Rubik's cube master enters! !

Before we begin, let's look at the basic structure of the Rubik's cube. The relative positions of the six central squares of the Rubik's Cube are fixed. You'll know this when you dismantle the Rubik's cube. I'm sure that when you start wriggling in the following way, it's easy to forget what color you started with, so it's messy. So be sure to set a direction you like at the beginning. Here I choose blue as the top, green as the bottom, red as the front, orange as the back, white as the left and yellow as the right. Of course, your sticker may be different from mine. There should be 5*3 stickers on six sides of the Rubik's Cube! =30 kinds of stickers, why? Because if you specify the blue face as the top face, then the bottom face should have five options, and the remaining four faces form a ring, except for rotational symmetry, there are three! This is a paste method, right:) I chose the following picture.

It will be slower to open the animation for the first time, and the animation behind it will open almost instantly.

Java applet about playing animation: Click the button above and a window will pop up. If your window only displays an X, or doesn't display it at all, you need to manually install the Java runtime environment: I recommend you to download it with Sina, and use tools such as Thunder and Express to speed it up, which is the most efficient; You can also download it from JAVA official website. The official website is a web page. Single-threaded download is usually slow, but it will automatically identify non-Windows operating systems such as Linux. Official website Java Runtime Environment (Simplified Chinese Version), either here (English Version) or here (Traditional Chinese Version).

If you want the source code of this java applet, you can go here and have a look. Thanks to Werner Randelshofer for his excellent work. This animation is very simple and convenient to use.

If you want to change the colors of six faces in all post-animation, you can set them here.

Please choose a color from here.

Then click on the small box below to assign colors.

Last/better/previous/last name

Left front and right back

under

finally

It seems that there are too many words prepared, and everyone is bored. Let's talk about how to play the Rubik's Cube first.

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Before we begin, I'd like to suggest a learning method. Just remember three points, 1. Look at pictures, animations and videos. I suggest watching the video first, and then watching the text tutorial. 2. Think more, explore for yourself, let yourself lead, and don't rely on tutorials. Think simple, don't complicate the problem, all the steps are simple. If in doubt, look at the text in the tutorial carefully. At this time, look at it with questions. The more detailed, the better. In addition, hundreds of thousands of people have successfully recovered according to this tutorial. There should be no mistakes in it. Please believe it. That's all, let's start challenging the Rubik's Cube:)

If you want to study with our Rubik's Cube video tutorial, you should read the introduction of the video tutorial first.

(Step 1) Make a cross on the first side to form the following appearance: (You can also watch the video explanation of step 1)

Note, be sure to look at the cross as shown above, and the edge and center of each side are the same color. There are many ways to do this step, so I suggest you play it freely. If it is really difficult, I provide a definite solution here, that is, replace the blue prism block in the middle layer with the bottom surface, then color the side surface and turn it up. Let me give you an example here. You should understand that for position B on the left, you only need the following three steps, Rubik's cube.

The animation will play automatically, or you can watch it step by step by using the and on the right side of the playback bar. The leftmost one returns to its original state.

F D R2 180

In the initial state, turn the blue-yellow block to the bottom, rotate the bottom and turn up the yellow side.

Did I make myself clear? The D position is exactly the same as the B position, that is, the blue prism block in the middle layer is replaced by the bottom surface, and then the side surface is colored and turned up. For the A and C positions, you can rotate the surface so that it becomes the B or D position. If the blue surface of a prism is already on the top or bottom surface, I believe everyone will have a solution. What you have to remember is that if you encounter difficulties, you can change the blue color to the bottom surface and rotate it at will.

Sometimes, you will encounter the situation shown in the left picture. When the blue-yellow block turns to the bottom, it affects the aligned red face. At this time, you need to restore the position of the red face to the previous step. See the figure below for specific operation.

Cube station)

F D F '

The initial state flips the blue-yellow block to the bottom, but

This will affect the rotation of the bottom surface of the good red surface and the recovery of the red surface of the good yellow surface.

R2 180

According to the above, you should be able to make a cross by repeating four sides.

Here, I suggest a clearer and faster method for beginners. After the blue edge becomes the bottom surface, there is no need to turn it up in a hurry. You can turn it into the left picture. Note that the four sides of the bottom surface can be in any order, which will reduce your difficulty. Here are two examples to broaden your mind.

Finally, turn them over one by one. For example:

Now I want to talk about marking. You may have noticed some strange letters in the last table. Their meaning is simple.

F = front, front, B = back, back, R = front, right.

L = left, left, U = top, top, D = bottom, bottom.

Take the marks in the above table as an example. F stands for clockwise rotation of 90, F' stands for counterclockwise rotation of 90, and R2 stands for right rotation180. It's that simple. You got it?

In addition, if your Rubik's cube is a Rubik's cube with numbers, or a Rubik's cube with figures and patterns, then your six-sided central block has orientation problems. In this step, you can refer to this page to align the side center block.

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(Step 2) Align the first side and add a T-shape to the four sides to form: (You can also watch the video explanation in Step 2)

To do this well, you only need to learn one trick. That blue character block, after turning around, has six positions.

For position a, only the following three steps are required. For positions C, D, E and F, please go to the back first and see how to become A or B. ..

Note that the color of the small corner we return must correspond well. For example, the small corners of blue, red and yellow here must go up to the red and yellow corners, and you can't make mistakes, otherwise the T word will not come out. Maybe some friends already think I look like the Tang Priest, but some friends do have this problem, so I'll talk about it in detail. A position conversion method is as follows: Rubik's cube

F D F '

In the initial state, this step is very clever, and at the same time, it achieves two purposes: one is to make the target corner position at the top level "meet" with the blue, red and yellow corner blocks at the bottom, and the other is to make the blue, red and yellow corner blocks ready for their proper positions. Turn the blue, red and Huang San corners to the target position. Turn back to the top floor.

For position b, it is exactly the same, that is, the last three steps are made into a mirror image of the diagonal line at the top, a square.

As shown on the left, we will encounter the mirror image of the top diagonal for countless times in the future, so please pay attention to the meaning of this mirror image.

The diagonal mirror image of F D F' above is R' D' R, please see,

The animation is set not to play automatically.

Play, please press the play key to start r'd 'r.

The graph of position B is a diagonal mirror image of position A, so his algorithm is that FDF looks at the mirror diagonally. The diagonal mirror image of f is R', which you should understand very well. Please refer to the picture of the mirror above. The mirror image of d is the mirror image of D' F' and r.

For positions C, D, E and F, you can turn them to position A or B by rotating the sides and bottom. Here are a few examples: (Don't learn these algorithms by rote, you can find them by yourself for a few laps.)

For f, for c, for d and e.

If you can't see the animation temporarily, you can click the algorithm below to see a simple diagram.

F D2 F ' D ' F ' D ' F ' D ' D ' R ' D ' D ' F ' F '

Repeat four corners and you will get it.

So we have laid the foundation, let's make it simple.

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(Step 3) Put the prism block on the second floor and make it look like it (you can also watch the video explanation in Step 3).

From the previous step to this step, you must have seen that in this step, we have to deal with four prism blocks in the middle layer: red, white, red, yellow, orange, white and orange. This time, you turn the Rubik's Cube upside down, with the blue side facing down and the green side facing up, and then see which of the four prismatic blocks is on the top (the green center). Pick any one and we'll start with it. Take red and white as an example. Usually, you will encounter two situations.

We want to insert the red and white color block at the top into the position indicated by the red arrow in the above picture. You should put the corner between red and white in the nearest position (right front), and then one or two situations are very easy to identify, and the rows of the same color are in front and right respectively.

For the first case, the following algorithm is used,

Hello, hello'

Hello, hello.

The whole algorithm is URU'R'+U'F'UF, is it regular? Let's see, it seems that the second half of U'F'UF is just a diagonal mirror image of the first half of URU'R', right? We see that the first four steps of URU'R' are used to combine the two small blocks we want in the left picture. The fifth picture marked with red in the above table shows the combined two color blocks, and the last four steps of U'F'UF are used to fill the two small blocks we have combined in the correct position. Rubik's Cube

So, if you meet,

What should I do? Maybe many friends see that our algorithm should be a diagonal mirror image of the above algorithm, because all we have to do is look at the diagonal mirror image, because the first half and the second half are diagonal mirror images of each other, so the algorithm is to turn the first half and the second half upside down and turn them into U'F'UF+URU'R', the Rubik's Cube.

Hello, hello.

Hello, hello'

In some cases, the prism you need is not at the top, but in the wrong position or direction on the second floor. What should I do? First of all, the prism block at the top you have to do will become top by itself. If they are still disobedient in the end, as shown in the left picture, we will use the above algorithm to get an irrelevant prism block in place, and the red and white prism block we want will naturally become the top, which is a bit troublesome, but we can only endure our elementary solution, and maybe it will inspire everyone to learn advanced solutions:)

Besides, you can also try this algorithm, F' U2 L' U L U2 F, which is similar to the above algorithm. Please note that the starting states are not the same.

And his diagonal mirror image: R U2 B U' B' U2 R'

Repeat the other three sides, and the third step is completed. We have learned two algorithms so far. Come on.

Mofang station

Step 4) Draw a cross on the new top of the Rubik's Cube (you can also watch the video explanation in Step 4).

Become:

Next, we will learn a new algorithm. The algorithm will switch the top level in the following four situations. After the four prism blocks on the top surface are rotated, only these four situations may occur.

1 2 3 4

Probability 1/8 probability 1/4 probability 1/2 probability 1/8

In this step, we treat all the character blocks as gray and only look at the prism blocks. For example, if you look at the left picture, it is the third situation above, and if you look at the right picture, it is the second situation above. (Reprinted from Rubik's Cube Station)

Before applying the algorithm, you should determine the direction of your Rubik's cube by referring to the green appearance at the top of the picture above. We just need to go through it, and we don't need the color on the side of the cross to match the two layers below. Please note that this algorithm will switch these four situations from left to right in turn, that is, if you encounter a "point" (that is, the first picture above), you must apply this algorithm three times (you must position yourself according to the above picture before each time), and if you encounter a "one", you must apply the algorithm twice, which makes you feel more and more like Tang Priest.

R' U' F' U

F R

In addition, you can also try it at the time of "centralized".

Fall fall

Through observation, we can see that this algorithm is the inverse of the above algorithm. He can make a good cross directly from the word "one"

If you want to speed up the crossing, you can also visit the second page of advanced gameplay. The method introduced in it is similar to this method, but the technique is smoother, which can effectively improve the speed of crossing, especially in the case of "minutes".

When learning an algorithm at first, it is always easy to make mistakes. It is impossible to remember clearly at first, so it is easy to screw up and often depressed. I suggest that you should find some hints on the pattern of this figure, especially some relatively "whole" figures. I usually remember that the biggest hint of an algorithm is the bottom blue color block, because they are the most complete graphics, how they are separated and reassembled, and then how they are reassembled. Imagine a process or a "story" so that the algorithm is easy to remember, including the following algorithm.

Another small idea: here is a problem. Why do you say that there are only four situations, so it won't happen?

The answer is no, if your Rubik's cube is really the above situation, then your Rubik's cube must be assembled incorrectly. If he assembles randomly, he has a probability of 1/2 misplacing the edge (corresponding to the following steps, he may also misplace the angle and put it in the wrong order). The solution is that you can flip an edge at will, and the edge you flip may not even have a green edge at the top, which means Rubik's cube. The specific principle, you can look at this page if you are interested.

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(5) rotate that four corners of the top surface of the Rubik's cube and color the top surface to form the Rubik's cube.

(You can also watch the video explanation in step 5. )

There are only eight possible situations in the four corners at the top of the Rubik's Cube. The first one is already aligned, and the other seven are as follows. Rubik's Cube

Probability 4/27 4/27 4/27 2/27 4/27

Want to know how the above probability is calculated, you can look at this page. The above seven numbers add up to 26/27, and the probability of 1/27 is the right one.

If your patterns are not in these eight categories, as shown in the following example, then your Rubik's cube must be assembled incorrectly. You need to remove a corner block, adjust the green direction, and then put it back. Correct orientation is one of the above eight situations. The following are just some examples. You may encounter 16 kinds of errors except rotation, but once adjusted, the wrong graphics will never appear again.

I'll tell you again why there are only eight cases. If you are in a hurry to see the algorithm, you can skip it first:)

First of all, we observe two cases: 1 2. In both cases, the three dislocated blocks are in the same position in the sense of rotation, right? This is one of their characteristics. Green has three directions at each corner. If we mark four corners, we might as well call it the case of 1 (from the upper right corner113), the case of 2 (2223), the 3 in brackets indicates that the green block is already on it, and the 3 (1233) is. 6 situation (12 12), 7 situation (2 1 12), have you found any rules? The sum of the numbers in brackets must be an integer multiple of 3! Why does it have to be an integer multiple of 3? I suggest you look at the total variables of the original Rubik's cube and prove that the sum of the angles of the corner blocks should be an integer multiple of 360 degrees. This restriction determines that we can only have eight situations.

This problem is not particularly simple. First, let's ask a question. If the four corner positions of the top surface of the Rubik's cube can be marked as 1, 2, 3 as above, they can be marked as (1113) (1233) and so on. The same situation can be removed after rotation.

If the same rotation is not removed, then the four angles can be distinguished. The answer is simply 3 4 = 8 1? But if the same rotation is removed, it will be more complicated, for example,113,311.

This is a classic problem of combinatorial mathematics, called the necklace problem (that is, wearing a necklace with several colors of beads), or called Polya theorem. You can go here if you are interested, but I still suggest you think about it yourself first. The formula here will make you dizzy at once, if you are unfamiliar with the concept of "Euler number" or have never heard of it.

In this case, we don't need the formula in mathworld, just enumeration:) But if we think about it again, the answer is 24. I looked it up and gave the same answer as the horror formula. Among these 24 kinds, the remainder of the "sum" of 4 numbers divided by 3 should be evenly distributed to 0, 1 2, which I haven't proved yet, hehe, so there should be 8 divisible by 3. That's right+these 7 kinds:

Now let's talk about the algorithm. For the first case, we should put the corner whose top surface is already green at the top (that is, the "left back corner"). At this time, you don't have to care which of the two floors faces forward, Rubik's cube.

Apply the following algorithm. The function of this algorithm is to keep the orientation of the upper corner (left back corner) unchanged, and at the same time turn the green of the lower three corners upward.

Algorithm 1:

Hello, hello.

Ruhr R.

For the second case, we should find that it is a diagonal mirror image of the first case, right? So use the above algorithm to do diagonal mirror image to get the algorithm of the second case: Rubik's cube.

Algorithm 2:

Fu, fu, fu.

F U2 F '

For case 3-7:

You have a two-thirds chance of meeting them. In fact, you can try the algorithm of 1 2 several times to see what will happen and find the law slowly. 3-7 cases were all solved by 1, 2 algorithm, with at most 2 algorithms. Rubik's Cube

If you can't wait or feel that your method is not fast enough, you can see my method in References 3-7 here.

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(Step 6) Adjust the order of the four corners to form: (You can also watch the video explanation in Step 6)

This step is simple. Turn around the top surface first to see if it is right (probability 1/6). If not, first find an edge with two corners of the same color (probability 2/3). Like the following example, there is also a probability 1/6 that you can't find such an edge. We'll talk later. Rubik's Cube

We don't have to care about the color of the edge between the two corners and the color of the two layers below. Now put this side on the back, taking the last one in the above table as an example, it becomes,

Front and back

The follow algorithm is then applied,

B2

B2·L2

If after applying the algorithm, the four corners have not matched the colors of the lower two layers, turn around. The basic function of this step is to exchange the positions of the first two corners. Or do this counterclockwise rotation, and the two effects are equivalent after the top surface rotates. Rubik's Cube

In the second case, two edges with the same corner color cannot be found.

If you can't find such an edge with two corners of the same color, you can definitely find it by applying the above algorithm with your eyes closed. If you are interested in why, you can look at this page. In this case, you actually need to exchange two corners on a diagonal line.

In addition, you can also try the left and right mirror images of this algorithm, using the same method and the same effect.

B2·B2·R2

Ok, the sixth step is completed, just the last step! Let me tell you a good news first. In the last step, we don't need to learn new algorithms. We can do it with algorithm 1 and algorithm 2 in the fifth step:)

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(Step 7) Arrange the last prism blocks in sequence (you can also watch the video explanation of Step 7).

Last step, are you excited? Finally, victory is ahead. The last step is simple, you just need to look at the direction of the Rubik's cube. Rubik's Cube

In the first case, you want the three sides to rotate counterclockwise. (probability 1/3)

First of all, you have to put the color-matched edge in front.

Then use the fifth step algorithm 1+U2+ algorithm 2+U2. namely

R ' U ' R U ' R ' U ' 2 R U2 F U F ' U F U2 F ' U2

Step 5 algorithm 1 Step 5 algorithm 2

You can go up and look at the picture of step five. You can also have a look.

U2 between the algorithm 1 and 2 can also be replaced by rotating your whole Rubik's Cube 180, so the final U2 is not needed.

That's it,

In the second case, you want the three sides to rotate clockwise. (probability 1/3)

Then put the color matching side on the right. At this time, you will find that the second graph is a diagonal mirror image of the first graph.

So it is the fifth step: algorithm 2+U2+ algorithm 1+U2.

U2 U2 U2 U2 U2 U2 U2 U2 U2 U2

Step 5 Algorithm 2 Step 5 Algorithm 1

Or, remove U2 in the middle and rotate the whole Rubik's Cube 180.

How to swing clockwise and then counterclockwise, which algorithm does not need to be memorized, is also difficult to memorize. You just need to pay attention to: 1. The direction from the second step and the fourth step to the top surface is the direction of the three arrows on the top surface; 2. The orientation of the Rubik's Cube will allow you to "cut" to the right side in the first step, and you will know which algorithm to use first and how to put the Rubik's Cube.

Probability112 probability 1/6

If you encounter such a situation that needs to be changed. It's actually quite simple. You can apply the above clockwise or counterclockwise algorithm at will, and then it becomes clockwise or counterclockwise. If the situation you encounter is not one of the above four situations, then you must remove two sides and exchange positions. As long as you adjust them once, this will never happen

Although we don't need to remember the new algorithm, the method described above is very long and needs 16 steps. You can remember another algorithm if you like. Rubik's Cube

R2 R2 R2 R2 R2 R2

These two algorithms are mirror images of the top horizontal centerline. This is much easier.

If you think the station has brought you some help, please link the website of the station on your website or blog, so that more people can see the station and more friends can like the Rubik's Cube. It's simple. Just select and copy (Ctrl-C) and paste (Ctrl-V) the following words, and link them to your webpage or blog editor.

Mofang station

If your Rubik's Cube is a Rubik's Cube with numbers, or a Rubik's Cube with figures and patterns, please refer to the last page to adjust the orientation of the center block.

At this point, our Rubik's Cube has finally been completed, and everyone can celebrate:) If you have just finished watching this introductory game or the Rubik's Cube for the first time, you'd better post on the Rubik's Cube forum, share your experience and comment on this webpage, so that I can know how you feel after reading it. If you want to make yourself better, go to the Advanced Rubik's Cube. Give you a stopwatch I made to measure your speed:)

There is no need to learn advanced gameplay. A good Rubik's Cube can make it easy for you to play the introductory game in less than 2 minutes. If you want to buy a good Rubik's Cube, go to our own Rubik's Cube Taobao shop and have a look:) New! Video demonstration of the national team.

In addition, after learning Rubik's Cube, I recommend every friend who loves life to watch this speech, from Steve Jobs, CEO of Apple Computer Company, who gave a speech at the graduation ceremony of Stanford University in 2005. The last sentence is to stay hungry and stay stupid. I think if you read it carefully, you will gain something.

If you want to make your Rubik's Cube cooler, you can change your Rubik's Cube a little.

Rs2 Fs2 Us2 or (Rs Fs)3 Rs Us Fs Rs' Us2 (Fa Ra)3.

Among them, marks such as Fs, Fs', Ra, Ra' indicate that you move back and forth or left and right like a clip, s = slice, a = reverse slice, for example,

Mark Fs Fs' Ra Ra'

draw

He is equivalent to F B' F' B R L R' L'

Other please and so on. Want more beautiful patterns