The impossible is possible, or how to solve the basic models of a Rubik's cube. Simple rules for solving a Rubik's cube

How to solve a Rubik's cube?

Don't rush to put the puzzle on the far shelf. After reading the article, you will be able to understand how to independently go through all the stages of the “cubic” assembly.

Step-by-step diagram and method of assembling a 3x3 Rubik's cube for beginners and children

If you decide to discover the secret to assembling a popular puzzle toy, then you should start by studying its internal structure and how the puzzle functions. The cube is sold in stationery stores, supermarkets and shopping centers, on the shelves in the toy department.

But out of billions of combinations, it’s unlikely that an adult will be able to find the only solution to this 3D puzzle without devoting a lot of time to studying and assembling it, let alone children.
After watching enough videos about quickly solving a Rubik's cube, you might think that it's easy. But it's not that simple. So, the first and important step before starting to solve a puzzle is to parse it into individual elements.
The 3x3 Rubik's Cube is made in the form of a mechanical cube with sides of a strictly defined color.

Each face is structured identically and consists of:

central segments(one side includes one such segment), capable of rotating around an axis while remaining in “their” cell (in our example, these are the brown central squares on each side)
8 corner segments, the square parts of which are painted in three different colors (in the example, such segments are purple)
12 ribs, located between the corner segments and having two different colors(in the example these are pale blue squares)
Rubik's Cube consists of 20 moving parts- these are edges and corners. Knowing how the 12 edges and 8 corner segments can move will help you understand how the puzzle works.

What happens if you rotate one face? The centers are static (do not move), the edges change positions, taking the place of other edges, and the corners move into the corner.

With each shift and rotation of the sides of the cube, the edge remains the edge, and the segment located in the center remains the center.

How to solve a Rubik's cube easily, quickly and correctly: formula, order of assembly, combinations

A completed Rubik's cube means that all the elements are in their “right” places. The reference points for the correct location of the squares are the centers fixed in one place.

The sides of the rib between the red and green centers are colored red-green. So, have solved rubik's cube the green center segment will have a green edge next to it, and the red center segment will have a red edge next to it.
The correct location of the three-color corner is between the centers painted with the corresponding colors.

Stage 1: Edge Assembly

Let's start assembling the Cube with one color. In our diagram it will be yellow. If you prefer to start with a different color, then simply repeat all the steps with the elements painted in that color.
Place the cube with the yellow central segment facing up. Then a white center will be placed on the opposite bottom side (standard Rubik's cubes have the same arrangement of colored segments, so the yellow center is always above the white).
We set all the edges of the color we need around the central square. A cross should form on the top side of the cube yellow color.
But this is done as follows:
the edge, as we have already said, is painted in three different colors, so its second color should correspond to the center that is closer.

Without understanding the structure of the cube, this stage will be difficult to understand. But if you take the time to train (without tips from those who have mastered speed assembly), then everything will work out.

Anyone who first sets out to solve a tricky puzzle usually gives up his idea after folding the cross and one of the sides. They don't have the patience to move forward. But we will continue, because the puzzle is not solved yet!

So, the main thing for us now is not to give up and try to fold the cross on your own. It’s better to close the article at this time, but if the solution doesn’t come to you, then look at the examples below.
The diagram below will help you understand how to arrange squares of the same color in a cross. Repeat this step 4 times, because each color must be laid out crosswise.

Start of assembling the cross

How to lay out a cross:

Flip the puzzle over with the yellow center facing up (if you chose a different color, place the side with the center segment of your chosen color at the top). The white center will be at the bottom.
We are looking for edges painted yellow on the underside. Let's not forget that the two colors of each edge are important to us now.
Find the bottom edge, painted yellow, and scroll it so that the yellow square of the edge takes “its place” on the top edge.

Let's do the following:

The yellow center is pointing down.

Yellow “looks” down

The yellow center is facing forward.

Yellow “looks” forward

We place the edge between two intermediate layers.

IMPORTANT: The yellow top edge segment may be oriented incorrectly relative to the other segments, or in the wrong position relative to the nearest center segment.

To return such an element to the right place, you must move another element to its position.
The edge will then end up in one of the three positions described above. We install it in the “right” place.
We assemble each yellow edge in the same way as the diagram above until we get a cross on the top side of the cube.

Stage 2: continuing to assemble the top face:

After assembling the cross, we continue to assemble the upper side: we move the corners to their places one after another.
But here too one should collect, adhering to certain rules, and not as your heart desires. The color of each corner depends on the place allocated to it.

There are several ways to get through this stage. Assembling each corner is carried out in 4 steps:

Turn the cube over with the yellow side up. The white side should be on the bottom. We are looking for a corner on the white side, one square of which is yellow.

Yellow “looks” to the left

Scroll this “white” layer so that the yellow corner takes “its” place.

Yellow “looks” to the right

set the cube with a corner element painted yellow to the left
flip it over, pointing the yellow element to the right
turn again, pointing the yellow to the underside

IMPORTANT: if there is no yellow corner at the bottom, then it has moved to the top side, which means it has taken a “foreign” position. To return the yellow corner to its place, rotate any corner of the bottom side up. After this, the yellow corner will be at the bottom. Turn until the top layer is completely assembled.

Stage 3: Assembling the second layer

We collect the edges of the second layer. We remember that the centers of the cube do not move and there is no need to move them to find the right place for them. We repeat the steps 4 times. After all, we have 4 edges:

Place the cube with the white layer facing up. The yellow one, which is below, has already been assembled.
We find an edge on the top edge, both sides of which are not white.
We turn the top so that the color of the edge found in the previous step is the same color as the center. We should end up with an inverted T.
To do this, repeat one of the steps below. You need to find a solution in which the edge took a position on the left or on the right: follow the example that suits you.

Here are the ways to assemble this part of the Rubik's cube:

We move the edge from the position where it stopped to the right side.

Move the edge to the left.

IMPORTANT: lack of edge, any side of which is not white, means that he did not take “his” position in the middle layer.

Move the other edge so that it takes up top layer the position of that extreme element that took the “alien” position.
Now there is no white square on the top edge, which can be scrolled according to the scheme described above.
We repeat all the steps again 4 times, thus collecting 4 edges.

Stage 4: assembly of the second cross

We have collected 2 faces. Next, you need to carry out such manipulations, after which the 4 white edges of the upper edge form a cross. Let's focus exclusively on the outermost elements. We shouldn't be interested in angles right now.
The top layer may have four white edges, two white edges, or no white edges at all. There may be such a position: on the top face there are all 4 white edges. In this case, you can immediately move on to the next stage.
The version with two white ribs is assembled according to the diagram below. We pay attention to how these ribs are located - next to or opposite each other.

If the white edges are adjacent:

If the white edges are opposite:

White squares are missing in their places:

It is necessary to perform the above-described manipulations to obtain 2 squares on the top face.
Next, we fold a cross depending on how the white squares are arranged.

Stage 5: placement of the second cross

When the second cross is folded, we need to place the sides of the cross so that they become a continuation of the central elements of the faces that match in color.
Again, we focus solely on the white edges, not taking into account the color of the corner elements.
We need to rotate the top face so that the color of the two edges matches the color of the central squares of the corresponding faces.
If only one edge matches, you need to continue rotating.
Follow the examples above. Here everything depends on the lateral extreme elements: they are located sequentially or are on opposite sides.

If on adjacent edges:

If on opposite edges:

We should now have a correctly positioned second cross.

Stage 6: corners

Now we proceed to arranging the corner elements of the last layer. The orientation of the corner pieces is not important now. The main thing is to determine whether the corner element is in the correct position.
This is not difficult to determine: with a correctly positioned corner element, the colors of nearby centers coincide with the color of the 3 squares of the corner.

The following examples will help you understand when a corner element is positioned correctly:

If the 4 corners are in the correct position, then you can proceed to step 7.
If only one corner piece is placed correctly, or there is no correctly placed corner at all, then choose one of the appropriate examples to place all the corner pieces in “their” places.

If all three corner parts are not in their “right” places, here are the possible solutions:

Three corners in place (option a)

If there are no correctly positioned corner elements:

In the latter case, it is necessary to follow one of the examples described above so that at least one corner element takes the desired position.
After that, continue depending on how the elements are arranged.

Stage 7: Assembly

The corners have taken their positions, and we just have to do the last steps: solve the puzzle by rotating the corner elements of the last layer.
Now on a Rubik's cube there may be 2, 3 or 4 corner pieces of the last layer that are oriented incorrectly.

In a situation where 2 corner elements are oriented incorrectly, do the following:

Before rotating the faces of the cube, pay attention to several important points:

The first option for solving the puzzle may have sub-options. It all depends on which one is right for you. It is necessary to perform the first sequence of actions, and then act in accordance with the result obtained.

Option 1:

with two incorrectly oriented elements: it is necessary to rotate the “neighboring” corner clockwise.

Option 2-3:

with three incorrectly oriented corner elements, the Rubik's Cube is solved according to the first example to reach 2 incorrectly oriented corner elements. Further manipulations are carried out based on the results obtained.

Option 4:

in the absence of correctly oriented corner elements, it is necessary to act according to the first example described above, and then select the solution that corresponds to the result obtained.

Assembly option for all incorrectly oriented corners

Are you still following our instructions and everything is done correctly? Our congratulations! Your Rubik's Cube has been solved! And you yourself solved this puzzle!

Video: How to solve a 3x3 Rubik's cube | NEW SCHEME 2017

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 in various ways in order to do this, because the best minds at one time spent effort 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 the color of 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. Best Method 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 most quick methods solving a Rubik's cube.

In 1981, Jessica Friedrich developed her own assembly plan, which has all the same main points and fundamental differences does not, but it speeds up the process significantly. 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 an 8-step build involves many more moves. The God algorithm given below has twenty such moves.

Belongs to the discovery of such quick assembly 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 a 3*3 cube is good for the hand and its surface is already quite slippery and rotates well, but for more success You can purchase a special, not very expensive lubricant for such items.
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 a cube with tied or eyes 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, a professor and sculptor using this model to explain to his students the basics of mathematics, namely mathematical theory 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", this is how 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 82 famous magazine « Young Technician"an article appeared that provided diagrams and methods for making a foreign toy 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, as best invention, 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.

Do you know which toy deserves the title of the most sold in the world? No, not the beautiful Barbie and not even 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 minimal amount 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 sides 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.

In 1975, sculptor Erne Rubik patented his invention called the Magic Cube. For more than 40 years, all rights to the puzzle belong to the company close friend inventor - Tom Craner - under the name Seven Towns Ltd. The English company controls the production and sale of the cube throughout the world. In Hungary, Germany, Portugal and retained its original name, in other countries the toy is called a Rubik's cube.

Types of puzzles

The classic Rubik's cube measures 3 by 3 squares. Over time, they came up with a huge number of shapes and sizes for toys. No one can be surprised by a puzzle in the form of a pyramid or a cube size of 17x17. However, humanity never stops there.

Obviously there is no beginner's guide to building this cube. The process of assembling and solving the puzzle can take years. IN Lately Interest in the cube is growing not only in Asia and Europe, but also in places where the toy was not very popular, for example, in the USA. One of the fans of the Rubik's cube filmed the assembly of a 17 by 17 puzzle. The total length of the video was 7.5 hours, filming took place over the course of a week.

Growing demand creates supply. Sometimes the models sold are incredible and it is not always clear what they will look like when assembled. Each country has its own favorite types of toys.

What is speedcubing?

Fans of the game organize real competitions in how quickly they solve the cube. There are special “speed” puzzles available for sale. The rotation mechanism of such Rubik's cubes is very high quality, and rotations of faces and rows can be done with the movement of one finger.

World Cube Association (WCA) is non-profit organization, supporting the speedcubing movement. The WCA regularly organizes competitions around the world. There are representatives of the organization in almost all countries. Anyone can become a participant in a speedcubing event; you just need to register on the website and meet the assembly standards. The most popular discipline at such competitions is speed solving a 3x3 Rubik's cube. The standard for participation is 3 minutes, but even if a person cannot solve the problem in the allotted time, he will still be allowed to participate in the event. You can sign up for any discipline, but you need to come with your own puzzle.

The record for solving a 3x3 Rubik's cube belongs to the robot Sub1, created by engineer Albert Beer. A machine can solve a puzzle in a fraction of a second, while a human will need 4.7 seconds (Mats Valk's achievement in 2016). As you can see, participants in the speedcubing movement have someone to look up to.

What algorithms exist for solving a 3x3 Rubik's cube?

There are many ways to solve a famous puzzle. Variants of 3x3 Rubik's Cube assembly schemes have been developed for both beginners and advanced people with complicated schemes: 4x4, 6x6 and even 17x17.

The 3x3 version of the puzzle is considered a favorite classic among most fans. Therefore, there are much more instructions on how to solve a 3x3 Rubik's cube than any other.

What should the puzzle look like?

You can assemble the toy according to the diagram only from a pre-prepared position. If the patterns on the faces of the cube are located incorrectly, then it will not be possible to solve it using the algorithm for solving a 3x3 Rubik's cube for beginners. There is a set of such positions for different options solutions.

The figure shows or simply a “cross” - the starting point of the simple way solve a 3x3 Rubik's cube. It is recommended to disassemble and fold the toy correctly.

Designations of circuits and methods of rotating the cube

Before you start disassembling the 3x3 Rubik's cube formulas, it is worth learning the notations used in speedcubing. All puzzle movements are indicated in capital letters. The absence of an apostrophe above the symbol means that the rotation is clockwise; if there is a sign, then the rotation should be in the opposite direction.

The first letters of English (or Russian) words denoting movements are considered generally accepted:

front - F or Ф - rotation of the front side;
back - B or T - rotation of the back side;
left - L or Л - rotation of the left row;
right - R or P - rotation of the right row;
up - U or B - rotation of the top row;
down -D or H - rotation of the bottom row.

Pointers can also be used to change the position of the cube in space - interception movements. Everything is simple here too, from school course In geometry, everyone knows the coordinate axes X, Y and Z. Movement X means that the cube must be rotated with face F to the place of face U, when Y is shifted - F becomes in place L, and when rotated Z - F is moved to R.

The following group of notations is rarely used; it is used when drawing up pattern diagrams:

M - turn of the middle row, between right (R/R) and left (L/L);
S - rotation of the middle row, between the front (F/F) and rear (B/T);
E - rotation of the middle row, between the top (U/B) and bottom (D/H).

Why do they collect patterns on the faces of the cube?

At speedcubing meetings, people compete not only in solving the puzzle, but also in the ability to create various patterns on a 3x3 Rubik's cube. They do this in order to quickly and easily assemble the cube into the desired position.

There are a huge number of schemes for assembling a wide variety of patterns: “dots”, “chess”, “dots with chess”, “zigzag”, “maison”, “cube in a cube in a cube” and many others. There are more than 46 of them for the classic puzzle alone. Speedcubing masters consider it shameful to disassemble a toy. Also, making patterns on a 3x3 Rubik's cube is a great way to practice and improve your skills.

The picture shows variations of different puzzle patterns. Below are a few more formulas for assembling the most interesting patterns from the cross position:

chess - M 2 E 2 S 2;
zigzag - (PLFT) 3;
four z - (PLFT) 3 B 2 H 2;
Plummer's cross - TF 2 N"P 2 FNT"FN"VF"N"L 2 FN 2 V";
cube in a cube in a cube - V"L 2 F 2 N"L"NV 2 PV"P"V 2 P 2 PF"L"VP".

Algorithm for solving a 3x3 Rubik's cube for beginners

Although there are many ways to solve the puzzle, simple and understandable diagrams for beginners are not so easy to find. With each passing stage of assembly, the formulas for the 3x3 Rubik's cube become more complex. It is necessary not only to correctly change the pattern, but also to preserve what was done before. Below is one of the options for how to easily solve a 3x3 Rubik's cube.

Conventionally, the whole process can be divided into the following stages:

Assembling a cross at the top edge of the cube.
Correct composition of the entire upper edge.
Work on the middle layers.
Correct assembly of the ribs of the last row.
Assembling the cross of the bottom edge.
Correct orientation of the corners of the last face of the cube.

Solving the puzzle - preparatory work

The first stage is the easiest. Beginners can try their hand at making cube patterns using the instructions provided, but the process will take a long time.

You need to select the top edge and the color that will be assembled first. The algorithm for solving a 3x3 Rubik's cube for beginners is developed from the "cross" position. It is not difficult to make, you need to select a central color, find 4 edge elements of the same shade and raise them to the selected edge. The colored arrow in the picture points to the part you are looking for. Location options desired element may be different, depending on this, 2 sequences of actions A and B are described. The difficulty is to continue the cross along the sides of the cube. You can take a closer look at the final view of the stage in the image above.

Puzzle solution - working on the middle row

At this stage of the 3x3 Rubik's cube assembly scheme for beginners, you need to find and assemble the corner elements of the top face. The end result should be to completely solve the cross face and the top row of the puzzle.

The image shows three possible edge patterns. When choosing one of methods A, B or C, you must collect all 4 corners of the cube. By memorizing rotation algorithms and practicing them, you acquire the skills and mastery of assembling a puzzle. It is pointless to consider formulas and imagine the process; it is much easier to take a cube and try all the methods in practice.

The third stage seems simple, but it is only apparent. To solve it, two situations of patterns are described and two rotation formulas are compiled accordingly. When using them, it is worth remembering to preserve previously achieved results. Masters constantly keep the last 3-4 rotations in memory so that in case of failure, they can return the cube to its original state.

To solve a puzzle, you need to rotate it along the coordinate axis in search of the necessary elements and work with them. Such movements are rarely shown in formulas, only in special cases. It is recommended to start assembling the edge faces from the elements of the bottom rows; after such rotations, all the necessary cubes will descend from the middle to the bottom row.

Solving the puzzle - making the second cross

At the fourth stage, the toy is turned upside down. The solution to the last face is the most the hard part algorithm for solving a 3x3 Rubik's cube for beginners. The rotation formulas are long and complex, and their execution will require special care. The purpose of the action is to place the edge elements in their places for further composing the cross. The orientation of the rib parts may be incorrect. There is only one formula for cube movements and it should be applied until the goal of the stage is achieved.

The rotations of the fifth stage are aimed at turning the elements to the correct side. Its peculiarity is that the same rotation formula is used for all three patterns in the figure, the only difference is in the orientation of the cube itself.

The formulas for stage 5 movements are as follows:

(PS N) 4 V (PS N) 4 V" - option “A”;
(PS N) 4 V" (PS N) 4 V - option “B”;
(PS N) 4 V 2 (PS N) 4 V 2 - option “B”.

C H is the rotation of the middle row clockwise, and the exponent above the bracket is the number of repetitions of the actions in brackets.

Solving the puzzle - last spins

At the sixth stage, as at the fourth, the necessary cubes are placed in their places, regardless of their orientation. The puzzle should be rotated so that the element that is already in the right place is located in the far left corner at the top of the cube. The options proposed to solve the formula mirror each other. It is necessary to repeat the rotations until the desired result is achieved.

The seventh stage is the most solemn and the most difficult. When rotating the cube, violations in already completed rows are inevitable. You will need to fully concentrate on the movements, otherwise the result of the assembly may be irretrievably ruined. As in the fifth stage, there is only one sequence of movements, but it is repeated 4 times. First, rotations are performed to orient the element, then reverse rotations are performed to restore broken rows.

We should not forget about recording movements using signs English alphabet. The formulas for the movements of the faces and rows of the cube at this stage are as follows:

(RF"R"F) 2 U (RF"R"F) 2 - option “a”;
(RF"R"F) 2 U" (RF"R"F) 2 - option “b”;
(RF"R"F) 2 U 2 (RF"R"F) 2 - option “c”.

B - rotate the top face 90 degrees, B" - rotate the same face counterclockwise, and B 2 - double rotate.

The difficulty of this stage is in correctly assessing the location of the elements and choosing the required rotation option. It can be difficult for beginners to immediately correctly identify the pattern and match it with the correct formula.

Rubik's cube and children

This tricky puzzle is interesting not only for adults, but also for children. Teenagers have become world record holders for solving the Rubik's cube. In 2015, Colin Burns, who was only 15 years old at the time, assembled the toy in 5.2 seconds.

A simple but fascinating toy continues to interest the younger generation for the 5th decade. A childhood hobby often develops into a profession. There are mathematical ways to evaluate solutions to Rubik's cube problems. This section of mathematicians is used when compiling and writing solution algorithms for automated computers. Robots that actually look for ways to solve the cube, rather than following a pre-written algorithm of movements, solve the puzzle in 3 seconds, for example, CubeStormer 3.

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 faces, 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 corners planets have proven 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 from itself, but attracted more and more 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 get started simple option 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 you must first rotate the front 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 we 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 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) 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 rotate each cube correctly, and then 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',