Solve the Rubik's Cube 2x2 formula. The impossible is possible, or how to solve the basic models of the Rubik's cube. III epat. bottom layer
Good day! In this article I will tell you how to solve the Rubik's Cube. But not standard (3x3), but 2x2. To begin with, you can learn how to collect it, and then move on to more complex ones! So, let's begin:
Step 1. Let's make the top side white and the pairs of cells adjacent to it - solid
First, let me tell you about the formulas and notation that are used to solve Rubik's cubes:
- The right side is indicated by the letter R (right)
- Left - L (left)
- Top - U(up)
- Lower - D(down)
- Front - F(front)
- Back - B(back)
- clockwise - R (if we turn the right side)
- counterclockwise - R" (again, as an example - the right side)
- 180 degree turn or 2 turns - R2
Step 2. Turn over and collect the yellow side
As a result of the flip, we can get 7 different combinations of this cube. To solve all of them, we need to know only 2 formulas:
1. To collect right triangle. If we take the side of the hour dial, then we get the same color from 9 o'clock to 6. Formula: R U "L" U R "U" L.
2. To collect left triangle(from 6 to 3 hours). Formula: L" U R U" L U R".
Step 3. Assembling the Remaining Sides
To do this, we need to place the desired color in the upper right and these formulas:
- left triangle U" right triangle
- left triangle U2 right triangle
- left triangle U right triangle
If you did everything correctly, then it remains only with the missing sides to use the formula R "F R" B2 R F "R" B2 R2.
If everything is done correctly, then you will get something like this: 
- Right R (right).
- Left L (left).
- Upper U (up).
- Front F (front).
To collect the cube, you must first master the PIF-PAF combination, which consists of 4 movements:
- R- up;
- U- to the left;
- R- down;
- U- to the right.
Face rotations
Raise the right side (R) up.
Rotate the top face (U) to the left.
Lower the right side (R) down.
Rotate the top face (U) to the right.
If you follow the instructions and use the PIF-PAF algorithm 6 times in a row, then the cube will return to its original position.
Assembling the bottom layer
Now you can knead and start collecting the cube.
We will collect the white layer, placing it at the bottom of the cube. To do this, look for a green-orange-white square (it can be any other with a white square) and place it in white down.
To the right of the orange cube, you need to place the same orange-white cube white down. To do this, we are looking for the desired element by rotating the top layer and setting it on the right side.
In our case, the orange square looks straight ahead, and the white one looks to the right. After the necessary corner has taken its place, it must be lowered, for this we make a PIF-PAF combination until it falls into place.
In this case, it only took one bang-bang to get the orange and white cubes into position.
Bottom layer elements
We turn the cube and look for the same blue-white cube as in the left corner. To do this, rotate the top layer again and set the necessary element on the right side: the blue square looks to the right, the white one looks up. With the help of PIF-PAF (it was necessary to do the algorithm 3 times), we lower the cube to the desired position: two blue cubes are next to each other, and the white one goes down. It remains to put only one white square to collect the bottom layer.
Upper layer
Rotate the cube and look for the red-white corner by rotating the top layer. Red looks straight ahead, white looks right. We make the already familiar PIF-PAF (it turned out for 1 time) and all the cubes fell into place.
Top corners
We proceed to the second stage: we set the upper corners by rotating the top layer.
We examine the cube and check the corners. At least 2 must match. If this does not happen, choose the color of any lower cube (for example, red-green), look for the same in top layer, set it above the lower one, and check the coincidence of the corners. We repeat this manipulation until the 2 corners match.
In our case, red-green and red-blue matched.
The two corners blue-orange and green-orange are not above their pairs, so you need to swap them. To do this, we arrange the Rubik's Cube so that the corners that do not coincide with each other look to the right. In order to swap the corners, you need to make 1 PIF-PAF.
Arrangement of corners of the cube
When you have made 1 PIF-PAF, you need to perform a combination of F to the left, U to the right, F to the right. Let's consider in more detail.
- F (front layer) rotate to the left.
- U turn right.
- F rotate to the right.
In this way, we put all the corners in their places and now you can collect the next layer.
yellow layer
We proceed to the III stage of the assembly: we add the yellow layer. To do this, turn the cube with a white layer up and position the yellow squares at the bottom.
Rotate the cube so that the yellow square is in the lower right corner. In our case, it is turned to the right.
From this moment on, we do not turn the cube in different directions, but fix it and make PIF-PAF until the yellow square is at the bottom. We needed to turn the PIF-PAF combination 2 times for the yellow square to be in its place.
Hi all. Since there are already many varieties of Rubik's Cubes, and the simplest 2x2 cubes have become very popular, I decided to make instructions with photos and videos for assembling these small puzzles. If the result is already good, then the 2x2x2 cube can be dealt with without problems in 20-30 seconds.
For those who have already mastered the assembly of a 3x3 cube, it will not be difficult to solve a 2x2 cube, especially if you know a lot of formulas. Some of the formulas for solving a 3x3 cube are simply used when assembling a 2x2 Rubik's cube. I would break the whole assembly process into 3 stages. So, let's see how to solve the Rubik's Cube 2x2x2.
Before we move on to the assembly instructions, I suggest that you familiarize yourself with the assortment of high-quality cubes, because it will not work out quickly with a bad cube. Sale of cubes in Ukraine, the most low prices : Rubik's cubes 2x2 , .
More instructions for assembling puzzles on this site - http://magic-cubes.blogspot.com/.
Stage 1. Assembly of the first (lower) layer of the Rubik's Cube 2x2x2
We start assembling the 2x2 cube. I assemble the cube with the white side down and the entire instruction will be written exactly for the assembly with white down / yellow up. After you learn how to collect a cube like this, you can easily collect a cube from any color.
In order to collect half of the cube (with the white side at the base, as in the photo below), you need to put only 4 corner elements in their places (in a 2x2 Rubik's cube, all elements are corner =)). You can do all this without actually knowing the formulas, the only trick you have to learn is bang-bang. Assembly is mostly done intuitively.
Photo 1. Assembled first layer of the cube. White color must be at the bottom when assembled.
Step 1. We select an element with a white side, which will be the first in our base, the rest of the elements with white color will be placed next to it.
Step 2 We set correctly all 4 elements with white color that make up the lower half of the cube. We start installing the necessary elements that are in the upper half. If there are elements with white color on the second floor of the cube, they can be easily lowered down to the right place. Typical situations are described below.
Possible arrangements of elements with a white side in the upper part: white up, white to the side (see photo, video below).
What if the element is placed white to the side?
If the white edge of the element at the top of the cube is directed to the left (in the photo below, we will lower the white / green / red element diagonally down), first it needs to be placed to the left of its place where we plan to put it (rotating only the top layer) . It turns out that the element itself and its place will be placed diagonally. Then we perform the movements: RU'R' (look here how to read the formulas for the Rubik's cube). If the white edge looks to the right, then we place the cube to the right of its place in the bottom layer and make movements: L'UL.
Photo 3. The cube looks with the white side to the left. RU'R'
Photo 2. The cube looks with the white side to the right. L'UL
What to do if the cube is white up?
If the element in the top layer is placed white up, it must be placed (by rotating the top layer) directly over its placement and bang bang three times in a row. Bang-bang has the following formula: RUR'U", but for our situation we make them three in a row RUR'U" RUR'U" RUR'U' (thus the white / green / red element will go down while the white will look down , as we need).
Photo 4. The cube is placed with the white side up. RUR'U' RUR'U' RUR'U'
If a cube with a white face is in the lower layer, but not in its place
In such a situation, you just need to make one bang-bang and this cube will be in the top layer, after which we perform the actions as in the previous paragraphs.
Stage 2. Collecting the yellow side
By analogy with the assembly of the Rubik's cube 3x3, we collect the entire yellow side. If you know several assembly formulas from OLL, then it will be very easy for you, but if you have not collected a 3x3 cube, then it will be a little more difficult.
You can collect the entire yellow side if, after assembling the white side, we got only one yellow cube at the top, as in the photo below (this is an analogue of Rybka from the OLL assembly in 3x3).
Photo 5. To assemble the yellow layer, use L’U "LU'L" U2L (we hold the cube like ya photo, the location of the yellow cubes is important)
If you come across such an arrangement (yellow at the top right, yellow looks at you from the left, as in the photo), then feel free to follow this formula L’U "LU'L" U2L (if there is a mirror situation, then we do R U R’ U R U2′ R’)
and rejoice at the collected yellow side, the formula stands.
Other combinations when assembling the yellow side
If after assembling the first layer on the yellow side (at the top of the cube) something else fell out, it does not matter. All possible combinations in the photo below. Using the same formula, we can get the same one yellow cube at the top, and after repeating, the entire yellow side. In all of these locations (pictured below), the formula should be used R U R’ U R U2′ R’. The top layer of the cube should be unfolded exactly as shown in the photo! After completing the specified formula, a combination with one yellow at the top is sure to drop out. Next, your task is to rotate the top layer as in Photo 5 (yellow at the top should be on the right or left, yellow in front (looks at you) on the right or left) and run this formula again R U R’ U R U2′ R’ or L’U"LU'L"U2L.
Typical situations after solving the white side of the 2x2 cube:
Photo 6. Assembly of the yellow side (R U R’ U R U2′ R’)
Photo 7. Assembly of the yellow side (R U R’ U R U2′ R’)
Photo 8. Assembly of the yellow side (R U R’ U R U2′ R’)
Photo 9. Assembly of the yellow side (R U R’ U R U2′ R’)
Photo 10. Assembly of the yellow side (R U R’ U R U2′ R’)
Stage 3. Moving the cubes in the top layer
After you have collected the yellow side, we need to swap only 2 cubes. These two cubes stand either side by side or diagonally. I offer you 2 formulas that may be familiar to those who are already quite good at collecting 3x3x3.
- If the cubes are next to each other: R U2 R’ U’ R U2 L’ U R’ U’ L
- If the cubes are diagonal: F R U’ R’ U’ R U R’ F’ R U R’ U’ R’ F R F’
You need to perform the formulas from the position indicated in the photo.
This puzzle is a simplified version of the regular Rubik's Cube. It is called differently, for example, a pocket cube or a mini cube. The puzzle consists of 8 smaller cubes assembled into one large 2x2x2 cube. Each face can be rotated, thereby changing the position of 4 small cubes on the face. Each of the 6 faces of the puzzle has a different color and each small cube has 3 colors.
mini cube- this is the same Rubik's cube, only without the central parts. The lack of centers at the edges is a little confusing, since at first it is difficult to understand which edges are adjacent and which are opposite. 
The mini cube has more simple design than the Rubik's cube and has many guises. Some of them are shown in the pictures above. There are versions in the form of heads: the head of Mickey Mouse, the head of Darth Maul from Star Wars, head of Homer Simpson. There are also versions in the form of car models, balls, globes and even stars. Such puzzles change shape as they are assembled, sometimes very funny. Separately, it is worth noting the versions of the puzzle in the form of balls: Dreamball, K-8 ball, Octo. These puzzles have a unique internal mechanism, but are assembled in the same way as a regular cube.
Another similar puzzle is the Pyramorphix or tetrahedron or pyramid puzzle. This puzzle is the same cube, but the position of the four pieces doesn't matter. Because of this, it is a little easier to assemble than other versions. The description and solution of Pyramorphix and the similar Stern puzzle will be covered in a separate article.
- The pocket cube was patented by Erne Rubik on March 29, 1983.
- The Eastsheen 2x2x2 cube was patented by Chen Sen Lee on October 28, 1998, .
- The Mickey Mouse head puzzle was patented by Francisco Jos Paterman on May 22, 1996.
- The Darth Maul head puzzle was patented by Thomas Kremer on April 17, 2001, .
- The K-8 ball was patented by Saleh Khudari on May 11, 2000, .
Number of positions
Eight parts, with three positions, gives a maximum of 8! 3 8 positions. This limitation is not achievable because:
- The total number of turns of the cube is limited to three.
- The orientation of the puzzle in space is not important.
The introduced restrictions leave 7! 3 6 = 3.674.160 positions.
From any position, the puzzle can be solved in 11 moves (or 14 moves if you count half a 180-degree turn as two moves).
Terminology
Since solving the puzzle will require you to perform various manipulations with the cube, for clarity, simplification and familiarization, we will introduce a series of symbols to describe 10 basic movements. All images are clickable to enlarge.
Solution
Now that we are familiar with the terminology, we are ready to start building the Pocket Cube.
The decision will take place in three stages. First of all, we will collect the top layer. Then put the corners of the bottom layer in place. And finally, let's complete the puzzle.
I note that the presented solution and auxiliary pictures are based on the coloring of my cube. Therefore, if the colors of your cube differ from those presented in the solution, then you will have to adjust a bit.
So let's get started.
Upper layer
We will start by assembling the red side of the cube. Find the red-blue-green corner and rotate the puzzle so that the red edge of the corner is facing up as shown in the picture.
Comment: the gray color of edges or corners means that the actual color of these edges does not matter for the action being performed.
Congratulations, you have set the first corner of the cube =)!
One more note: we think this piece of the puzzle should be in the upper right corner of the front face of the pocket die. Further steps for assembling the top layer of the cube also use this assumption.
Second corner
Before we can set the second corner, we must turn the whole cube one turn to the left, so that the upper right corner of the front face is the wrong piece of the puzzle. Your cube should look like this: 
Now we can put the second part of the cube in place.
Leaving the first solved part in the upper left corner of the front face, rotate the bottom layer of the cube until we find the red-blue-yellow corner we need.
Comment: It may happen that the corner we need is located in the upper layer, and not in the lower one. In this case, you should go to the "Third corner" stage, and at the end return to this corner last.
When you find the right piece, keep rotating the bottom layer until the piece is in the bottom right corner of the front face, right below where it should be. As a result, the state of your cube should match one of the pictures below. Perform a combination of actions under the picture with which your cube matched. 
third corner
Before we can put the third corner in place, just like for the second corner, we must rotate the entire cube in our hands one face to the left so that the wrongly placed piece of the puzzle is in the upper right corner of the front face.
Rotate the bottom layer until you find the desired red-yellow-white corner.
Comment: It may happen that the desired part is in the top layer. In this case, you need to go to the "Fourth corner" stage and then return to this corner at the very end.
fourth corner
Before we can put the fourth corner in place, just like for the third corner, we must rotate the entire cube in our hands one face to the left so that the incorrectly placed piece of the puzzle is in the upper right corner of the front face.
Rotate the bottom layer until you find the desired red-white-green corner.
Comment: It may happen that the desired part is in the top layer. In this case, you need to go to the "Finishing the top layer" step.
Finishing the top layer.
At this point, all or almost all parts of the top layer are in place and correctly oriented. You can go back and try to replace the second or third corner.
If you are having trouble placing the pieces because they are in the top layer, in the right place, but its faces are not rotated correctly, then compare your cube with the pictures below and follow the appropriate sequence of actions:
bottom layer
At this stage, we will put the corners of the bottom layer in place. Do not pay attention to the fact that the edges of the corners may be incorrectly rotated. We will deploy them properly in the final assembly step.
Find two corners with green edges in the bottom layer. For now, it doesn't matter where the green edges are pointing.
If two corners with green faces are next to each other, then rotate the bottom layer of the cube so that it can be matched with the picture below. 
Comment: If the corners with green edges are not adjacent, that is, they are diagonally opposite each other, then go to the step " Diagonal Corners" for work with this option.
Comment: The set of green edges for the bottom corners in the figure only means that the green edges of the corners can be directed in any direction.
If the corners are in place, although their faces are not correctly located, then this stage is completed and we move on to the other two corners.
If the corners are adjacent, but are not in their place, then follow the following sequence of actions to swap them.
Diagonal case
If the corners with green edges are diagonal from each other, then rotate the bottom layer so that the lower left corner is in its correct place, and perform the following sequence. 
Two other corners
Now that we've set up the green corners correctly, let's move on to the remaining two. If they are already in place, then you are in luck and you can move on to the final stage of the solution. If not, then you must perform the following sequence of actions to swap them.
The final stage is setting the edges.
Rotate the entire cube to match one of the patterns below.
If, after completing the sequence, your cube is still not completed, find a suitable template again and repeat the sequence of actions again. In general, you will have to repeat this process no more than three times.
Comment: Since these pictures do not display the far or left side, I did not notice the presence of orange edges on them. Orange parts may or may not be present on invisible faces.
Congratulations. You have collected the cube! =)
The scheme for assembling a 2x2x2 Rubik's Cube (sometimes called a Mini Rubik's Cube) is simple enough so that in a maximum of 20 minutes after you open this instruction, your cube will take on its original form.
In descriptions of Rubik's cube assembly schemes, as a rule, special terminology is used, on the basis of which the sequences of turns of the sides of the cube are described.
The first thing you need to master is the notation of the planes (sides) of the cube. 
Hold the cube so that one of its sides is opposite your eyes. This side will be frontal F. The rest, respectively - the top IN, lower H, right P, left L, back T.
The sides of the cube are called so only because of their location, the color can be anything. If you turn the die over, the bottom side will become the top side, although the colors will change. So the bottom side always looks down and the top side always looks up.
Please note that having chosen the location of the sides at the very beginning of the combination, you must stick to it until the end!
There are only 2 types of turns: 90° clockwise and 90° counterclockwise. In the case of counterclockwise rotation, after the designation of the side to be rotated, the apostrophe symbol " " ". Sometimes the designation " ² ”, which means that the side needs to be rotated 2 times by 90 °, i.e. a total of 180 °.
Example: the Ф sign means that you need to rotate the front face clockwise, which will bring the cube to the form, as in the third figure.
And, on the contrary, the sign F" will mean turning the front face counterclockwise, which will return this cube to its normal position.
Step 1. First (bottom) layer
At this stage, you need to assemble the bottom layer so that the colors of all 4 cubes from the bottom are the same color, while the other two colors of each of the cubes correspond to the colors of the neighboring cubes. Assemble the first layer yourself, it's not difficult. After the bottom layer is assembled, you will get this cube:
Step 2. Placement of the cubes of the top layer
Now you need to put the cubes (elements) of the top layer in their places, but not necessarily matching the colors - this will be the last step. Now we need to make sure that the cubes stand in their places, but the colors may not match.
First you need to define the color of the top side (this is simple: the color of the top side will be the only color that did not appear in the bottom layer). Now rotate the top side until one of the top cubes is in the correct position, hitting the corner where all 3 colors of that element intersect. Recall that now we do not need the selected element to immediately stand so that all its colors match the colors of the adjacent sides of the Rubik's cube.
Now that one corner is fixed, you need to correctly position the elements in the remaining three. There are 2 combinations to help you do this. One combination swaps the diagonal cubes, the other swaps adjacent ones. Choose the combination you need and place all the corner cubes in the correct positions.
Step 3 Rotate the Top Layer Cubes
Combinations of this step need to be carried out only in pairs: first you rotate one corner (for example, clockwise), then the second, but in the opposite direction for the second combination (respectively, counterclockwise), or for three corners that need to be rotated in the same direction , but for one of these combinations - three times.
Don't be alarmed if the cube looks like it's tangled up again, just rotate the other corner in the opposite direction and the cube will return to its completed state. Between operations, simply rotate the top face until the corner that needs to be rotated is in the top right corner.
For three corners that need to rotate in the same direction, other combinations (5-10) can also be used. To do this, position the cube so that the correctly oriented corner is at the back left.
