home > Solitaire Solitaire > How to assemble a 3x3 mirror cube. The impossible is possible, or how to solve the basic models of a Rubik's cube. What are the formulas for the Rubik's cube

How to assemble a 3x3 mirror cube. The impossible is possible, or how to solve the basic models of a Rubik's cube. What are the formulas for the Rubik's cube

One of the most popular puzzles is still the well-known Rubik's cube. For those who consider it banal and outdated, experts never tire of offering various modifications to the familiar design. Today its mirror counterpart is gaining popularity. A real hit among lovers of minimalism. But how to solve a mirror Rubik's cube? This article will help you figure this out.

Origin

It's always difficult to imagine something second. The following modification of the Rubik's cube, however, has become very popular.

Japanese Hidetoshi Takei presented it to the public at the IPP26 event in 2006, held in the American city of Boston. The novelty immediately attracted the attention and interest of puzzle fans. Now many people are wondering how to solve a mirror Rubik's cube.

Appearance

It is called mirror only by analogy with its appearance. The material for the product is usually plastic. All its edges are painted silver or gold with a mirror finish. Nothing superfluous, flashy, anything that is designed to attract the consumer. Only true pleasure from assembling the cube.

The real beauty of the puzzle is hidden inside. As soon as the assembler rotates one of the edges, the product will take on an unusual appearance. It becomes like a sculpture by a modern author.

But how to solve a mirror Rubik's cube if it does not differ in color, and its shape has changed beyond recognition before our eyes? It is necessary to ensure that on each face there are parallelepipeds of large, medium and small sizes.

This puzzle will appeal to both children and adults. Developing your mind in such an elegant way is not only interesting, but also enjoyable.

Design and purpose

The mirror Rubik's cube is made on the basis of its predecessor with the parameters 3x3x3. It consists of 26 elements, which can be divided into three types based on their sizes: small, medium and large.

Once you start rotating the faces, you may assume that it is impossible to solve the puzzle, but to understand how to solve a mirror Rubik's cube, it is enough to apply the same algorithms as when working with a traditional model.

First stage

You should start small - collect a cross on the bottom side. To do this, find an edge with a parallelepiped of the largest size. The face on which it is located is rotated to the right so that it moves down. Then it is moved counterclockwise, and the desired rectangle should be in the central part. Next, rotate the top face twice - the edge is now located on top.

Sometimes the scheme is a little different. How to solve a mirror Rubik's cube if one of the necessary elements is on the opposite face? Then the front part is moved in a clockwise direction, the upper part is moved counterclockwise, then the right edge is moved in the opposite direction.

Collect corners

To arrange the corners, you need to rotate the right and bottom parts - counterclockwise, and repeat these two steps again.

Middle

The puzzle must be held so that the unfinished face is located on top. Find a large rectangle on it and move it to the corner. The combination is as follows: turn the top and then the right sides clockwise, the top - in the opposite direction, the right - in the same way, the top and front - counter-clockwise, the top - in the clockwise direction, the front side - in the same way.

Next stage

How to solve a 3x3 mirror Rubik's cube? It’s also worth twisting the puzzle: Rotate the front face clockwise, repeat this movement with the top and right sides, then the right side reverse side, top - similar, front - against.

Rib collection

The cube itself must be rotated so that two of the existing four edges are equal in size. The best option, if they are squares. They should form an angle. Two unfinished edges are assembled using the following combination: the right side - in the direction of movement clockwise, the top - according to the same principle, the right again - in the opposite direction, the top - clockwise, the right side - similarly, the top - twice clockwise, the right - in the opposite side, the top - clockwise.

Assemble the corner

Should be found corner element, which is equal to the size of the part on the middle edge, but is rotated incorrectly. You need to keep this corner close to you. The remaining corner parts are assembled as follows: the top side - clockwise, the right side - in the same way, the top - counterclockwise, the left side - counterclockwise, the top - clockwise, the right side - counterclockwise, the top - in the same way, the left side - in the opposite direction.

Completion

Now let's look at how to solve the last layer of the mirror Rubik's cube. To do this, you need to work with the corner elements. Among them, you should find the one that is not yet positioned correctly. It should be facing you and to the left. Then you should do the following algorithm: the right part - counterclockwise, the bottom - in the same way, the right - clockwise, the bottom - in the same way.

The combination should be done so many times that the angle is at Right place. Then the top side is rotated counterclockwise. The next corner appears and the algorithm repeats.

Such a puzzle can become a child’s favorite pastime and distract him from newfangled gadgets. It can also be solved big company: collectively or competing against time. It's worth testing yourself with a Rubik's cube!

how to assemble mirror rubik's cube formula

Expert F2L (Expert First Two Layers) is, in ordinary language, the same F2L, but any pair is viewed from different angles and with different twists of the top layer. Thus, there are even more different situations than 41 (as in ordinary F2L). The advantage is that using the methods from Expert F2L, you reduce the number of interceptions of the cube in your hands, thereby reducing the assembly time, although in many situations it is considered that it is more profitable to intercept and perform the usual method, there is a huge amount of controversy about this among speedcubers.

Mirror Blocks. Mirror cube. 1st, 2nd and 3rd stages

OPF2L (Orientation-Preserving F2L) is one of the methods for forcing OLL Skip, which is the last F2L pair, but with all the other targeted edges and corners on the top layer, which greatly simplifies the determination. The methods presented below allow you to solve this very the last pair, while maintaining the desired orientation of the parts of the top layer in order to preserve OLL Skip, leaving OPF2L (OPLS) includes 29 situations (14 F2L situations on the right, 14 mirrored ones on the left, 1 situation without a mirror).

VHF2L (Vandenbergh-Harris First 2 Layers) consists of several situations ZBF2L (Zborowski-Bruchem First 2 Layers). The goal of this technique is to orient all the edges of the last layer at once, solving the last pair using one method. The complete ZBF2L method (ZBLS) consists of 302 situations, including mirror cases. VHF2L is the first 32 situations, consisting of a “three-way” and a ready “pair”, both on the right side and mirrored to the left - a total of 32 cases.

WV (Winter Variation) is an OLL Skip forcing technique that solves the last pair immediately with the orientation of the corner parts of the top layer. With all this, all the edges of the top layer must be correctly aimed. WV is, in fact, part of the RLS.

SV (Summer Variation), as you can guess from the name, is some kind of opposition to Winter Variation, but the essence is the same. We have the last pair - a three-move, with all this, all the edges are aimed in such a way that if we solve it in the standard usual way - R U R", we will get a "cross OLL". But if we take into account the orientation of the edges and apply the appropriate method from this base , then skipping OLL, we will immediately go to PLL.

COLL (Corners and Orientation of the Last Layer is a technique for a 3x3 cube that solves (orients and permutes) the corners of the last layer for the "cross" OLLs, leaving only the permutation of the edges as the final step in assembling the cube. In fact, COLL is part of OLLCP (Orientation of Last Layer and Corner Permutation) and contains 7 cases of OLL, where all 4 edge elements top layer targeted. COLL has 40 situations - 6 situations for any of the 7 OLLs, not counting “double eyes”, where there are 4 of them.

OH COLL (Corners and Orientation of the Last Layer) – COLL methods for one hand. Speedcubing techniques for advanced techniques for solving a Rubik's cube with one hand (OH).

OLC (Orientation of the Last Corner) is a technique for solving the last pair along with OLL in one method in the case where we have the corner element of the last pair, located upward in snow-white color, while all the edge elements are aimed at the top cap.

OLE (Orientation of the Last Edge) is another technique for forcing OLL Skip", provided that we have the last pair with an angle (correctly aimed at its own place in its own slot) and an edge (in the top layer), and directional edges of the top layer.

Abstracts

The mirror Rubik's cube is a variation of the classic cube. It contains all the parts of the same color, but different sizes. When rotated, the puzzle takes on a chaotic appearance and loses its cubic shape, making the assembly process more difficult. But if you already know how to solve a 3x3 cube, then just focus not on the colors, but on the shape.

This cube, like the others, consists of faces: top, left, right, front and bottom.
Step 1

Lower cross

To begin with, we assemble a cross on the top edge. To do this, we look for the edge with the largest rectangle. Rotate the face on which the element is located to the right so that the edge is at the bottom.

There is an option when one of the parts is on the opposite edge. Then you need to turn the front part clockwise, the top counterclockwise, and the right side clockwise.

The remaining ribs are assembled in the same way.
Step 2

Corners with details

We put the corners with the details in place. At each corner there should be a rectangle from smallest to largest.

We make this combination:

bottom - counterclockwise;
bottom - clockwise.

Step 3

Middle layer

We put the ribs of the middle layer in their places.

The cube should be turned over so that the unassembled side is on top. The outermost parts that protrude beyond the boundaries of the cube must be kept on top until the end of the assembly.

On the top edge you need to find the largest rectangle and place it on the corner. There may be two options:

The edge should go down and to the right. This can be done using this combination:

The upper part is clockwise;
right side - clockwise;
top - counterclockwise;
front part - counterclockwise;
top - clockwise;
the front part is clockwise.

In the second case, take the cube with the desired part with the center towards you. The edge should go down and to the left in this way:

Top - counterclockwise;
top - clockwise;
the left side is clockwise;
top - clockwise;
the front part is clockwise;
top - counterclockwise;
the front edge is counterclockwise.

Sometimes the required edge is not on top, but in the middle layer. It must be removed from there using any upper edge, using the combination for the first case.
Step 4

Upper cross

At the top, find the parts that are assembled correctly. They should form a cross. It may turn out that there is a central piece on top without a line, corner or cross. If there is a three-piece corner, it is important that it faces to your left. If it is a line, it needs to go from right to left.

To make the top cross, do the following combination:

The front part is clockwise;
top - clockwise;
right side - counterclockwise;
top - counterclockwise;
the front part is counterclockwise.

Step 5

Rib collection

Turn the top so that two of the four ribs are the same size (preferably squares) and are at an angle to each other. If you can’t do this, do the following combination from any position:

the upper part is clockwise;
right side - counterclockwise;
top - clockwise;
the right side is clockwise;
the upper part - twice clockwise;
the right side is counterclockwise.

Take the cube so that the right edges are facing away from you and to the right. Arrange the two remaining edges as follows:

The right side is behind the clock hand;
top - clockwise;
right side - counterclockwise;
top - clockwise;
the right side is clockwise;
top edge - twice clockwise;
right side - counterclockwise;
the upper part is clockwise.

Step 6

Assembling corners

Find an element on the corner that is the same size as the part on the middle layer, but is rotated incorrectly. Take the cube with this angle towards you. Place the remaining corners in their places with the following combination:

The top edge is clockwise;
the right side is clockwise;
top - counterclockwise;
left side - counterclockwise;
top - clockwise;
right side - counterclockwise;
top - counterclockwise;
the left side is counterclockwise.

The combination should be done several times.
Step 7

Last layer

If some corners are turned correctly, select the one that still needs to be turned. It should be facing towards you and to the left. Do the combination 2-5 times:

The right side is counterclockwise;
bottom - counterclockwise;
the right side is clockwise;
bottom - clockwise.

The combination is done several times until the first corner is correct. Then turn the top edge counterclockwise. There will be another corner in front of you that needs to be turned around. Do the combination again. And so on with all angles. The lower parts may get tangled, but they will fall into place as you go.

The main thing in this step is not to change the position of the cube.

Hi all!

Today our article is dedicated to all puzzle lovers. Solving problems, crosswords, puzzles, riddles, etc. has always attracted people, young and old. And this is not only a fun pastime, but also good for the mind and the development of logical thinking.

Puzzles can be either drawn in some publication or made in the form of objects, often toys. One of these is the Rubik's Cube, famous in the 20th century.

There are probably still fans of this puzzle. Or maybe someone, after reading this article, will want to get acquainted with this almost ancient puzzle toy.

The Rubik's cube (sometimes erroneously called the Rubik's cube; originally known as the "magic cube", Hungarian bűvös kocka) is a mechanical puzzle invented in 1974 (and patented in 1975) by the Hungarian sculptor and architecture teacher Ernő Rubik. From Wikipedia.

In the mid-70s of the last century, the Hungarian teacher Erne Rubik, in order to somehow help his students learn some mathematical features and understand three-dimensional objects more clearly, made several wooden cubes and painted them in six colors.

Then it turned out that putting them together into a whole cube with sides of the same color was a rather difficult task. Erne Rubik struggled for a month until he achieved the result. And so, on January 30, 1975, he received a patent for his invention called the “Magic Cube.”

However, this name was preserved only in German, Portuguese, Chinese and, naturally, Hungarian. In all other countries, including ours, it is called the Rubik's Cube.

At one time this puzzle was a bestseller. It was sold all over the world in the 80-90s. only, more than 350 million pieces

What is a Rubik's Cube

What is this puzzle? Externally it is a plastic cube. Now it comes in various sizes, with 4x4x4 considered popular. Initially it was made in the 3x3x3 format. This cube (3x3x3) looks like 26 small cubes with 54 colored faces that make up one big cube.

The faces of the cube rotate around its three internal axes. By rotating the edges, the colored squares are rearranged in many different ways. The task is to collect the colors of all faces equally.

There are a lot of different combinations. For example, a 3x3x3 cube has the following number of combinations:

(8! × 38−1) × (12! × 212−1)/2 = 43,252,003,274,489,856,000.

As soon as this puzzle gained popularity, mathematicians all over the world, and not only, set the goal of finding the number of combinations that would be the smallest when assembling it.

In 2010, several mathematicians from different parts of the world proved that each configuration of this puzzle can be solved in no more than 20 moves. Any rotation of a face is considered a move.

Fans of the cube didn’t just solve it, but began to organize competitions in how quickly they could solve the puzzle. Such people began to be called speedcubers. The result is not calculated based on a single assembly, but as the average time of five attempts.

By the way, along with popularity, as it happens, opponents also appeared who proved (even with examples) that solving a cube, especially at speed, entails dislocations of the hands.

But, be that as it may, the cube not only did not turn away, but attracted more and more people. And competitions took place both in a separate city, and in the country, and internationally. For example, at the European Championships in 2012, a participant from Russia won. His average build time was 8.89 seconds.

The cube became so popular that other modifications of its shape began to appear. For example, a snake, a pyramid, various tetrahedrons, etc.

How to assemble a 3x3 cube, diagram with pictures for beginners

So. Let's 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 it is necessary to first rotate the façade edge counterclockwise by 90°, then the right edge as well. Next, rotate the bottom edge twice - this is 180°. Then rotate the right edge 90° clockwise, and also rotate the front edge 90° clockwise.

In the diagrams this is indicated as follows:

So, let's begin the assembly steps.

At the first stage it will be necessary to assemble the cross of the first layer.

We lower the desired cube down, turning the corresponding side face (P, T, L) and bring it to the front face by turning H, H’ or H 2. We finish everything by turning the same side face back

In the diagram it looks like this:

At the second stage, we arrange the corner cubes of the first layer

Here we need to find the required corner cube, which has the colors of the faces F, B, L. Using a method similar to the first stage, we bring it to the left corner of the selected front face.

In the diagram, the dots show the place where you need to place the desired cube. For the remaining three corner cubes we repeat the same operation.

As a result, we get the following figure:

At the third stage we will assemble the second layer.

We find the required cube and initially bring it down to the front face. If it is located at the bottom, then we do this by rotating the bottom edge until it matches the color of the facade.

If it is located in the middle belt, then lower it down using formula a) or b). Next, match the color with the color of the front edge and do a) or b) again. As a result, we will already have two layers assembled.

Let's move on to the fourth stage. Here we will assemble the third layer and the cross.

What to do here. We move the side cubes of one face, which do not violate the already assembled order in the layers. Next, select another face and repeat the process.

This way we will put all four cubes in place. As a result, everything is in its place, but two, or even all four may be oriented incorrectly.

First of all, you need to see which cubes sitting in their places are oriented incorrectly. If there are none or one, then we rotate the top face so that the cubes on the adjacent faces fall into place.

Here we apply the following turns: fv+pv, pv+tv, tv+lv, lv+fv. Next, we orient the cube as in the figure and apply the formula written there.

Let's move on to the fifth stage. Here we unfold the side cubes of the third layer.

The cube that we will unfold should be located on the right side. It is marked with arrows in the figure. The dots there also mark all possible cases when the cubes may be oriented incorrectly (Figures a, b and c).

Figure a). Here you will need to rotate B' to bring the second cube to the right side. Next, finish with rotation B, which will return the top edge to its original position.

Figure b). Here we do the same as in case a), only we turn B 2 and finish in the same way at B 2

Figure c). We perform turn B three times after turning over each cube, after which we also finish with turn B.

We proceed to the sixth stage, placing the corner cubes of the third layer.

It should be simple here. We set the corners of the last face according to the following scheme:

First, a straight turn, with which we rearrange the three corner cubes clockwise. Then the reverse one, with which we rearrange the three cubes counterclockwise.

And finally, final stage, during which we orient the corner cubes.

At this stage, the sequence of turns PF'P'F is repeated many times.

The figure below also shows four options when the cubes may be incorrectly oriented. They are marked with dots.

Figure a) we first make a turn B and end with a turn B’,

Figure b) here we start with B 2 and end with it.

Figure c) turn B must be performed after we 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 different opposite sides: F 2, Z 2, N 2, F 2, Z 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',