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. A clockwise rotation of the outer layer by 90° (if you look at this layer) is considered “straight” and will be denoted by a capital letter, and a counterclockwise rotation is “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 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 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 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 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, select 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 some edge was affected, then you need to 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 beautiful one 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). The top right corner should contain 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, we first 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, 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. 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 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 the third one remains to be turned over odd number ribs, then you don’t have to worry about it any longer, 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 swap 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.
Let's remember 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 match the already assembled 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. On 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 do not 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 speedcubers say, “gotten”) 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 absolutely relative position colors are 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, Ф·ПВ"П"В"·ПВП"Ф"·ПВП"В"·П"ФПФ", 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.
The correct name is " Rubik's Cube». Rubik- Hungarian sculptor and inventor of the popular puzzle. The Rubik's Cube was invented back in 1974, and since then its solution has occupied the thoughts of all mankind.
This puzzle is a plastic cube consisting of 26 cubes that can rotate around the three internal axes of the cube. Each side is painted a specific color and consists of 9 squares.
By rotating the sides of the Rubik's cube, you can change the arrangement of the squares. The goal is to return the squares to their original position so that each face consists of squares of the same color. This is not so easy to do. Many people can solve only a certain part of the cube on their own.To complete the puzzle, there are certain rotations and algorithms calculated using formulas.
We invite you to familiarize yourself with one of the algorithms for solving a 3x3 Rubik's cube
The easiest way to solve a Rubik's cube - remember which rotations were used to disassemble it and repeat them in reverse order. However, this option only exists if the cube was originally solved. If the cube is disassembled, it is difficult to reassemble it. Intuition, spatial thinking or chance can help here. But it’s better to remember the algorithm for collecting the cube. There are several of them.
The traditional name of the algorithm is smallest number moves of a Rubik's cube solver - “God's algorithm”. The maximum number of moves with this algorithm is the “number of God”. In July 2010, it was proven that this number is 20. That is, with known algorithms, you need to make at least 20 moves to solve a Rubik's cube.
Solving a cube for speed is a whole sport called speedcubing ) . There are competitions between speedcubers, and even blind assembly competitions!
You can also look video on how to solve a Rubik's cube step by step for beginners:
Do you know which toy deserves the title of the most sold in the world? No, not the beautiful Barbie or even the Lego constructor. The absolute leader in sales is considered to be a much more intellectual thing - a Rubik's cube. This year, the colorful puzzler of Hungarian origin celebrates its forty-first birthday. Over four decades, millions tried to conquer it. And today we will tell you a way to solve a Rubik's cube using only two movements and one little secret.
In 1980, a mailing list for Rubik's Cube enthusiasts was opened. Since then, thousands of puzzle enthusiasts, including a staggering number of mathematicians, engineers and programmers, have joined forces to find "God's algorithm": a way to solve a cube in minimum quantity moves. In July 2010, Palo Alto programmer Thomas Rokicki, Darmstadt math teacher Herbert Kozemba, Kent University mathematician Morley Davidson and Google Inc. engineer. John Detridge proved that each Rubik's Cube configuration can be solved in no more than 20 moves. A current record – 4.94 seconds. Well, the method described below does not guarantee a speedy solution. But why not test the theory in practice?
Just rotate the left side.
Now rotate the top edge.
Repeat these two combinations one after another. How many times? Until you collect it!
Video demonstration This method has already collected more than 14 million views. Of course, there were many dissatisfied people in the comments who were unable to solve the puzzle. Maybe they just didn't repeat the combination long enough?
Have you noticed how quickly the faces of the cube “fly” in the hands of professionals? It turns out there is a little trick here too. To speed up the process, you need to use...lubricant! Liquid silicone will do.
Rotate the faces of the cube to the position as in the photo.
So, you have chosen and bought your first one. It's time to learn how to assemble it.
You can either learn how to assemble it directly from this page. So, how to solve a 3x3 Rubik's cube? Let's get started!
3x3 cube design
The 3x3 Rubik's Cube has six different colored sides and consists of 26 elements that are fastened together and move freely among themselves.
Cube elements are divided into three types
What does a 3x3 Rubik's Cube consist of?Fig.1 basic elements of a Rubik's cube
Fig.2 The crosspiece is the internal mechanism for attaching the Rubik's cube.
To solve a Rubik's cube you need to know the formulas for assembling it. Therefore, first of all you need to learn the language of rotations.
The language of rotations. What do the letters mean in the formulas for solving a Rubik's cube?
Main
- The cube has a top, a bottom, a right, a left. When rotating, keep the cube in one position relative to you, and simply rotate the desired side. REMEMBER THIS!
- The centers of the cube do not move anywhere, they always remain in their places relative to each other, because they are fastened together by a cross (Fig. 2).
Rubik's cube formulas are written with letters that indicate the rotation of a certain side of the cube 90° clockwise. If there is an apostrophe (’) next to a letter, the side is rotated counterclockwise. The number before the letter indicates the number of turns.
We remind you: when you rotate the sides, the cube itself remains motionless, you simply rotate the desired side.
Practice rotating the desired sides of the cube clockwise and counterclockwise. Let your fingers remember the movement, and your mind – what and where to rotate if there is a certain letter in the formula. This will make it a lot easier for you to learn assembly algorithms.
As a respite, we recommend that you learn about the differences between professional speed cubes and beginner cubes. And is it worth it for a beginner to immediately invest in the purchase of an expensive sports cube? Briefly, our opinion: on the one hand, it’s damn nice to twirl the cosmically mobile MoYu Hualong in your hands, for example. An elite cube can be a great motivation for speed building. On the other hand: beginners may not notice the difference between a budget cube and a sports one, if the budget cube is good and fast, but we don’t keep others :)
Stage one - assembling the first (bottom) layer of the Rubik's Cube.
Assembling the cross
Assembling the cross is the first step in assembling the first (bottom) layer. Take the cube at your convenience and study the position of the centers. Remember the color of the bottom and top. In our case it is blue. Until the end of the first assembly stage, keep the blue center at the bottom and the green at the top.
Your task when assembling the cross: one by one, find four on the cube ribs With blue color and move them down to blue center so that they second rib colors coincided with colors of the lateral centers. The picture shows ribs with a blue color that have become at the bottom, and their second colors yellow And red matched the colors of the side centers - this is correct.
In order to assemble a cross, you do not need special algorithms, but for example, let’s look at situations that may occur and test your understanding of simple algorithms.
Attention! As soon as you have started to perform an algorithm not an algorithm for assembling a cube, do not twirl the cube itself in your hands until you complete the combination. Centers different colors must maintain their position. For example, yellow is in front of you, blue is below, red is to the right.
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Assembling corners
So, the cross is assembled. We move on to assembling the corners - the final stage of assembling the first layer. Take the cube with the cross facing down. Please note colors of the three centers, between which there should be corner, find it on the cube. In our case we are looking for blue-yellow-red corner. There is only one in the cube.
We put the corner in the top layer above the place where it should go down and do the URU’R’ algorithm. If the corner is in its place and the colors from the centers match, then we move on to the next corner. If not, then we repeat the algorithm until it becomes as we need.
Interesting fact: if the cube is solved and we repeat this algorithm (URU’R’) six times, then the cube will get confused and then solve.Let's see what happens to our corner after each algorithm. All of the following options may be available to you during assembly.
Stage two - assembling the second (middle) layer of the Rubik's cube
Hold the cube with the blue side facing down and the green center facing up.
In order to assemble the second layer, we need only one algorithm, but before executing it we need to prepare the cube - bring it to one of the two possible situations shown below. Find in the top layer any edge who has no green. Rotate the top layer (movements U or U') so that the side color of the edge matches any of the side centers. Now take the cube so that the coinciding center is facing at you, and blue, as before, remained at the bottom. In our example we found yellow – red edge. Lateral rib color – yellow. Rotate the top layer and align the edge with the yellow center. You may also have an option when you combine red edge with a red center, and yellow the rib color remains on the top side.
We take the cube with the yellow or red center towards us and get one of three possible cases.
THIRD CASE
The rib is already in place, but twisted. We need to “replace” it with any edge with green from the top layer, then again we bring to the two cases that are indicated above and solve.
The third stage of assembly is assembling the top layer of the cube
Let's approach last stage– assembly of the 3rd (top) layer of Rubik. First, we need to arrange the edges on the top layer so that they form a green cross. After assembling the first two layers, on the top layer you will get one of the four cases shown in the pictures. Find the one you have and perform the algorithm FRUR'U'F' to make a cross. You can start with a “dot” and consistently come to a “cross”.
Important! Before each start of the algorithm, hold the cube in your hands exactly as shown in the pictures!
So, at the top we have a cross.
We combine the side colors of the ribs with the side centers.
By rotating the top face (U or U’) trying to combine side ribs colors With lateral centers. All four colors must match (yellow, orange, white, red). If four do not match, then put the layer so that they match at least two ribs.
If you don't find two matching edges, then run the algorithm R U R’ U R 2U R’ U and look for the ribs again.
So, on the top layer we have a cross assembled and the ribs are correctly placed.
We put the corners in place.
Check that the corners of the top layer are in place; the corners may be twisted. But the main thing is that they have the same colors as the centers between which they stand. If so, then skip this step and move on to the next one.
If the corners need to be placed correctly, then take the cube in your hands so that there is a corner on your right that is in its place and perform the algorithm without changing the position of the cube: U R U’ L’ U R’ U’ L
If there is not a single corner that stays in its place, then do the algorithm given above from any position and the corner will appear.
The cube is almost complete, all that remains is to twist the corners.
You may have two, three or four twisted corners. Corners are twisted by a simple algorithm R' D' R D R' D' R D,
Important!!! This algorithm only works for one corner, which is located to your right. The secret is that when the corner becomes correct, you need to turn the top edge (U or U’) and substitute the next corner that needs to be twisted in its place. We can repeat the algorithm from 2 to 5 times and it will seem to you that the cube is confused, don’t worry, it will come together. The main thing is not to let go of the cube, not to twist it in your hands until you have completed the entire sequence of algorithms.
Let's consider the most difficult case with four twisted corners:
Congratulations!
Now you know exactly how to solve a Rubik's cube! Disassemble and assemble your cube according to these instructions until you remember all the algorithms!
And then a huge world of mechanical puzzles will open before you, the assembly formulas of which are based on the formulas of a 3x3 cube!
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 you want, 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.
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, it takes a lot of practice to quickly learn to find the optimal sequence. 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 collect 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 to the 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 are 1/54, some are 1/108, and two are 1/216 (including lucky combination, when OLL assembled 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. At the same time, 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, sometimes it is 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 completion next stage you should move on to the next one without pausing. 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.Tags: Add tags