How long does it take to complete the Rubik's Cube? Good and optimal solutions. External search history

The Rubik's Cube is the most famous puzzle in the world, and also one of the most useful. It develops logic, spatial thinking and even the muscles of the child's arms! Rambler / Family learned how to assemble a classic toy quickly and with a minimum number of moves. Tip: read the instructions with a cube in your hands!

Cherished moves

Scientists have been looking for the "number of God" for many years - the minimum number of actions that would be enough to solve the Rubik's cube. It is assumed that God alone knows all the right moves, so he can easily solve any puzzle, even if it has 43 quintillion - billion billion - original options.

Of course, there are algorithms for assembling a colored cube, but more than thirty years have passed since the creation of the toy in 1975, which took computer geniuses to "teach" a supercomputer to check all possible options and find the simplest solution. As a result, Daniel Kunkle and Zhene Kuperman created an algorithm for checking every 15 thousandth initial position of the cube.

The computer worked for 63 hours in a row and calculated that even the most complex variants of the initial position can be assembled in 29 moves, and most of the variants in 24-26 moves. Mathematicians report that the ideal way to fold a Rubik's cube would take about 20 moves.

We start assembly from the cross

So let's start with the notation. If you put the cube in front of you, then the face looking up will be indicated by the letter B, lying on the table - H, looking to the left - L, and to the right - P.

In this case, there will be a side that looks directly at you, the front - F, and the one that you do not see, the end - T. It is believed that a normal turn is an offset of 90 ° clockwise. Counterclockwise is indicated by a prime - Ф ', and two turns - by the number 2 - Ф2.

Before starting the assembly, place the cube so that there is a white square on the top side of it in the center. Now we are going to collect the cross. You can probably do this yourself, for this you need to find all the white squares located in the middle of the line and unfold them so that they fall into place on the upper edge, simply turning them one or two turns up.

But if it suddenly turns out that, when turning, the white square will fall into the place of the same white one, then it is enough to make one turn of the upper face clockwise or counterclockwise and again try to collect the cross.

The next step is to connect the center squares on the sides with the squares of the same color in the neighborhood. To start, rotate the top face until two of the four are aligned. Then turn the whole cube so that there is still a white cross on top, and the side in which the color of the central and the cube above it does not match is looking at you.

Make two turns of the front edge - the white fragment will be at the bottom. With it, there is a color square, which must be placed close to the central one of the same color. For example, if there is a white-red square at the bottom, then we need to rotate the bottom face until the red square is under the red center.

After that, we again make two turns with the same side to return the white to its place - up. In this case, the other white will again be at the bottom, but we will do the same with it - we will set its neighbor color under the corresponding central cube and return the white to the top. As a result, there will again be a white cross at the top, and blocks of two cubes of the same color under its sides.

Displaying the first face

Now we collect the top white face completely. First, in the bottom layer, look for a white corner cube and remember its other two colors. We twist the bottom side until this cube is between the centers of the corresponding two colors.

For example, you found a white-red-blue cube. Rotate the bottom face until the corner cube is at the junction of the sides with the red and blue centers, and it does not matter how it is rotated. If the white square looks directly at you on the frontal side, then perform the operations: F, N, F '. If to the right, then: P ', N', P. And if down, then: F, H2, F ', N', F, N, F '.

This cycle must be repeated four times so that all the white cubes take their places. If it turns out that the white cube is in the upper line, but turned to the side, then a universal method can be used that “lowers” \u200b\u200bor “lifts” the fragments.

Rotate one of the sides one turn clockwise or counterclockwise, make one turn of the bottom edge, then return the white cubes up, turning the same side in the opposite direction and another turn back with the bottom edge.

Top two layers

Now it's time to put together the top two layers. To do this, in the lower part we find the middle elements of a non-yellow color, which have no place here. Then we see if the color coincides with the centers on the left or right.

It may be necessary to rotate the bottom layer several times to achieve the desired position. If the color of the middle cube on the front side coincides with the central one on the left, then we perform the sequence: F ', N', F, N, L, N, L '. And if on the right, as in the picture, then: F, N, F ', N', P ', N', P. These actions must be repeated until all the top two lines are collected.

Turning the work over

At the next stage, we collect the yellow cross, as it was with the white at the very beginning. Therefore, we will turn the cube, now our working area will be at the top. Don't worry if after the operation the integrity of the white layer below is broken, we will restore it later! There are four possible initial options.

Firstly, if the yellow squares already form a straight line from left to right, then to assemble the cross, you need to make a combination: T, L, V, L ', B', T '. If there is a yellow check mark or the letter "G" at the top, then unfold the cube so that it looks to the left and back, and complete the combination: T, B, L, B ', L', T '. If there is not a single yellow square on top, except for the central one, you need to try the first or second methods until they appear. As soon as the cross is assembled, the task is completed!

Now we will collect the yellow side completely. To do this, unfold the cube so that the blue side looks at you and is frontal (F). Find a corner with a yellow color that does not look up, and rotate the top face to position it so that it is in the upper right corner.

If it is in the frontal position, as in the picture, then make a combination: F, N, F ", N", F, N, F ", N". When the yellow color is located to the right, you need to perform a combination: N, F, N ", F", N, F, N ", F". Now, keeping the front blue piece of the puzzle, rotate the top face to find the next unfinished corner. Repeat the process from start to finish until the entire top side is yellow.

Done!

Roll the top side in any direction until one of the side pieces is the same color as the center cube below it. Please note that if all four sides coincided immediately, at the initial stage, then you do not need to do anything further.

And if suddenly there are no such, then try the combination: P2, N ", P", L, F2, L ", P, B2, N, P2 and again twist the upper face. Now the entire Rubik's cube needs to be rotated so that on the left the face of the upper left corner coincided in color with the center, and on the frontal one - the middle upper cube - with the right center. Now make a combination: P2, N ", P", L, F2, L ", P, B2, N, P2 and get almost completed cube with irregular angles.

Twist the top side to see if it has a corner in the absolutely correct position? The cube must be placed so that this corner looks to the right. Repeat the combination L2, T2, L ", F", L, T2, L ", F, L" once or twice until the whole cube is completely solved.

Collecting patterns

If you are already so good at solving the Rubik's Cube that this activity seems boring, we advise you to practice drawing intricate patterns. They are based on correctly assembled edge colors, which deliberately need to be confused so that the same pattern is obtained on each side.

Moreover, their designations are the same. If you put the cube straight in front of you, then H is the bottom edge, B is the top, R is right, L is left, F is front, T is rear or back. You can rotate each of them clockwise or counterclockwise, then on the assembly diagram it will be indicated with a stroke, B '. If you need to rotate a face 180 °, that is, make two turns, then it is indicated by the superscript number 2 - B2. For convenience, it is best to start assembling any pattern by placing the cube with the white side up, blue - to the left and red - to the right.

Checkers

It couldn't be easier! This pattern will be obtained when two colors are staggered on each of the faces. To make it from an already assembled cube, perform the following sequence of face rotations: P2, L2, B2, H2, F2, T2. The patterns may seem complicated, but if you have a cube in your hands and follow the instructions exactly, then the pattern will certainly work!

And to reassemble the original puzzle, do all the operations in reverse order: T2, F2, H2, B2, L2, P2.

Windows

This pattern - one colored cube enclosed "in a window" of a different color - can be done in just eight steps, and you do not have to unfold the cube - it will be in the same position all the time. To make a window appear on each of the faces, sequentially perform the combination: B, N ', T, F', P, L ', V, N'.

And if you want to leave the two sides monochromatic and collect only four "windows", then make a combination: F2, T2, V, N ', L2, P2, V, N'.

Herringbone

This pattern is a herringbone or check marks nested inside one another, on each of the faces of the Rubik's cube. From the outside, it looks like a volumetric illusion and will surely please children. To fold the herringbone, follow the combination: F, N, F ', H2, L', T ', V, L, N, P, V, L', F ', V, L, B2.

Stripes

This is a difficult figure, it will require attentiveness and strict adherence to the sequence of actions. It is better not to twist the toy in your hands, so as not to get confused about what has already been turned and what has not yet been turned. We begin to add the combination: F, V, F, P, L2, T, N ', P, H2, L, N', T, P2, L, F, V, F. sides - multi-colored stripes.

Letters "T"

Gather on each of the faces the letters "T" of different colors: F2, P2, B2, F ', T, H2, L2, F, T.

Cube in a cube

If we look at one of the faces of the cube during such an assembly, we will see a small solid 2x2 cube and a strip of contrasting color framing it. To make this pattern, follow the combination: F, L, F, V ', P, V, F2, L2, V', L ', T, N', T ', L2, V.

Enjoy your solutions to the most famous puzzle in the world!

Images from WikiHow.com were used.

Correct name " Rubik's Cube». Rubik Is a Hungarian sculptor and inventor of the popular puzzle game. The Rubik's cube was invented back in 1974, and since then its assembly has occupied the thoughts of all mankind.

This puzzle is a plastic cube made up of 26 cubes that can rotate around the three inner axes of the cube. Each side is painted in a specific color and consists of 9 squares.

By turning the sides of the Rubik's cube, you can change the location 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 only solve some of the cube by themselves.For the complete collection of the puzzle, there are certain rotations, algorithms calculated using formulas.

We invite you to familiarize yourself with one of the algorithms for collecting the Rubik's cube 3x3

The easiest way to solve the rubik's cube - remember with what rotations it was disassembled and repeat them in reverse order. However, this is only possible if the cube was originally assembled. If the cube is disassembled, it is difficult to rebuild it. Intuition, spatial thinking, or randomness can help. But it's better to remember the algorithm for collecting the cube. There are several of them.

The traditional name for the algorithm that collects the Rubik's cube in the least number of moves is “God's algorithm”. The maximum number of moves in this algorithm is “God's number”. In July 2010, it was proved that such a number is 20. That is, with known algorithms, you need to make at least 20 moves to solve the Rubik's cube.

Collecting the cube for speed is a whole sport called speedcubing. ) ... There are competitions between speedcubers, and even a blindfold competition!

You can also watch video how to solve rubik's cube step by step for beginners:

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 35 (thirty-five) years of computer time donated by Google to do this.

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, differing 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. In the end, 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 the 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 fits easily 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 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 coverage” 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, 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.

Most difficult 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 they are quite possible to meet 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. On 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 God algorithm.

If you have long wanted to learn how to solve the Rubik's cube, then this post is for you. Let's end this task once and for all and have a little party for ourselves. Having done this, you can safely put a plus sign in the list of your achievements and then trump your friends 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 size 3x3x3.

Party designations:

F - frontal (front)
Z - back
L - left
P - right
IN - upper
H - bottom

Now let's deal with turn nameswhich 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 (eg, " F"Means that we turn the front side by a quarter of a turn clockwise, i.e. one shift).

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.

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 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 you must first lift it up, rotate it as we need it and put it in its rightful place. We look at the picture and apply the techniques given there. Each turn corresponds to the formula, which we dealt with a little above.

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 do not 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.

On the top facet, a cross of the desired color turned out, but as you could understand from the previous paragraph, the side cubes of the upper facet 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.

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 the central squares of those faces at the junction of which it is located.

Here 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 got 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 has kept and does not allow millions of people to sleep.

Naturally, you didn’t memorize all the steps and formulas of turns and movement at once. Here you just need to practice and fill your hand.

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

Do you know which toy has earned the title of the most sold in the world? No, not a pretty Barbie or even a Lego. The absolute leader in sales is considered to be a much more intelligent thing - the Rubik's cube. This year the colorful puzzle of Hungarian origin celebrates its forty-first birthday. For four decades, millions have tried to conquer it. And today we will show 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 fans opened. Since then, thousands of puzzle connoisseurs, including a dizzying number of mathematicians, engineers and programmers, have joined forces to find "God's algorithm": a way to collect a cube in the minimum number of moves. In July 2010, Palo Alto programmer Thomas Rokicky, 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. AND 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 edge.

Now rotate the top face.

Repeat these two combinations one after the other. How many times? Until you collect it!

Video demo this method has already collected over 14 million views. Of course, there were a lot of dissatisfied people in the comments who couldn't solve the puzzle. Maybe they just didn't repeat the combination long enough?

Have you noticed how rapidly the edges of the cube “fly” in the hands of professionals? It turns out that there is a little trick here. To speed up the process, you need to use ... a lubricant! Liquid silicone will do.

Rotate the edges of the cube to the position shown in the photo.