is the opposite side that is not visible when you hold the cube in your hands.
• AT(Upper) - the side facing up.
• H(Lower) - the side facing down.
• P(Right) - The side to your right.
• L(Left) - The side to your left.