How to solve a Rubik's Cube

In a nutshell: if you remember 7 simple formulas of no more than 8 rotations each, then you can easily learn how to solve a regular 3x3x3 cube in a couple of minutes. This algorithm will not be able to solve the cube in less than a minute or a minute and a half, but two to 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 edge of the Cube, then it becomes even more difficult to assemble.

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

Solving a Cube means returning it from being stirred to its original state. This, in fact, is the main point of the puzzle. Many enthusiasts find pleasure in assembling "solitaire" - patterns .

ABC of the Cube

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

6 single color centerpieces (6 “centers”)

12 two-color side or rib elements (12 “ribs”)

8 three-color corner elements (8 “corners”)

1 internal element - cross

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

Elements can be rotated in “layers” - groups of 9 pieces. Rotating the outer layer clockwise by 90° (if you look at this layer) is considered “straight” and will be designated capital letter, and a counterclockwise turn is “reverse” to a straight line - and we will denote it with 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 only use rotations of the outer layers. In the world of speedcubers, it is customary to use Latin letters for 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 another. If some rotation of a layer needs to be repeated twice, then a degree icon “2” is placed after it. For example, F 2 means that you need to turn the front twice, i.e. F 2 = FF or F "F" (whichever is more convenient). In Latin notation, instead of F 2, F2 is written. I will write formulas in two notations - Cyrillic And Latin, separating them with this sign ⇔.

To make it easier to read long sequences, they are divided into groups, which are separated from neighboring groups by dots. If a sequence of turns needs to be repeated, 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 of notation for rotation of the layers of the Cube, you can proceed directly to the assembly process.

Assembly

There are many ways to assemble the 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 allow you to solve 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 assemble the Cube in a couple of minutes. When I was 7 years old, I mastered this algorithm in a week and solved 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 assemble the Cube in horizontal layers, first the first layer, then the second, then the third. We will divide the assembly process into several stages. There will be five of them in total and one additional one.

6/26 At the very beginning, the cube is disassembled (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- edge 2 layers down and to the right

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

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

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

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

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

Stage 1 - cross of the first layer (“upper cross”)

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

So, the Cube is completely disassembled. Actually not completely. Distinctive feature The classic Cube is its design. Inside there is a cross (or ball) that rigidly connects the centers. The center determines the color of the entire face of the Cube. Therefore, 6 centers are always already in place! First, choose the top. Typically, assembly begins with a white top and green front. For non-standard coloring, choose what is more convenient. We hold the Cube so that the upper center (“top”) is white and the front center (“front”) is green. The main thing when assembling is to remember what color is the top and what is the front, and when rotating the layers, do not accidentally turn the entire Cube and get lost.

Our goal is to find an edge with top and front colors and place it between them. At the very beginning, we look for a white-green edge and place it between the white top and the green front. Let's call the required element a “working cube” or RK.

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

If the RK 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 do the same 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 advisable to drive it out so that the color of the paint turns out to be the color of the top down, then it will be easier to install it in place. When driving the RK down, you need to remember about the ribs that are already in place, and if any edge has been affected, then you must remember to return it later to its place by reverse rotation.

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

Once the RK is in place, there can be two options: either it is rotated correctly or not. If it is turned correctly, then everything is OK. If it is turned incorrectly, then we turn it over using the formula FV"PV ⇔FU"RU. If the RK is “kicked out” correctly, i.e. color from top to bottom, then you practically won’t have to use this formula.

Let's move on to installing the next rib. Without changing the top, we change the front, i.e. turn the Cube towards you with the new side. And we repeat our algorithm again until all the remaining edges of the first layer are in place, forming a white cross on the top edge.

During the assembly process, it may turn out that the RC is already in place, or it can be put in place (without destroying what has already been assembled) without first driving it down, but “immediately”. Well, good! In this case, the cross will come together faster!

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

Stage 2 - corners of the first layer

The goal of the second stage is to collect the entire top layer, installing in addition to the already assembled cross four corners. In the case of the cross, we looked for the right edge and placed it in front at the top. Now our RK is not an edge, but a corner, and we will place it in the front at the top right. To do this, we will do the same as at the first stage: first we will find it, then we will “drive” it to the bottom layer, then we will place it in the front lower right, i.e. under the place we need, and after that we’ll drive it up.

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

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

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

Let's turn the Z-switch! If the corner is not in place, or is in place, but is rotated incorrectly, then turn the Z switch again, and so on until the RK is at the top in place and correctly rotated. Sometimes you need to turn the Z-switch up to 5 times.

If the RK is in the upper layer and is not in place, then we drive it out of there with any other one using the same Z-commutator. That is, first we turn the Cube so that the top remains white, and the RK, which needs to be kicked out, is located at the top right in front of us and turn the Z-commutator. After the RK has been “kicked out,” we again turn the Cube towards us with the desired front, rotate the bottom, place the already kicked out RK under the place we need and use the Z-commutator to drive it to the top. We turn the Z-switch until the cube is oriented correctly.

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 are still in place!

Let's admire this beauty for a while and turn the Cube over so that the collected layer is at the bottom. Why is this necessary? We will soon need to start assembling the second and third layers, and the first layer has already been assembled and is in the way on top, covering all the layers that interest us. Therefore, let’s turn them upside down 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 start assembling the second layer.

I want to warn you that with each step the Cube becomes more assembled, but when you twist the formulas, you already assembled parties stir. The main thing is not to panic! At the end of the formula (or sequence of formulas), the cube will be assembled again. If, of course, you follow the main rule - during the rotation process you cannot spin the entire Cube, so as not to accidentally get lost. Only separate layers, as written in the formula.

Stage 3 - second layer

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

Select any edge on the top layer 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 the color of some side center. We 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 RK is already in the second layer out of place, or in its place, but incorrectly rotated, then we “kick it out” with any other one, 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’ll have to start assembling again. It's okay, even champions sometimes get confused during assembly.

As a result, after this stage we have two assembled layers - 19 out of 26 cubes are in place!

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

Stage 4 - cross of the third layer (“lower cross”)

The goal of this stage is to assemble the cross of the last unassembled layer. Although the unassembled layer is now on top, the cross is called "bottom" because in its original state this layer was at the bottom.

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

A) all are turned incorrectly

B) two adjacent ones are incorrectly rotated

C) two opposite ones are turned incorrectly

(There cannot be any other options! That is, it cannot be that there is only one edge left to turn over. If two layers of the cube are completed, and on the third there is an odd number of edges left to turn over, then you don’t have to worry about it any further, eh.)

Let's 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 turn the Cube so that two correctly rotated edges are on the left and behind, twist the formula and get case B).

In case B), we turn 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 of correctly oriented, but out of place edges. Now you need to make a correct volumetric cross from a flat cross, i.e. move the ribs.

Let's remember the new formula: PV · P"V · PV" 2 · P"V ⇔RU · R"U · RU"2 · R"U(“fish”)

We twist the top layer so that at least two edges fall into place (the colors of their sides coincide with the centers of the side faces). If everything falls into place, then the cross is assembled, we move on 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 the opposite ones are in place, then we twist the formula and get the adjacent ones in place. If the neighboring ones are in place, then we turn the Cube so that they are on the right and behind. Let's twist the formula. After this, the ribs that were out of place will change places. The cross is assembled!

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

Stage 5 - corners of the third layer

All that remains is to install it in place, and then turn the four corners correctly.

Let's 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 all that remains is to turn them correctly, then look at the next paragraph. If not a single corner is in place, then twist the formula, and one of the corners will definitely fall into place. We are looking for a corner that stands still. We turn the Cube so that this corner is at the back right. Let's twist the formula. If the cubes do not fall into place, then twist the formula again. After this, all the corners should be in place, all you have to do is turn them correctly, and the Cube will be almost solved!

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

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

All. The cube is complete!

I hope you find this guide useful!

Stage 6 - Rotation of centers

Why won't the cube assemble?!

Many people ask the question: “I do everything as written in the algorithm, but the cube still doesn’t fit. Why?" Usually an ambush awaits on the last layer. Two layers are easy to put together, but the third is not easy. Everything is stirred, you begin to reassemble, again two layers, and again when assembling the third, everything is stirred. Why might this be so?

There are two reasons - obvious and not so obvious:

Obvious. You are not following the algorithms exactly. It is enough to make one turn in the wrong direction or miss a turn for the entire Cube to get mixed up. At the initial stages (when assembling the first and second layers), an incorrect turn is not very fatal, but when assembling the third layer, the slightest mistake leads to complete mixing of all assembled 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 most likely this is exactly the point. Chinese manufacturers make Cubes of varying quality - from professional championship cubes for quick assembly to those that fall apart in your hands at the very first spins. What do people usually do if the Cube falls apart? Yes, they put back the fallen cubes, and don’t worry about how they were oriented and in what place they stood. But you can’t do that! Or rather, it is possible, but the likelihood of solving a Rubik's Cube after this will be extremely small.

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

On a cube with two layers assembled, you need to carefully pry up the lid of the central cube of the third layer with a flat screwdriver or a knife, remove it, unscrew the screw with a small Phillips screwdriver, without losing the spring attached to the screw. Carefully pull out the corner and side cubes of the third layer and insert them correctly color to color. At the end, insert and screw the previously unscrewed central cube (do not tighten too much). Twist the third layer. If it turns tightly, loosen the screw; if it turns too easily, tighten it. It is necessary that all faces rotate with the same force. After this, close the lid on the central cube. All.

Without unscrewing, you can rotate any edge by 45°, pry one of the side cubes with your finger, knife or flat screwdriver and pull it out. You just need to do this carefully, because you can break the cross. Then, one by one, pull out the required cubes and insert them back into their places, now correctly oriented. After everything is assembled color by color, you will also need to insert (snap) the side cube that you pulled out at the beginning (or some other, but side cube, since inserting a corner cube definitely won’t work).

After this, the Cube can be mixed and calmly assembled using the above algorithm. And now he’ll definitely get it together! Unfortunately, you cannot do without such “barbaric” procedures with a knife and a screwdriver, since if, after falling apart, the Cube is folded incorrectly, it will not be possible to assemble it by rotation.

PS: if you can’t assemble even two layers, then first you need to make sure that at least the centers are in the right places. Perhaps someone rearranged the center caps. The standard coloring should have 6 colors, white opposite yellow, blue opposite green, red opposite orange. Usually the top is white, the bottom is yellow, the front is orange, the back is red, the right is green, the left is blue. But the relative position of the colors is absolutely determined by the corner cubes. For example, you can find a corner white-blue-red and see that the colors in it are arranged clockwise. This means that if there is white on top, then there should be blue on the right, and red on the front.

PPS: if someone made a joke and not only rearranged the elements of the cube, but re-glued the stickers, then it is generally impossible to assemble the Cube, no matter how much you destroy it. No screwdriver will help here. You need to figure out which stickers were re-glued, and then re-glue them in their places.

Could it be even simpler?

Well, how much easier is it? This is one of the simplest algorithms. The main thing is to understand him. If you want to pick up a Rubik's Cube for the first time and immediately learn how to solve it in a couple of minutes, then it is better to put it aside and do something less intellectual. Any learning, including the simplest algorithm, requires 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.

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

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

For children and adults sometimes the task may seem overwhelming how to solve a 3x3 rubik's cube. A diagram with pictures for beginners in this matter is one of the main assistants.

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

You can solve a Rubik's cube in different ways and methods. You can do this in 15 moves, 7 moves, or even as many as 20. For many years, all sorts of smart people have been struggling to find the optimal solution to this problem. After all, the Rubik's Cube is a mechanical puzzle that can be solved quite logically. All you need is step by step instructions, as well as a small supply of logic and patience.

Before starting the assembly algorithm itself, you should study 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 counterclockwise. Letters of the Russian alphabet the names of the faces will be indicated as follows:

F – facade;

T – rear;

P – right;

L – left;

B – top;

N – bottom.

Many descriptions and diagrams contain designations for the faces of the cube in English.

The next secret of the Rubik's cube lies in the arrangement of small colored elements.

1. Central cubes Determine the color of the entire side of a Rubik's cube. We will call these cubes by analogy with the name of the faces (F, T, P), etc.
2. Edge cubes are adjacent to two faces at once, therefore the name will be double (for example, FP, PV) - depending on the faces with which they interact.
3. Corner cubes contain 3 letters in the name at once, since they refer to three faces simultaneously (FPV).

And one more mini-secret - when you study the face rotation patterns, letters without any additions will mean rotate 90 degrees clockwise, and the letters s additional sign‘ - counterclockwise.

Having understood all these symbols, it will be much easier for you to solve the Rubik's cube and you will do it correctly and quickly. Also, for a change, you can learn how to do.

How to solve a 3x3 Rubik's cube: the easiest way, assembly diagram

The easiest and most reliable way to assemble our Rubik's cube starts with the bottom cross. Make a cross on the bottom edge of the cube and proceed to a step-by-step solution to the problem of how to solve a 3x3 Rubik's cube: the easiest way, the diagram of which is right in front of you.

And, of course, the most understandable guide for assembling a cube is a video lesson with detailed description an experienced virtuoso.

Scheme for assembling a 3x3 Rubik's cube for beginners in pictures

In the first stages of practice in solving a Rubik's cube, we will use the same cross method, but this time we will have a cross made of colored cubes on the top edge. As you understand, high-speed solving of the Rubik's cube awaits you ahead, at this stage you should learn to correctly determine the location of the edges and moving them in the plane of the cube.

There are different methods for solving a cube, and Now you have to learn how to solve a 3x3 Rubik's cube: the scheme for beginners consists of 7 stages. Pictures describing the assembly process are available for each of the steps. You may spend more time on this puzzle than expected, but you will solve a problem that not everyone on our planet can achieve! It's worth the sweat.

By the way, the last one world record for solving a rubik's cube was set to speed in 4.73 seconds. And it belonged to Australian student Felix Zemdegs, who defeated the previous record holder by just 0.01 seconds. We are in no hurry in this matter, so we carefully study the instructions and begin to assemble the first layer.

The principle of assembling a Rubik's cube from the starting cross not that complicated. Here it is necessary to correctly study the location of the edges. And then it’s a matter of technique, as they say. We have already gone through the basic concepts and rules for assembling a Rubik's cube for dummies.

We are sure that the diagram for assembling a 3x3 Rubik's cube 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 you watch the video, which shows the whole process in detail using the example of a virtual Rubik's cube.

3x3 Rubik's cube formulas: calculating moves

If you think that previous methods of solving the notorious cube were intended exclusively for stupid people, catch a few formulas.

752 1 763 434 0

Have you tried numerous times to solve a Rubik's Cube without success? All the instructions presented on the Internet were written by professionals, but for “dummies” the solution seems very confusing? Do you think it is impossible to solve this puzzle? Following our step-by-step instructions, you will not only be able to completely solve the world's most popular puzzle without formulas, but also understand how you did it.

You will need:

Where to start

So, your goal is to solve the Rubik's Cube. It will not be possible to do this without knowing how it works, what it consists of and how it functions.

A standard 3x3 Rubik's cube is a mechanical 3D cube, each face of which is painted a different color.

The traditional option is blue, green, white, yellow, red and orange. Edges:

In total, the Rubik's cube has 20 moving elements (12 edges and 8 corners) and the solution depends directly on knowing how they can change their position.

When we rotate one side, we see that the center elements remain in place, the edge moves to where the edges should be, and the corner takes up space in the corner.

It follows from this that each element has a specific type, which does not change after rotation (the edge remains an edge, the center remains the center).

Frequently asked questions and answers

What should a Rubik's cube be like?

If you are not going to participate in competitions, you can take any cube. It is better for young people and children to buy a puzzle from Chinese manufacturers. When choosing, consider the following:
- It is better to take the cube of the latest models, it takes into account the shortcomings of previous versions, and it is more improved.
- The correct cube should spin easily and cut corners well.
- Cubes for professionals can be disassembled and customized.

How many edges does a Rubik have?

The classic Cube consists of 12 two-color side or edge elements (12 “ribs”).

How many schemes for solving a Rubik's cube?

There are many ways to solve the Cube. There are those that allow you to assemble a couple of formulas, but in a couple of hours. Others, by memorizing a couple of hundred formulas, allow you to solve a cube in 1 minute or even 20 seconds.

Basics

Our goal is to put all the elements in the right place. To determine the direction in which to turn and the “right place” of this or that square, you need to pay all your attention to the central elements, because, as we have already said, they have a fixed position.

For example, the edge that is located between the red and green centers is, respectively, red-green, so you need to focus on placing an edge of the same color near the green center, and a red edge near the red central element.

The corner is always three-colored, so care must be taken to place it between the centerpieces of the corresponding colors.

Step 1. Gather the edges of one side

The first thing you need to do is choose a color to start with. In this example, the main color is yellow, it will be represented in all diagrams. Everyone is free to choose the option that he likes best and start from there.

So, if our top central element is yellow, then the bottom, accordingly, is white (in almost all models of the Rubik's cube it is on the opposite side).

In order to solve a 3x3 Rubik's Cube, you must first make a cross on its upper edge - place all the edges of the selected color (in our case, yellow) in the corresponding positions around the central element.

This must be done in a certain order so that the second color of the edge matches the nearby central element.

This step is the hardest to explain to those who don't know how to solve a Rubik's Cube. It is easier to solve this problem on your own and you will undoubtedly be able to do it after a short training.

It is at this step that most beginners stop - they collect the cross, then one side - then, unfortunately, few advance.

For those who cannot do this, below is a diagram of how to assemble the cross. Keep in mind you will have to repeat this step 4 times - once for each side.

1. Take the Rubik's Cube in your hands and turn it over so that the center is yellow (or another color of your choice) on top and white on the bottom.
2. Look for yellow edges on the bottom plane. Pay attention to both rib colors.
3. If you find a yellow edge at the bottom, rotate the layer until the edge with the yellow square takes a position under its “place” on the top edge.
4. Do one of the following:

a) Yellow “looks” down

b) Yellow looks forward

c) Rib in the intermediate layer

Note: If the yellow square is on the top layer, but it is not positioned correctly or oriented correctly relative to the nearby center, change its position by placing another element in its place.

After this, the edge will be in one of the three positions described above. Using the diagram, place it in the “correct” place. Repeat all steps for each yellow edge and make a cross on the top layer of the Rubik's cube.

Step 2. Assembling the top face

If you were able to fold the cross, then it is worth collecting the entire top layer, that is, putting the corners in place one after another. We cannot place them as we want, because each corner has a specially designated place for it, which is determined by the colors of which it consists.

Just like the previous step, there are several solutions that we will follow.

Remember that you will have to repeat all steps 4 times - one for each corner.

1. Turn the Rubik's Cube over so that the yellow layer is at the top and the white layer is at the bottom.
2. Look for a corner with a yellow square in the bottom layer. Notice the 2 other colors on it.
3. Rotate the bottom layer so that the corner is under “its” place.
4. Use one of the solutions below:

a) yellow looks to the left

b) yellow looks to the right

c) yellow is at the bottom

Please note : If the yellow corner is not in the bottom layer of the Rubik's cube, then it means that it is in the top layer, but not in its place.

You need to put any corner from the bottom layer up (executing the first solution, for example). This way you will get a yellow corner in the bottom layer.

Repeat for each corner until the top layer is completely assembled.

Step 3. Algorithm for assembling the second face

We want to solve the second layer of the cube. Remember that the central elements are fixed, so there is no need to change their places and think about how to place them. Keep in mind that you will have to repeat the steps below 4 times - once for each edge.

1. Take the cube so that there is a white layer on top and a yellow layer on the bottom - the one we have already collected
2. Look in the top layer for an edge with no white on both sides.
3. Rotate the top layer until the color of this edge and the center piece on the side match, forming an inverted T.
4. Follow one of the solutions below, choosing an example depending on whether the edge is placed on the left or right.

There are several possible options:

1) The edge should move to the right from where it is.

2) The edge should move to the left from where it is now.

Note: If the top layer does not have an outermost element without white on either side, it means they are in the middle layer but not in their proper places.

Place any other edge from the top layer in its place. In this way you will get an edge in the top layer without a white square and you can move it according to the instructions above.

Repeat this step 4 times, once for each edge.

Step 4. Second cross

So, we have solved the first 2 layers of the Rubik's cube. Now we must ensure that the 4 outermost elements of the top layer are white, forming a cross. At this stage we will focus only on the outer elements, not paying attention to the corners.

The top edge of the cube may have four white edges, or two, or none. If all four white edges are on the top side, then you can skip this step and move on to the next one. If there are two edges, then you need to use one of the following options depending on how they are located relative to each other: next to or opposite.

1) Adjacent edges

2) Opposite edges are white

3) Not a single white square is placed correctly

If there are not a single white square in the top layer, do one of the two options described above and you will get 2 white squares in the top layer. After this, perform the necessary sequence of actions, depending on the situation.

Thus, we folded the second cross.

Step 5. How to place the second cross

At the previous stage, we folded the second cross. At this stage, we will make sure that the side parts of the cross match the color of the central elements of the corresponding faces. We will focus our attention only on the white edges of the cube, not paying attention to the corners.

1. Rotate the top layer of the Rubik's Cube until two edges match the color of the center of their respective faces. If only one edge matches, continue rotating.
2. Use one of the examples given, depending on what position the side edges will take - sequentially or oppositely relative to each other.

a) adjacent edges

b) opposite edges

Thus, we have placed the second cross of the Rubik's cube correctly.

Step 6: Place Corners

We have already put all the elements of the Rubik's Cube in place, except for the corner parts of the last layer.

The goal of the penultimate step is to place the corners correctly, without paying attention to their orientation. This way you need to know exactly when the corner is in the correct position.

So, the corner is placed correctly if the nearby central elements match the color of the 3 parts of the corner.

Let's look at a few examples of when the corners are placed incorrectly and when they are in the right position to solve a Rubik's Cube.

It is possible that all 4 corners will be in place from the very beginning (feel free to move on to the next step), or only 1 corner will be placed correctly, or none. If only one corner occupies its place, follow one of the examples below, choosing the one that will allow you to place all the elements in their place.

1) 3 corners are not in their position (a)

2) 3 corners are out of position (b)

3-4) None of the corners are placed correctly

If none of the 4 corners is in its “right” place, do one of the examples described above - this way you will be able to put one of them in place. Next, follow the steps depending on what you got.

Thus, we solved a 3x3 Rubik's cube, putting the corners in their positions. The last step is to rotate the corners of the last layer to solve the puzzle completely.

Step 7. How to assemble

At the previous stage, we put all the elements in their places. All that remains is to rotate the corners to solve the Rubik's cube and solve it completely. At this point there may be two, three or four misdirected corners left in the final layer.

If there are 2 incorrectly oriented corners, follow one of the examples below depending on the situation that arises.

Be sure to read this before rotating the faces of the cube.

Very important! This step is not as easy as the others, but it is also much more difficult. There are a few things to know before you get started. Option 1 has several sub-options, so first of all you need to understand which one is right for you. To solve this step, follow the first sequence of actions. After that, take the necessary steps depending on the red table option you have received.

Option 1. Two corners are not oriented correctly. Please note that the “neighboring” corner needs to be rotated clockwise.

Option 2-3. Three corners are oriented incorrectly.

If 2 corners are not oriented correctly, solve the Rubik's Cube following the first example - this way you will get only 2 incorrectly oriented corners. Finally, perform a sequence of actions, depending on the situation you have.

Option 4. All corners are not oriented correctly.

If none of the 4 corners are oriented correctly, follow the first example given. Then choose a solution that suits your situation.

If you did everything correctly and followed our instructions so far, then congratulations! You solved the Rubik's cube yourself!

And other logic games.

And here, by the way, there is something to prove yourself in:

• You can become the fastest. The current record is 5.5 seconds. People who do high-speed assembly are called speedcubers.
• Maybe you want to become the most original? Rubik's cube solved with eyes closed, kicks, etc. There are also records here and you can beat them.
• And the most creative and inventive ones draw with the help of a Rubik's cube and, by the way, create real masterpieces of incredible beauty.

We hope we inspired you and helped you understand how to solve a Rubik's cube. If you are interested in thinking games and puzzles, you will probably be interested in learning the secrets of playing dominoes. A mixture of options 1 and 2 is suitable for us, option 2 as a last resort.
If you lubricate it very thinly, its sides will begin to adhere to each other too tightly. The thick one takes away the rotation speed. If you mix two types of lubricant, this is the optimal consistency.

I can't solve a Rubik's cube...

Many people ask the question: “How to solve a Rubik’s cube, if I took it apart, I can’t put it back together?” Most often this happens on the last layer. You may not be following the algorithms exactly. But if you follow the diagrams exactly, you should get it together. If not, the problem may be the following - Chinese manufacturers make cubes of varying quality - from professional to those that fall apart in your hands at the very first rotations. If the cube falls apart, it must be assembled correctly.
On a cube with two layers assembled, use a flat screwdriver or a knife to pry up the lid of the central cube of the third layer, remove it, and use a small Phillips screwdriver to unscrew the screw (do not lose the spring attached to the screw). Carefully pull out the corner and side cubes of the third layer and insert them correctly color to color. At the end, insert and screw the previously unscrewed central cube (do not tighten too much). Twist the third layer. If it turns tightly, loosen the screw; if it turns too easily, tighten it. It is necessary that all faces rotate with the same force. After this, close the lid on the central cube.

Even if we assume that the record holder was very lucky, the world ranking table based on the average of five results no longer leaves any doubt: if more than 80 people on average do it in 12 seconds, obviously they know something. In this brief overview I will try to reveal the secrets of high-speed assembly. Let me make a reservation right away that after reading this article you will not become champions: here are only the main points and links to more detailed information. In addition, even after learning the method completely, you will need long training to achieve good results. But you will get a good idea of ​​how this is done, and, if desired, you will know where to move next. I think that with enough perseverance, after several months of training, many will be able to achieve an average result of around 30 seconds.

I'll be linking mainly to the SpeedSolving Wiki and Badmephisto. So, let's go.

CFOP method

The most popular method of speed cube solving is the CFOP method, also known as the method of Jessica Friedrich, who refined and popularized it, although other people have also contributed. If everything is done correctly, on average the cube can be solved in 56 moves (alas, not twenty). There are other methods with which you can get good results: Petrus, Roux, etc. They are less popular and for the sake of brevity we will limit ourselves to considering the CFOP method.

CFOP is the name for the four stages of assembly: C Ross, F 2L, O LL, P LL:

• Cross - assembly of a cross, four rib cubes on the bottom edge;
• F2L (First two layers) - assembly of two layers - bottom and middle;
• OLL (Orient the last layer) - correct orientation of the cubes of the top layer;
• PLL (Permute the last layer) - placement of the cubes of the top layer.

Let's look at these stages in more detail.

Cross - cross

The goal of the stage is to correctly place four edge cubes on one of the faces. Anyone who knows how to solve a cube at least somehow can handle this, but solving a cross in a few seconds is not so trivial. According to the rules of the competition, before assembling, you are given 15 seconds to study the combination (inspecting), during which you at least need to find these four edge cubes, and it would be nice to create a complete sequence of moves in your head. It has been proven that assembling a cross on a pre-selected face always requires no more than eight turns (a 180° turn counts as one), with eight being extremely rare, and even seven infrequently (the average is slightly less than six). In practice, in order to quickly learn to find the optimal sequence, a lot of training is required.

You can choose a face for assembling a cross in different ways. The most popular way is to always collect it on the same edge (often the white one). Then you know exactly the relative position of the colors at all stages of assembly, which makes the process easier. Some people collect the face that is easiest to assemble first. On average, this saves one turn, but you constantly have to adjust to a different color arrangement. A compromise option is also used - to assemble one of two opposite faces(say, either white or yellow), then the set of colors of the side faces does not change.

The main trick to assembling a cross is that it must be assembled relatively. For example, if you are solving a cross on a white edge and a white-blue edge cube is already on it with white color towards the white center, then it is not so important to you whether the blue side of this cube is aligned with the blue edge. It is enough to place a white-green cube on the opposite side, and a white-red and white-orange cube on the left and right. During the assembly process, you can twist the white edge as you like, and at the end, in one movement, immediately align all the side centers with the cross cubes. It is only important to remember the exact order of the colors on the cube: if you look at the white side, then clockwise there are blue, red, green, orange (yellow at the back).

Professionals assemble a cross on the bottom edge. This seems difficult for beginners, since it is almost impossible to see what you are collecting, but this gives a great advantage when moving on to the next stage: you do not have to waste time turning over the cube, and in the process of assembling the cross you can notice the arrangement of the cubes needed to assemble F2L and outline a plan for further assembly.

Some advanced tricks for assembling a cross are described in this video.

F2L - first two layers

Perhaps the longest stage, the goal of which is to completely assemble two layers: the layer with the cross and the intermediate layer. Essentially, you need to place eight cubes in place: four corner bottom layers and four side edges in the middle layer. Unlike assembly methods for beginners, a pair (column) from a corner and edge cube is assembled immediately (that is, you need to assemble four such pairs). Depending on the initial arrangement of the cubes of the pair, you need to apply one or another algorithm (sequence of rotations). There are more than 40 such algorithms in total; you can simply memorize them, but almost all of them are derived intuitively. There are two simplest cases when a pair gathers in three movements:

Two more cases are mirror to these. Everything else needs to be reduced to one of these four. This requires a maximum of 8 moves, that is, no more than 11 moves per column will be required. Perhaps you will not find the most optimal method, but if you first learn to intuitively put together any combination somehow, then you can look at individual cases in cheat sheets.

The main difficulty of the stage is to quickly find paired cubes. They can be in 16 different places: 8 places in the last layer and 8 in the columns. The columns are more difficult to view, and the fewer columns you have collected, the greater the chance that the uncollected ones contain the cubes you need. If you didn’t pay attention to the cubes for F2L when assembling the cross, when moving to this stage you can lose a lot of time just searching. It is also not always wise to start with the first pair found: perhaps it is collected through a long algorithm, and if you start with another, then in the process the first one will be rebuilt into a more successful combination.

OLL - orientation of the last layer

At this stage, the cubes of the last layer are oriented so that the last (in our case, yellow) face is assembled. It doesn’t matter that the cubes are essentially not in their places: we will deal with this at the last stage.

There are 57 different initial situations, each of which has its own assembly algorithm, from 6 and somewhere up to 14 moves. It is necessary not only to learn all these algorithms, but also to quickly identify which one needs to be applied at the moment. Here is an example of one of the OLLs:


The picture on the left shows the initial situation up to rotation (it is assumed that we are assembling the yellow edge). To apply this OLL, the locations of the yellow squares must match not only on the top edge, but also on the side ones (we ignore squares of other colors). It is not always necessary to compare the cube with the diagram completely, you just need to compare enough squares to distinguish it from other combinations. On the right are two algorithms (for some it is more convenient to do one, for others another) in standard notation, below is the OLL number and the probability of its occurrence. Almost all come up with a probability of 1/54, some with a probability of 1/108 and two with a probability of 1/216 (including a lucky combination when the OLL collected itself).

For beginners, learning 57 combinations may seem like torture, so a simplified but slower option was invented - 2-look OLL. In this case, the OLL is divided into two stages, first the cross is assembled, and then the corners. Here you need to memorize only 10 algorithms (3 for the cross, 7 for the corners). Having gained experience in 2-look OLL, you can slowly begin studying the full set. In this case, 2-looks will come in handy in any case: firstly, they are all in a complete set (say, if the cross is assembled by itself, then the complete OLLs coincide with the 2-look OLL for the corners), and secondly, if you come across another unfamiliar OLL, you can go back to 2-look.

PLL - permutation of the last layer

The final stage of assembly is to arrange the cubes of the last layer on the right places. The approach is approximately similar to the previous stage, but there are fewer combinations and algorithms here, only 21 (13, if you count mirror and inverse ones as one). On the other hand, they are somewhat more difficult to identify, since here you need to take into account different colors, and the colors on the diagram may not coincide with your colors (up to cyclic permutation):


The arrows indicate the cubes that this PLL rearranges. The probabilities of most combinations are 1/18, occasionally 1/36 and 1/72 (including the lucky case when you don’t need to do anything).

Again, a simplified version is offered - 2-look PLL, when the corners (two combinations) are placed first, and then the centers (four combinations), they are quite easy to learn.

Cube and lube

Even if you master the given method perfectly, you will not achieve good results with a bad cube. The sides of the cube should rotate easily with a push of one finger, and it should not be too loose. The layers should hang on springs so that one layer that is not completely rotated does not interfere with continuing rotation in the other direction (within reasonable limits, of course). The central squares of the correct cube can be pulled out and the bolts located under them can be tightened. It’s difficult to find a good cube in regular stores; they recommend ordering online, for example.

For best results, the cube needs to be lubricated. Sometimes lubricant comes complete with the cube, or is purchased separately. Silicone grease, which can be purchased at car dealerships, is suitable.

Cube rotations

Rotating the entire cube in your hands (and not individual faces) takes significant time, so when assembling it, try to avoid it as much as possible. For example, at the F2L stage, it is sometimes easier to collect a column in the corner farthest from you, without seeing it, than to turn the cube with this column towards you. At the OLL stage, in order to rotate the cube as in the algorithm diagram, it is enough to rotate the top layer, rather than rotating the entire cube - this is faster (the position of the top layer relative to the bottom ones at this stage is not important).

Look ahead - looking ahead

After completing the next stage, you must move on to the next one without pause. While you automatically perform the next algorithm, your head is free. Use this time to find the cubes that are important for the next stage and understand which algorithm you will have to use next.

Fingertricks

Also, the key to significantly speeding up assembly is fingertricks, the skillful use of all fingers to rotate. Some commonly used combinations can be performed at lightning speed, 5 turns per second or more, if you use your fingers correctly. Note that a shorter algorithm is not always faster; it may turn out. that you will have to make awkward turns. BadMephisto has several videos dedicated to fingertricks, for example, about F2L.

Practice

Nothing will come of it without long-term training. Get ready to solve the cube thousands of times.

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

But success came to this puzzle only when the German entrepreneur Tibor Lakzi drew attention to it. He, together with 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 high-speed assembly Rubik's cubes.

By the way, the people who are involved in assembling this puzzle are called speedcubers (“speed” - speed). It’s not hard to guess that the high-speed assembly of a “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 solving the cube online. Yes, and in our article we will call all the action with this puzzle, according to established expressions.

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

At the end of the cross there is a rigid square with one of six colors. Around it you need to collect the remaining 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 opposite red, and green is opposite blue. And if you take a puzzle apart and then put it back together incorrectly, it may never be able to be put back together.

In addition to the centers of the cube, the corners are the constant components of this puzzle. Each of the eight corners consists 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 solved by placing the corner and middle sectors to match the colors of the central sectors.

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

In the process of solving 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 interceptions. This is shown schematically like this:

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

Simple and easy assembly method: Instructions for children and beginners

The most detailed instructions assembly for beginners looks like this:

• 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 the color of the edges and centers will be the same.
• To do this, find the white center and white edges and collect the crosses according to the diagram shown below:

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

• Let's move on to the next step of assembling the puzzle. Find the white corner on the bottom layer and place the 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 assemble the second layer. To do this, find four edges without yellow color and place them between the centers of the second layer. Then we spin the cube until the color of the center matches the color of the edge element.
• As with the previous layer, to achieve this goal you may need one of several options:

• After we have successfully completed the previous step, we move on to assembling the yellow cross. Sometimes he gets ready on his own. 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 assemble the corners of the top layer. Take one of the corners and move it into place using the U, U' and U2 movements. This needs to be taken into account. So that the corner colors are identical to the colors on the lower layers. When using this step, keep the white cube facing you.

Next build step

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

The fastest way. Jessica Friedrich Method

This puzzle assembly method was developed by Jessica Friedrich in 1981. It is conceptually no different from most known methods. But it focuses specifically on assembly speed. Thanks 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 solving speed becomes less than 2 minutes.

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

2. At the second stage, you need to assemble two layers of the puzzle at once. He is called "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 assemble the top layer completely. You shouldn'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 assembling the cube. PLL (from the English Permutation of the Last Layer - arranging the elements of the last layer in their places). Its assembly can be done using the following algorithms:

Scheme for solving a 3x3 Rubik's cube in 15 moves

Since 1982, when competitions for high-speed solving of the Rubik's cube appeared, many fans of this puzzle began to develop algorithms that will help correctly arrange the sectors of the cube with a minimum of moves. Today, the minimum number of moves in this puzzle is called "God 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-move algorithm for assembling this puzzle was developed. But, it cannot be used from all positions of the cube, which is why it was rejected as the fastest.

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

How to easily solve a Rubik's cube: Video