How long does it take to complete the Rubik's Cube? How to solve a Rubik's cube with your eyes closed? stage - OLL

For many decades, this puzzle continues to be popular. Records are set - both by humans and robots, the puzzle-solving algorithm is being improved. And now computers can already teach how to assemble a Cube of a person with any level of experience (we are talking here about educational applications, of which there are many). After a couple of days of training with the help of a computer, even those who took the toy in their hands for the first time will be able to correctly assemble all the facets.

By the way, the Rubik's cube world champion (yes, there are such champions) solves the puzzle in just 4.9 seconds. The champion's name is Lucas Etter, a teenager from the United States. A similar record for a robotic system is (although this result has not yet been confirmed). But how to learn how to quickly solve the Rubik's cube yourself? You can train (this can take many years). Or you can use a special program that will help you collect the cube in the minimum number of moves (the so-called God algorithm). No workouts are needed here, the app does everything by itself.

This is how the human champion solves the die:

And so - the champion-computer:

Generally speaking, there are many algorithms for solving a puzzle. For the average person, the average number of moves is about 40. Few champions know how to solve the god's cube. In short, this is the name of an algorithm that requires a minimum number of moves to assemble any initial configuration. For a Rubik's cube, this number is 20.

Now let's get back to augmented reality. A developer named Martin Španěl created Mistr Kostky app, which helps a person to solve a Rubik's cube. Moreover, the number of moves is exactly the same - exactly 20. The application can determine the state of 2-3 cube faces at the same time, and the OpenCV library is used to recognize the resulting images.

Augmented reality shows how to rotate the edges of the puzzle in order to achieve the optimal number of moves. The developer created his program as part of his scientific work - he is a student at Charles University (Prague).

The program works in two stages. At the first stage, the state of each face is recognized. After the system completes the first stage, the second begins - the application shows the user where and how to rotate the edges of the cube to solve the puzzle (sometimes it can be done in less than 20 moves).

Interestingly, if the owner of the puzzle is wrong, then the application has to be restarted - it is not able to rebuild on the fly. Note that applications for solving the Rubik's cube have not appeared yet. This is one of the best, yes, but back in 2009, the Cube Cheater program was added to Apple's app catalog. She helped the user find a solution for the face photo.

Any Rubik's Cube position can be solved in no more than 20 steps.

Several years ago it was proven that there is a 23-move solution for the Rubik's Cube. Now that number has dropped to 20. It took thirty-five (35) years of computer time donated by Google to do it.

Each block of the solution used its own algorithm - a sequence of steps to achieve the desired configuration. For example, one algorithm was for solving the top edge and another for positioning the middle edges. There are many different algorithms that differ in the degree of difficulty and the number of steps required, but those that a human can remember usually require more than 40 steps.

It is reasonable to believe that God can use a more efficient algorithm that solves the problem in the shortest possible number of steps. This algorithm is known as the “God algorithm”. The number of steps in the worst case is called the number of God. Ultimately, the number was shown to be 20.

After the invention of the Rubik's Cube, it took fifteen years to find a position, which is probably solved in 20 steps. 15 years after that, we will prove that 20 steps is enough for any position.

History of the number of God

By 1980, the lower bound was 18 and the upper was probably around 80. The table below summarizes all the results:

How we did it

How did we deal with 43,252,003,274,489,856,000 Rubik's Cube positions?

• We have divided all positions into 2,217,093,120 sets - 19,508,428,800 positions each.
• We have reduced the number of sets to solve to 55 888 296 based on symmetry and set coverage.
• We were not looking for an optimal solution, but only solutions with a length of 20 or less steps.
• We wrote a program that solves one set in 20 seconds.
• It took 35 years of computer time to find solutions to all configurations in each of the 55,888,296 sets.

Division of position space

We split the large problem into 2,217,093,120 smaller subtasks, each containing 19,508,428,800 different positions. One such subproblem easily fits into the memory of a modern computer, and this method made it possible to quickly obtain a solution.

Symmetry

If you turn the Rubik's Cube left-right or up-down, then, in fact, nothing will change: the number of steps in the solution will remain the same. Instead of solving all of these positions, one can get a solution for one and extend it to rotated positions. There are 24 different orientations in space and 2 mirror positions of the Cube for each position, which allows to reduce the number of solved positions by 48 times. If we use similar reasoning and use the search for the “set covering” problem, then the number of subproblems decreases from 2,217,093,120 to 55,882,296.

Good and optimal solutions

The optimal solution contains a sufficient number of steps, but not more than necessary. Since one position is already known, for which 20 steps are required, then we may not look for the optimal solution for each position, but only solutions in 20 or fewer steps. This speeds up the task many times over.

Equipment

We had the opportunity to solve 55,882,296 subtasks on Google's facilities and complete all the calculations in a few weeks. Google does not disclose the characteristics of the computers, but it took 1.1 billion seconds of computer time (Intel Nehalem, four-core, 2.8GHz) to perform the calculations.

Hardest position

We've known for 15 years that there are positions that require 20 steps, but we've proven that no position requires more.

Positions with solutions in 20 steps are rare, but it is quite possible to meet them in reality. The probability of encountering such a position varies from 10 ^ (- 9) to 10 ^ (- 8). We do not know for sure the exact number of such positions. The table gives an estimate of the number of positions for each solution length.

For lengths 16 or more, the numbers are approximate. Our research has confirmed all the original data up to and including line 14, and line 15 is the new result. As of August 11, we found 12 million positions with a solution length of 20. This position was the most difficult for our programs:

How to entertain yourself when you have a free minute, but nothing to do? Solving all sorts of puzzles is a great option!

The most popular puzzle in the history of mankind is rightfully considered the famous Rubik's cube, invented back in 1975 and named after its inventor. After his birth, he immediately "took over the whole world." At a minimum, everyone tried to solve the Rubik's cube, but not everyone was able to do it.

How to solve a Rubik's cube? It is quite difficult to do this without outside help, absolutely independently, this is far from a child's task. You need to know the algorithm for solving the Rubik's cube.

By the way, it has been proven that for any initial situation, a 3x3x3 cube can be completely assembled in no more than 20 moves (turns). The number 20, therefore, is also called the number of God, and the algorithm that collects the cube in the minimum number of moves is called the algorithm of God.

If you have long wanted to know how to solve the Rubik's cube, then this post is for you. Let's end this task once and for all and have ourselves a little party. Having done this, you can safely put a plus sign in the list of your achievements and then trump your acquaintances who do not know how to do this. So, we present to your attention the algorithm for solving the Rubik's cube.

The pictures show the schemes of actions, following which, in the end, we will be able to arrange the colors on the sides of the cube.

First, let's figure out the designations that are used in the diagrams, and with which we will operate in the process of studying the algorithm for solving the Rubik's cube of the classic 3x3x3 size.

Party designations:

• F - frontal (front)
• Z - back
• L - left
• NS - right
• V - upper
• N - bottom

Now let's deal with turn names which we will apply to the sides described above.

The letter without any prefixes denotes the rotation of the indicated side by a quarter of a full turn (90 degrees) clockwise(for example, " F"Means that we turn the front side by a quarter of a turn clockwise, i.e. one shift).

The letter c " ’ "Means the rotation of the indicated side by a quarter of a full turn (90 degrees) counterclock-wise... Thus, the inscription “ F '"Means that we must turn the front side by a quarter of a full turn counterclock-wise.

The letter c " ’ ’ "Means that we turn the indicated side in any direction half turn(180 degrees)

Let's fix: the inscription L ’ ’ PF ' means that first we rotate the left edge half a turn, then we make a quarter turn of the right edge clockwise and end the combination with a quarter turn of the front edge counterclockwise.

Arrangement of flowers.

Select the bottom color, it will remain at the bottom throughout the entire cube assembly process. Instead of the gray color, which is shown in the diagrams of the Rubik's cube solving algorithm, there can be any color, it does not matter. The place where we moved the part we need will be shown in black. See the first drawing.

We pass directly to the assembly and the answer to the question "How to solve the Rubik's cube?"

Step # 1.

You need to collect a cross on the bottom side of the cube, so that all the middle side squares correspond to the midpoints of the side faces (look at the diagram). Unfortunately, there is no ready-made algorithm here. We'll have to tinker a little and use our brains.

Step # 2.

The second step is to assemble the bottom layer. We need to put the bottom corner cubes in place. Everything is much simpler here than in step 1 - there are ready-made turn templates.

If the corner is in the bottom layer, but is incorrectly oriented, then it must first be lifted up, rotated as we need it and put in its rightful place. We look at the picture and apply the techniques given there. Each turn has a corresponding formula, which we dealt with a little higher.

Step # 3.

The bottom layer is assembled. Let's move on to the second, middle layer. We place 4 side cubes of the second layer in their rightful places. If the side cube is in its place, but not rotated correctly, then you can turn it over by performing the following actions - see the diagram.

Two layers are assembled. There is a final spurt left, but you shouldn't relax ahead of time.

Step # 4.

The task is to turn the middle cubes of the upper layer with the color we need upwards. At the same time, it does not matter in their place they are or not, at this step it is not so important. Applying one of the proposed schemes of actions, we turn the sides of the upper side with the desired color upwards.

Step # 5.

A cross of the desired color turned out on the upper face, however, as you could understand from the previous paragraph, the side cubes of the upper face may not be in their places. The task of the 5th step is to put them in their place.

There are 4 options, each of which has its own effective algorithm of actions. We apply them and put the sides in place. The cross of the upper edge can be considered fully assembled.

Step 6.

Are we continuing to figure out how to solve the Rubik's cube? And we almost reached the home stretch.

We set the corners of the upper face to their places, but at the same time they can be turned over.

In this case " in place”Means that the corner contains the colors of all central squares of those faces at the junction of which it is located.

There are three rotation formulas that correspond to the three ways to move the corner cubes. We remind you that the corners may be incorrectly oriented, but they must fall into place.

Step 7.

Friends, we made it to the finish line! The last step in solving the Rubik's cube remains.

Corner cubes are in place, but some may not be oriented correctly. They need to be turned over. To do this, perform the operations described in the diagram of step # 7 in pairs (see the figure above).

Happened? Well, of course it worked! In just 7 steps, we have coped with the puzzle that did not let and does not let millions of people sleep.

Naturally, you did not memorize all the steps and formulas of turns and movement at one time. Here you just need to practice and get your hands on it.

The main thing is that you now know exactly the answer to the question " How to solve a Rubik's cube»?

Surely everyone from childhood knows the famous puzzle, named after its creator - Ernö Rubik. She quickly gained popularity and reached the most remote corners of the planet.

Without the proper skill, it will not work to put the puzzle together, even after doing a hundred manipulations, but relatively recently, experts from Inc. learned how to solve a Rubik's cube in 20 moves. They managed to achieve this phenomenal result with the help of a computer, which was given the task of analyzing all possible combinations.

Where did the Rubik's cube come from?

Back in 1974, Ernö Rubik, a Hungarian architect and teacher at the Academy of Applied Arts, thought about the optimal way of learning

He wanted a new invention to help students in the study of the world, and one day he had a sensational idea - to create a puzzle. The task, it would seem, is elementary - to rotate the rows of the cube until each side becomes one color. But the scheme for assembling a Rubik's cube is not so simple and can take even several hours in time without giving any result. The students appreciated and took a great interest in the new toy. At that moment, the creator did not even suspect that in many years scientists would puzzle over solving the puzzle until they figured out how to assemble a Rubik's cube in 20 moves.

How worldwide popularity came

At first, the original toy was not popular with investors. It was believed that its production would not be profitable, since the assembly of the Rubik's cube could be of interest only to intellectuals. Nevertheless, one small company decided to invest in this unusual project, and the puzzle began to conquer Budapest.

A few years later, Tibor Lakzy, an intermediary of one of the German firms, arrived in the city and became interested in the original puzzle, which was very popular among the townspeople at that time. Realizing that the spread of an amazing invention around the world could bring huge profits, he decided to promote the Rubik's Cube. For novice businessmen Lakzy and Rubik, the main difficulty was finding investors. But thanks to Tibor's economic education and commercial streak, the owner of Seven Towns Ltd, Tom Kremer, was soon involved in the project. He took up large-scale production and distribution, which helped the cube become popular all over the world.

"God's Algorithm"

Since 1982, competitions have been regularly held in many countries, in which the main task of the participants is to quickly solve the Rubik's cube. In order to solve the puzzle as quickly as possible, it is not enough just to have good dexterity and quick wits. A person should be aware of the optimal scheme for solving the Rubik's cube, which allows him to spend as little effort as possible. The minimum number of steps required to solve a given problem is the "Algorithm of God".

Many learned minds and ordinary amateurs have tried to find a solution. At one time it was believed that the minimum number of steps from any position was 18, but later this theory was refuted. It took many years to find the optimal sequence, and only in 2010 did scientists manage to find out how to solve a Rubik's cube in 20 moves, regardless of the position of the puzzle before the start of the assembly. It is currently an absolute record.

Who is faster - a car or a person?

Colin Burns, an American high school student, is currently the fastest human being - he managed to solve the puzzle in less than 5.5 seconds. And the robot, assembled by British engineers from EV3 construction kit parts, coped with this task in 3.253 seconds. The advantage of the mechanism is not only that the work of all its parts is more harmonious than human actions. Scientists gave him as many as 4 hands, which allow him to perform all operations 2 times faster.

How to learn to collect it

There is more than one standard Rubik's cube scheme that allows you to quickly learn how to solve this original puzzle. Different build systems allow you to approach the issue in different ways. Which one to choose is up to you. Of course, it is unlikely that without the computer power of Google, you will learn how to solve a Rubik's cube in 20 moves, but you will learn how to find simple solutions in a short time. The main thing is that you have enough perseverance. No technique will help you solve the puzzle without problems if you are not ready to spend your precious time learning.

But you shouldn't give all your time to this toy. Doctors have noticed an increase in the number of patients in psychiatric clinics after the appearance of the Rubik's Cube. And traumatologists began to regularly encounter symptoms, later called "Rubik's syndrome". It manifests itself in the form of acute

Assembly diagram

There are several schemes that allow beginners to quickly learn how to add a Rubik's cube. One of them is attached to this article:

1. First you need to collect a cross, the ends of which are continued on adjacent faces. There is no universal method - everything comes with practice.
2. Next, you need to complete the entire side on which the cross was assembled and assemble the belt from the parts around it. It is important to make sure that each belt is the same color.
3. Now you need to collect the second belt and go to the opposite side of the cube.
4. We collect the cross on this side in the same way as at the very beginning.
5. We complete the entire side.
6. Now we put in order the corners of the cube - we make it so that the colors on them correspond to the colors of the sides to which they are turned.
7. It remains only to correctly rotate the parts that have only 2 sides. The cube is assembled.

Now you can learn how to solve one of the most popular puzzles in the world. The universal Rubik's cube scheme will help you with this.

For a long time, Rubik could not figure out how to approach the implementation of this idea. Once, sitting on the banks of the Danube, he watched melancholy as the waves rolled over the pebbles, building out of it three-dimensional geometric shapes and grinding the sharp edges of the stones. And… eureka! Returning home, Rubik begins feverishly to think over the project. Discarding cardboard and wood, he opts for plastic. So that the elements in the form of small cubes could rotate along three axes, the inventor used an internal cylindrical mechanism. After going through many options, Rubik chose a simple six-color scheme for the appearance of the puzzle. The students were delighted with the cube, and then Ernö realized that by creating a textbook, he had created a toy that could become popular all over the world.

Conquest of the planet

At first, toy manufacturers were cool about the puzzle: they say, manufacturing is not cost-effective, and only a person with high intelligence can solve the problem. The grandiosity of the idea was understood only at the small enterprise "Polytechnic". Despite the fact that it was necessary to seriously invest in the technical re-equipment of the plant, two years later the first batch came off the assembly lines of the enterprise. This is how the puzzle began to slowly but surely gain popularity - so far only at home.

Fortunately, Tibor Lakzi, a Hungarian by nationality traveling salesman from one of the German firms, arrived in Budapest. Having watched with amazement how the capital's residents, young and old, twist the cube in their hands, he went into the store and also bought himself a multi-colored toy. Graduated from the University of Vienna, an economist by profession, Tibor believed that he would cope with the task in a matter of minutes ... He came to himself only in the morning, stating with surprise that he had collected only one facet. And after that, he firmly decided to start promoting the cube on the international market. He brought the owner of Seven Towns Ltd, Tom Kremer, to Budapest. He, too, was shocked by the number of colored cubes in the hands of the townspeople and took up the large-scale production of the toy. So, in 1980, the Rubik's cube began its triumphant march across the planet. Toy manufacturers did not expect such a stir - almost all countries of the world have fans of this game.

Divine Algorithm

In 1982, the first world championship among fans of speedcubing took place in Budapest - speedcubing. Then the Vietnamese schoolboy became the winner, having collected the cube in 23 seconds. The following year, Englishman Pergle improved the result by another five seconds. But the absolute record was set in 2007 by Shotaro Makisumi, who solved the problem in just 15 seconds. Today the unofficial speedcubing record is less than 5 seconds!

Unfortunately, there is also a negative component to this entertainment. With the advent of the puzzle, the number of patients in psychiatric clinics first increased, then traumatologists sounded the alarm - patients who applied to them complained of pain in their wrists. As a result, a new term has even appeared in medicine - "Rubik's syndrome". And, of course, a multi-colored toy takes a lot of time - you can even get hooked on it, like playing computer games ... as a result, some gamers suffer from their personal and professional lives.

The history of the search for the "God algorithm" for the Rubik's cube began in 1980 - since then mathematicians, programmers and just amateurs began to purposefully search for an algorithm that would allow solving the Rubik's cube in the minimum number of moves. In July 2010, Palo Alto programmer Thomas Rokiki, mathematics teacher from Darmstadt Herbert Kotsemba, mathematician from the University of Kent Morley Davidson and engineer at Google Inc. John Detridge proved that each Rubik's cube configuration can be solved in no more than 20 moves (with any turn of the face counting as one move). The amount of computation was about 35 years of CPU time donated by Google.

How to solve a rubik's cube?

1. On one of the cubic faces (usually on the top), you need to collect a cross, consisting of 5 fragments. To build a cross, any color is selected, one fragment of which is located in the middle of the face, and then a cross is built around it. The method of assembling the cross is different in each case (there is no general method). For faster collection of the cube, it is necessary to fold the correct cross, when the branches of the cross have a continuation on the next faces, consisting of two identical cube fragments.

2-3. The second and third actions are similar in that they focus on building the cube layer by layer. In the second action, you need to collect the side on which there is already a cross, completely, that is, the entire side must be of the same color. Moreover, you need to make sure that the fragments of the cube on the sides form a belt located near the already assembled edge. The third action is a continuation of the second, where you need to collect the second belt.

4-5. The fourth and fifth actions are mirror images of the first and second actions. At the fourth stage, it is necessary to collect the cross on the side opposite to the one on which the cross was assembled in the first act, and in the fifth act, this side must be completely assembled.

6-7. In the sixth step, you need to arrange the corners of the cube in the correct order so that all three of their sides match the color of the faces. It remains only to place the side parts of the cube (which have two edges) in place so that they correspond to the edges of the cube - now the puzzle is completely assembled!