How to solve a Rubik's cube step by step instructions. How to solve a Rubik's cube using the layer-by-layer method
Solving a Rubik's cube can be difficult for both adults and children, and if after several attempts you have not succeeded, do not despair, simple and understandable 3x3 diagrams will help you figure out the puzzle. There are many different ways to do this, because the best minds spent their time on this and gave amazing results in the form of schemes and algorithms.
The easiest way to assemble for those who are just starting out
This scheme is considered the simplest and is great for children. It starts with assembling a cross, in other words, each edge should have the same color of the central die and corner elements. At the beginning of the assembly, the Rubik's cube must be disassembled. Assembly diagram 3*3 in 8 stages.
First, you need to take the cube in your hands and turn one of the sides towards you, respectively, taking its frontal side - F, all the rest according to the diagram. Assembly must begin from the bottom (H).
Below is a diagram of this approach:
- Having chosen the color you want to start first, we begin assembling the lower cross. This is a simple step, the complexity of which ends solely with the choice of color. What is on the other sides of the cube at this stage should not attract attention.
Stage of solving a Rubik's cube
- The cross must be assembled correctly - the cross must end on adjacent edges. This means that the edges located at the top of the mating sides should have the same color as the cross at the bottom. If this did not happen during assembly, then there are two available algorithms that can correct the situation:
- The discrepancy on two adjacent sides is corrected by the scheme:
P V P»V P V2 P V
- If the error is on opposite parts of the cube, then you can try the following formula:
F2 T2 N2 F2 T2
When working with these algorithms, the cross should be at the top.
- Completely solve one side of the Rubik's cube. To do this, you need to put the corners in place. Turning the puzzle over with the already assembled cross facing down, you will notice that the upper corners of the sides adjacent to H have acquired the same color as the cross. That is, if the cross is yellow, then the corner elements in question will also be yellow. With such a scheme, only three options for the position of the base color can be possible: on the left, on the right, or on top, and for each such position there is its own assembly scheme:
The result of applying such algorithms is one completely assembled color, and the upper stripe of the adjacent side has one color.
We continue the assembly
- If you want to solve a Rubik's cube at speed, then there are a few more important and relevant formulas for you to remember. We turn the side that is already completely ready up. We begin to twist the bottom edge until the color of one of the side elements matches with any of the sides and form the letter T. Then, it is necessary to move the side element from the bottom edge to the middle until it matches the color of the adjacent sides. As a result, we get two variants of positions in which:
- Left turn required: N L N»L» N» F» N F.
- Move to the right: N» P» P N P N F N» F».
- Now it’s time for the third layer. We turn the toy itself over so that the side that has not yet been folded is at the top. Most likely, the opposite color became white if you chose the most popular color to start the build, yellow. If there are white dies in front of your eyes with any position described below, then I proceed according to the following formulas:
White dies: central and 2 opposite F P V P" V" F".
White dies: center and two on the side F V P V" P" F".
White dies in the center, choose the pattern you like and repeat 2 times.
- Another correct cross with the top edge matching in color with the adjacent ones, in which 2 outcomes are most often possible:
But, if this does not affect the situation in any way, then you can use any options.
- Quite a difficult stage at which it is necessary to put the corner elements in their rightful places. And it's not that simple. Most often there is a lot of confusion in the layers, but if you do it right, eventually each color block will fit where you want it.
- Stage number eight is associated with the same angles and circular turns:
Clockwise P2 B2 “P F P” B2″ P F P .
And in the opposite direction: P" F P" B2″ P F" P" B2″ P2 .
Any of these algorithms will also be useful when moving in corners: crosswise or opposed.
The mirror cube is also assembled using the same algorithms, but those who want to break the record should know that only the 3*3 model applies to this indicator.
For clarity, the assembly of the 3*3 model can be seen in the video below:
How to solve a 3x3 Rubik's cube - quickly and easily. The best technique for beginners.
Seven steps to assemble
- First, make sure that the cube is disassembled. This will mark the beginning of stage number 1. The stage ends by assembling a cross on the top side of the cube, and the upper middle edges of the sides should match the center in color. One of the dies of the upper cross should be located on the edge of the bottom. To do this, we take either the first or second option.
The operation is repeated for all remaining cubes of cross B.
- Stage two starts with the upper part of the cross assembled and ends with the upper part fully assembled. How does this happen? The diagram popularly explains the entire sequence of actions. We take the corner element of face B and move it to H. Depending on the color distribution, you need to choose your solution.
With three cubes of the corner of the upper face, you need to repeat exactly the same thing.
- It is not difficult to guess that the beginning of the next stage is always the result obtained from the previous one. As we remember, the previous goal was to assemble the face completely. If the goal is achieved, then you can begin to implement a new task: assembling the two top layers.
To simplify, let's again turn to the help of diagrams. It is necessary to move the selected side cube down. Next we select:
We continue the assembly
As usual, we repeat everything and stirrup with the last dies.
- The cube assembled with two belts must be placed in layers down. This part will end with the cubes from cross B in their place, but upside down. You just need to rearrange the cubes in the middle part until everything falls into place.
These actions will have the effect of breaking, but do not be afraid. Repetition is the mother of learning. Let’s fix the algorithm and voila – we have a cube in front of us where everything is in its place. But you need to change the irregular cube in your hands a little spatially, turning it over to the face on the right.
- In this step, we take the beginning, as always, from the end of an already completed step. Let's go according to the scheme.
- At the end of the step, the cube will be completely assembled, but it will begin with all the corners being where they should be, but possibly upside down.
There may be two positions.
To perform a revolution we perform the following steps:
The algorithm is applied until the PV becomes correct. Again, things can go wrong, but that's okay if you trust consistency over and over again. Before repeating, place another “wrong cube” in the corner on the right. Repeat until the cube is completed.
Jessica Friedrich Method
Jessica Friedrich's method is one of the fastest methods for solving a Rubik's cube.
In 1981, Jessica Friedrich developed her own assembly plan, which has all the same main points and has no fundamental differences, but it significantly speeds up the process. You just have to learn “only” 119 rules. If you want to break the record, you'll have to use your brain.
If you are just starting out and spend two minutes or more on assembly, then this method is not for you yet; practice using the eight-step instructions.
- This method begins with the same assembly of a cross with edges on the sides. In English, the name of this step sounds like Cross and translated means cross.
- The second stage involves assembling two layers of the cube at once and is called F2L (an abbreviation for the phrase First 2 Layers, which literally translates as the first two layers). Algorithms describing this path are given below:
- The OLL stage means solving the top layer of the Rubik's cube. It will be described by 57 formulas.
- The final, fourth stage is called PLL and means placing all the elements in their places. The last stage can be described by these algorithms:
15 steps to assemble a 3*3 cube
In 1982, competitions appeared for the first time, in which those who wanted to complete the puzzle the fastest took part. In connection with the discovery of such games, more and more new formulas and algorithms for solving the problem began to appear. But in fifteen moves no one has yet managed to cope with the task. Even a build using 8 stages involves many more moves. The God algorithm given below has twenty such moves.
The discovery of such a quick assembly belongs to a team from Google; in 2010 they released their solution to the Hungarian sculptor’s puzzle.
Now, if you hear somewhere again about the 15-step solution system, you can safely argue with him, there is no chance that his resource will exceed the resources of such a powerful company. Those who want to learn how to solve a cube with the fastest and probably the youngest method among the fastest ones can pick up toys and use the diagram shown in the picture below.
Secret assembly technology
Those who want to cope with the task in a time equal to or less than a minute should learn a few simple rules.
- White and yellow colors will be an excellent solution for starting the build.
- Many precious seconds are spent turning the Rubik's cube in your hands, which, of course, negatively affects the temporary results. That is why they begin the assembly by assembling the cross on the bottom edge of the puzzle. This way you will save time on turning the toy over in confusion.
- The size of the 3*3 cube is good for the hand and its surface is already quite slippery and rotates well, but for greater success you can purchase a special, not very expensive lubricant for such objects.
- Always be one step ahead: at the moment when mental stress has already subsided and you are completing one of the algorithms that will definitely lead to success, it’s time to think about the next step.
- Use all your resources: all your ten fingers. This is what will lead to new records in solving the cube.
With your eyes closed? Easily!
Do you want to surprise everyone with your ability to solve a Rubik's cube without watching the process? Learned algorithms will help you deal with this. In addition, follow a few simple rules:
- Keep a picture of the puzzle in your head, it should always be mentally before your eyes and remember the golden rule, which states that it is best to start assembling from the bottom edge. And do not forget about the immobility of the centers relative to the sides.
- Solving the cube with your eyes blindfolded or closed will definitely amaze those around you. The invented algorithm says: orient the corners correctly! As a rule, all corners contain two colors: it is either yellow or white.
- Correctly position the side elements of the puzzle and whether its orientation is correct.
Modern varieties of Rubik's cube
The Rubik's Cube was created by the Hungarian scientist Erno Rubik; the professor and sculptor used this model to explain to his students the basics of mathematics, namely the mathematical theory of groups. In that same 1974, Rubik could not even imagine that this attempt to clearly demonstrate mathematics would make him a millionaire.
The assembly of the item took about a month, during which time it underwent many changes, mainly related to size. The scientist tested the future toy on his friends and loved ones. The patent was received in 1975, and the first batch was published only in 1977. “Magic cubes,” as the invention was dubbed, first appeared in Budapest, in a small cooperative just in time for the Christmas holidays. Several pieces from that very first batch ended up in the USSR.
Such mathematics soon interested the minds of other people. Tibor Lakzi started promoting the cube as a puzzle game. It was with his help that the world recognized the now beloved cube. Lakzi lived in Germany at that time, but often visited his homeland, where the object he liked was discovered. In one of the cafes where the entrepreneur was having lunch, he saw a funny little thing in the hands of the waiter. He, as a mathematician and as a businessman in the computer field, immediately saw the prospects and contacted the inventor. Another game inventor, Tom Kremer, who had already founded Seven Town Ltd., was brought in for promotion.
First popularity
And already at the end of the 20th century, hundreds of millions of copies of the Rubik's cube went on sale, making it an exciting game and hobby. The thing spread in European countries in May 1980, and the USSR saw it a year later. Of course, in our country there were some oddities. Some officials were given bribes with these toys, to receive which citizens had to stand in line and go around the circle twice.
The desire to understand the puzzle and learn its secrets enlivened the minds of everyone, even those who did not have it themselves. And in 1982, an article appeared in the famous magazine “Young Technician”, which presented diagrams and methods for making foreign toys with your own hands. And, of course, they could not do without the stigma - a bourgeois toy that takes up a lot of the workers’ time. But these arguments did not exist for long, and soon articles with diagrams for assembling a Rubik’s cube appeared on the pages of scientific journals.
So that people who could not cope with this difficult task and did not drown out their failures in alcoholic binges, special plastic hatchets were developed to destroy the unsuccessful, nasty model.
A little more history
In 1982, the first puzzle assembly competitions were held. The venue was the capital of Hungary - Budapest, where the game was invented. The participants were 19 countries, represented by the best players and winners of local competitions. The winner was Minh Thai, an American student from Los Angeles, who was 16 years old at the time. He completed his task in 22.95 seconds. Although at that time there were persistent rumors about craftsmen who could complete the assembly in just 10 seconds. Of course, compared to Mats Volk's current record, these numbers seem simply huge.
The Dutchman manages this in just 5.5 seconds. Although there is a video where the previous record holder Felix Zemdegs solves the magic cube in 4.21, it has no official confirmation. But there is another record, which is also not officially included in the Guinness Book of Records. The CubeStormer-3 robot managed to beat Zemdegs, spending only 3.25 seconds on the problem. Let's hope that one day one of the people will be able to break the program's record.
Today it is the best-selling toy in the whole world, which everyone has tried to collect. She has several awards to her name: she has repeatedly received the National Hungarian Prize for the best invention, and won in France, the USA, Germany and the UK. In 1981 he received his rightful place in New York, in the Museum of National Art. There is even a special Rubik Foundation, established in 1988. It was founded to support young inventors.
You've been puzzling over this puzzle for a week. And finally, it’s solved!.. You will never understand the joy of a person who has solved a Rubik’s cube until you try to do it yourself.
For an inexperienced layman, solving a Rubik's cube is not an easy task. Of course, on the Internet you can find videos and instructions with, where there is a detailed description of step-by-step assembly. But not all methods can be successfully applied in practice.
For beginner assemblers
Let's figure out what a 3x3 Rubik's cube is made of and how you can spin it (although, most likely, at first it will be twisted by you!).
The cube has a frame - a cross, on which the central parts of each side are fixed. These parts are motionless, and the rest of the “brotherhood” revolves around them.
Now take the cube, turn one of the sides towards you (at your discretion) and carefully examine:
B ─ top side,
H ─ bottom side,
L ─ left side,
R ─ right side,
F – frontal (front) side,
Z ─ back side.
And, accordingly, it is important to learn combinations of turns:
F, W, V, N, L, P – rotation clockwise (or away from you) by 90 degrees;
F',Z',B',N',L',P' - counterclockwise (or self-directed) rotation by 90 degrees;
F”, Z”, V”, N”, L”, P” – rotation by 180 degrees.
The simplest scheme for assembling a 3x3 Rubik's cube consists of seven successive steps.
Step 1. Assemble the cross on the top edge.
Choose the side that will be on top. We will assemble the “correct” cross. This means that on the top side the center will be surrounded by details of the same color, and on the side faces the stickers on the top cube and the central one will be of a different, but also the same color.
To get this result, the easiest way is to use one of the above turns to move the cube we are interested in down, align it with the center of the same color and move it back up.
When you have collected several edges in this way, and the next one is positioned in such a way that if you lower it, you will break the top, the combination P’, N’, P comes to your aid, allowing you to return everything to its place.
Step 2. Arrange the corners of the top edge.
It's easiest to start with the corners that are at the bottom. We twist the bottom so that the desired angle is under its place, as in the picture below. Next, we move it upward with one of the turns, most likely breaking the upper cross, so we fix the angle by turning it in a completely different direction, put the center in place and return the angle. For example, for the case shown in Figure 4, we use the combination P, F', P', F.
The principle is based on the fact that we “knock out” others with some cubes. If the corner is on top, then it is better to move it down, for example, by turning P′, and then put it in its proper place
Expected Result:
Step 3. Assemble the middle layer.
First, we unfold the cube so that the assembled side is at the bottom. Now you can place the four edges of the middle layer in their places. There are three possible combinations here:
1. It is necessary to move the cube from the top right to the front face. Rotate B', F', B, F, B, P, B', P'.
2. You can move to the right using the combination V, P, V’, P’, V’, F’, V, F.
3. To turn an edge that is where it should be, but on the wrong side: P, V', P', V', F', V, F, V', P, V', P', V', F', V, F.
Result:
Step 4. Assemble the “wrong” cross on the “new” top edge.
The goal is to achieve the option shown in Fig. 10, collect the “white cross”:
1) combination F, P, V, P’, V’, F";
2) Ф, В, П, В', П', Ф";
3) any of the proposed combinations twice.
Step 5. Making a “correct” cross from an “incorrect” cross.
Rotate the top layer until any two edges match the colors of the centers from the middle layer. There are two cases here:
1. Two opposite ribs are in their places, the other two need to be swapped. We use the combination P, V, P’, V, P, V”, P’.
2. Two assembled ribs are at an angle, the other two need to be swapped with a combination of P, V”, P’, V’, P, V’, P’. You may have to repeat this combination several times.
Result:
Step 6. Place the corners of the top layer in their places.
To complete this step, use one of the suggested combinations:
1) P’, F’, L, F, P, F’, L’, F;
2) F', L, F, P', F', L', F, P.
Step 7. Turn the corners with the correct colors.
We hold the cube towards us with one side so that the “wrong” corner is on the top right. Using the combination P’, N’, P, N, we twist the cube until the angle is as it should be. Next, scroll the top to the next incorrectly rotated corner and use the same combination to set it correctly. We do not change the working side!
During these actions, the design of the cube may be damaged. But that's how it's written in the script. So don't worry!
Finally, you can turn all four corners to the correct sides - the rest of the cube elements also fall into place! Be proud of yourself - you did it! Congratulations on your successful result!
Photo: kak-sobrat-kubik-rubika.praya.ru, speedcubing.com.ua, ru.gde-fon.com.
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Correct name " 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 that solves the Rubik's cube in the least number of moves is “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:
Hi all!
Today our article is dedicated to all puzzle lovers. Solving problems, crosswords, puzzles, riddles, etc. has always attracted people, young and old. And this is not only a fun pastime, but also good for the mind and the development of logical thinking.
Puzzles can be either drawn in some publication or made in the form of objects, often toys. One of these is the Rubik's Cube, famous in the 20th century.
There are probably still fans of this puzzle. Or maybe someone, after reading this article, will want to get acquainted with this almost ancient puzzle toy.
The Rubik's cube (sometimes erroneously called the Rubik's cube; originally known as the "magic cube", Hungarian bűvös kocka) is a mechanical puzzle invented in 1974 (and patented in 1975) by the Hungarian sculptor and architecture teacher Ernő Rubik. From Wikipedia.
In the mid-70s of the last century, the Hungarian teacher Erne Rubik, in order to somehow help his students learn some mathematical features and understand three-dimensional objects more clearly, made several wooden cubes and painted them in six colors.
Then it turned out that putting them together into a whole cube with sides of the same color was a rather difficult task. Erne Rubik struggled for a month until he achieved the result. And so, on January 30, 1975, he received a patent for his invention called the “Magic Cube.”
However, this name was preserved only in German, Portuguese, Chinese and, naturally, Hungarian. In all other countries, including ours, it is called the Rubik's Cube.
At one time this puzzle was a bestseller. It was sold all over the world in the 80-90s. only, more than 350 million pieces
What is a Rubik's Cube
What is this puzzle? Externally it is a plastic cube. Now it comes in various sizes, with 4x4x4 considered popular. Initially it was made in the 3x3x3 format. This cube (3x3x3) looks like 26 small cubes with 54 colored faces that make up one big cube.
The faces of the cube rotate around its three internal axes. By rotating the edges, the colored squares are rearranged in many different ways. The task is to collect the colors of all faces equally.
There are a lot of different combinations. For example, a 3x3x3 cube has the following number of combinations:
(8! × 38−1) × (12! × 212−1)/2 = 43,252,003,274,489,856,000.
As soon as this puzzle gained popularity, mathematicians all over the world, and not only, set the goal of finding the number of combinations that would be the smallest when assembling it.
In 2010, several mathematicians from different parts of the world proved that each configuration of this puzzle can be solved in no more than 20 moves. Any rotation of a face is considered a move.
Fans of the cube didn’t just solve it, but began to organize competitions in how quickly they could solve the puzzle. Such people began to be called speedcubers. The result is not calculated based on a single assembly, but as the average time of five attempts.
By the way, along with popularity, as it happens, opponents also appeared who proved (even with examples) that solving a cube, especially at speed, entails dislocations of the hands.
But, be that as it may, the cube not only did not turn away, but attracted more and more people. And competitions took place both in a separate city, and in the country, and internationally. For example, at the European Championships in 2012, a participant from Russia won. His average build time was 8.89 seconds.
The cube became so popular that other modifications of its shape began to appear. For example, a snake, a pyramid, various tetrahedrons, etc.
How to assemble a 3x3 cube, diagram with pictures for beginners
So. Let's start with a simple version of assembling a cube measuring 3x3x3. It consists of seven stages. But first, about some concepts and designations that appear in the diagrams.
F, T, P, L, V, N– designations of the sides of the cube: front, rear, right, left, top, bottom. In this case, which side is the front, rear, etc. depends on you and on the diagram on which these symbols are applied.
The designations F', T', P', L', B', H' indicate the rotation of the faces by 90° counterclockwise.
The designations F 2, P 2, etc. indicate a double rotation of the face: F 2 = FF, which means rotating the front face twice.
Designation C – rotation of the middle layer. In this case: S P - from the right side, S N - from the bottom side, S’L - from the left side, counterclockwise, etc.
For example, such a notation (Ф' П') Н 2 (ПФ) means that it is necessary to first rotate the façade edge counterclockwise by 90°, then the right edge as well. Next, rotate the bottom edge twice - this is 180°. Then rotate the right edge 90° clockwise, and also rotate the front edge 90° clockwise.
In the diagrams this is indicated as follows:
So, let's begin the assembly steps.
At the first stage it will be necessary to assemble the cross of the first layer.
We lower the desired cube down, turning the corresponding side face (P, T, L) and bring it to the front face by turning H, H’ or H 2. We finish everything by turning the same side face back
In the diagram it looks like this:
At the second stage, we arrange the corner cubes of the first layer
Here we need to find the required corner cube, which has the colors of the faces F, B, L. Using a method similar to the first stage, we bring it to the left corner of the selected front face.
The dots in the diagram show the place where you need to place the desired cube. For the remaining three corner cubes we repeat the same operation.
As a result, we get the following figure:
At the third stage we will assemble the second layer.
We find the required cube and initially bring it down to the front face. If it is located at the bottom, then we do this by rotating the bottom edge until it matches the color of the facade.
If it is located in the middle belt, then lower it down using formula a) or b). Next, match the color with the color of the front edge and do a) or b) again. As a result, we will already have two layers assembled.
Let's move on to the fourth stage. Here we will assemble the third layer and the cross.
What to do here. We move the side cubes of one face, which do not violate the already assembled order in the layers. Next, select another face and repeat the process.
This way we will put all four cubes in place. As a result, everything is in its place, but two, or even all four may be oriented incorrectly.
First of all, you need to see which cubes sitting in their places are oriented incorrectly. If there are none or one, then we rotate the top face so that the cubes on the adjacent faces fall into place.
Here we apply the following turns: fv+pv, pv+tv, tv+lv, lv+fv. Next, we orient the cube as in the figure and apply the formula written there.
Let's move on to the fifth stage. Here we unfold the side cubes of the third layer.
The cube that we will unfold should be located on the right side. It is marked with arrows in the figure. The dots there also mark all possible cases when the cubes may be oriented incorrectly (Figures a, b and c).
Figure a). Here you will need to rotate B' to bring the second cube to the right side. Next, finish with rotation B, which will return the top edge to its original position.
Figure b). Here we do the same as in case a), only we turn B 2 and finish in the same way at B 2
Figure c). We perform turn B three times after turning over each cube, after which we also finish with turn B.
We proceed to the sixth stage, placing the corner cubes of the third layer.
It should be simple here. We set the corners of the last face according to the following scheme:
First, a straight turn, with which we rearrange the three corner cubes clockwise. Then the reverse one, with which we rearrange the three cubes counterclockwise.
And finally, the last stage, during which we orient the corner cubes.
At this stage, the sequence of turns PF'P'F is repeated many times.
The figure below also shows four options when the cubes may be incorrectly oriented. They are marked with dots.
Figure a) we first make a turn B and end with a turn B’,
Figure b) here we start with B 2 and end with it.
Figure c) turn B must be performed after we have rotated each cube correctly, and then do turn B2,
Figure d) we first make a rotation B, which is also performed after we correctly orient each cube. We also end with a turn B.
As a result, everything is collected
Assembly diagram for children
This scheme is also divided into several stages.
- Assembly begins with a cross on the top side. It is almost easy to assemble. Moreover, you can ignore the arrangement of colors on the other sides of the cube, but only for now.
It is usually advised to start assembling with yellow. But you can choose any one.
- We continue to collect the cross. Here it is necessary to take into account that all the upper elements of the mating sides must have the same color as the central elements located on the same faces. If something doesn’t match somewhere, we try to follow this algorithm:
A. if two adjacent sides do not match in color: P, B, P’, B, P, B 2 , P’, B
B. if the opposite sides differ: Ф 2, З 2, Н 2, Ф 2, З 2
- At this stage we place the corner cubes. This way we will assemble one side completely. Let's examine these corner cubes and see that the cubes of the color that we chose as the basis, in particular yellow, are in three options: on top, on the left or on the right. For each we use the appropriate combination:
For the one on top – P, B 2, P’, B’, P, B, P’
For the one on the left – Ф’, В’, Ф
For the one on the right – P, V, P’
The result is one fully assembled side, and the top layers of adjacent sides and their centers have the same color.
- Now we have to assemble the second layer. To do this, turn the assembled side up. Next, twist the bottom edge so that the color of the side element matches the color of the side, forming the letter “T”. In order to move a side cube from the bottom layer to the middle one and at the same time its two colors must match the colors of the adjacent sides, you must do the following:
A. Turn the cube to the left - N, L, N', L', N', F', N, F
B. Move the cube to the right - N', P', N, P, N, F, N', F'
- Assembling the third layer. Let's start by turning the cube with the unassembled side up. If the chosen color was yellow, then now we must make white up. Now we collect white cubes using these formulas:
A. White cube in the center + two opposite sides - F, P, B, P', B', F',
B. White cube in the center + two adjacent sides – F, V, P, V’, P’, F
B. Only one white cube in the center - use any combination, either A or B
- We collect the remaining layer completely. Below is an assembly diagram with two possible options. If you don't succeed in any of the above, use any of them.
A. The colors match when rearranged counterclockwise - P, B, P', B, P, B 2, P',
B. The colors match when rearranged clockwise - P, B 2, P', B', P, B', P',
- At this stage we place the corner cubes. This will be a little more difficult to do. However, practice and everything will work out.
A. The side cube with the color of the top edge is on the front side -
P', F', L, F, P, F', L', F
B. The side cube with the color of the top face is on the side -
F', L, F, P', F', L', F, P
- Last thing. Here you need to turn the corners correctly. We again need two options:
A. Clockwise – P 2, B 2’, P, F, P’, B 2’, P, F’, P
B. Counterclockwise - P', F, P', B 2 ', P, F', P', B 2 ', P 2
If you need to change the corner cubes crosswise or the corners that are opposite, you can use either of these two options.
As a result, the puzzle will be completed completely.
Video master class on cubes
And finally, a short video
For more than 40 years, the Rubik's Cube has sold 350 million copies across the planet and has become one of the most popular toys of the 20th century. In 1980, every fifth inhabitant of the Earth tried to solve it, and in the 2000s, robots and computer systems joined in solving the puzzle. Today there are more than 30 types of cubes.
They come in intricate shapes and levels of complexity. The 3x3 Rubik's cube is considered a classic cube. With his help, Erno Rubik, a teacher at the Hungarian Academy of Applied Arts and Crafts, hoped to clearly explain to students the mathematical theory of groups and the advantages of spatial thinking.
It is with this puzzle that beginners are recommended to begin their acquaintance with the Rubix family.
How the classic Rubik's cube works
The original toy with a 3x3 configuration consists of 26 cubes, which are divided into central and edge ones.In the very heart of the cube, in place of the “invisible” cube, there is a cylindrical fastening mechanism. It is connected to all external elements and is responsible for ensuring that they rotate freely relative to each other.
But there is one subtlety: the mechanism is connected directly only to the central parts. The side and corner cubes are held onto them (and each other) using special protrusions. The design of the model is designed so that only the edges can be moved. But there are no restrictions on the coordinate axes.
Rubik's Cube and God's Number
A colorful puzzle just seems like easy fun. It took the professor a month to develop an algorithm for assembling his own invention. According to combinatorics, the possible states of a Rubik's cube are 43,252,003,274,489,856,000. Translated into human language, this figure sounds like 43 quintillion. Surprisingly, this is not the limit: the value will double if we take into account the difference in the location of the central elements.
It would take a professional speedcuber 4,200 trillion years to go through all the combinations. The unattainability of the goal does not prevent fans from looking for the easiest and fastest way to build. A new world record was set last fall by 15-year-old Patrick Pons from the USA. The teenager solved the problem in 4.69 seconds and 17 rotations.
The minimum number of steps included in the algorithm for solving a classic cube from any position is 20. It is called the “number of God.” Not everyone can play by such strict rules. On average, an experienced speedcuber makes 40 to 50 moves.
Assembly formula for beginners 
The 3x3 puzzle follows a general principle. Much depends on its condition at the time of assembly. To better understand the structure of the cube, you can disassemble it into parts and then reassemble it again. It is important to place the edges correctly.
The instructions for assembling the classic Rubik's cube consist of seven points:
- Creating a cross on the top plane
- Working with the corners next to it
- Gathering the middle ribs
- Creating a cross from below
- Working with the lower ribs
- Adjusting the bottom corners
- Final spread
