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Saturday, December 3, 2011

Beginner's Method For Solving A 3x3 Rubik's Cube (Part 2)

You can find Part 1 of this guide here.

Now onto step 4.

Step 4: In this step, your aim is to solve the upper face (the green face in my case) to a cross. That is, I want to align the edges that involve green such that the green side is on the upper face of the cube. At the end of this step, you may not have those edge pieces placed correctly, but at least all their green faces will be on the green side of the cube. If you already have the 4 edge pieces involving green placed in such a way that their green sides are on the upper face, skip step 4 and proceed directly to step 5.

At the end of step 3, you may find yourself in one of three situations as far as the upper face is concerned.
No green edges on top
Step 4 Before, Option 1
Two adjacent green edges on top
Step 4 Before Option 2
Two opposite green edges on top
Step 4 Before Option 3

Ignore the corner pieces and concentrate only on the edge pieces involving green. You might find that none of the green sides are on the top face (option 1), or you might find two of them on the top face on adjacent sides of the cube (option 2), or you might find two of them on the top on opposite sides of the cube (option 3).

If you find yourself facing option 1, it does not matter how you hold the cube. If you face option 2, make sure that the two adjacent sides on which the green edges are on the top face are on the back and left. If you face option 3, make sure the green pieces form a bar parallel to the front face of the cube.

From all three options, you can execute the following algorithm to get to the point where all the edge pieces are placed such that their green sides are on the upper face: F R U R' U' F'. When you do this, you will notice that if you start from option 1, you will end up in either option 2 or option 3 when you execute this algorithm once. If you start from option 2, you will end up in option 3 after one execution of this algorithm. If you start from option 3, after one execution, you will be ready to move to step 5. If you want to cut down on one application of the algorithm, you can apply a modified algorithm from option 2 to skip option 3 and end up with a green cross on top. That modified algorithm is F U R U' R' F'.

Either way, you should now have the following configuration in front of you at the end of step 4 (ignore the green corners. You may or may not have them as shown below. All you need is a green cross on the upper face).
Green cross on top
Step 4 After

The edge pieces involving green may or may not be in the correct positions. We will deal with that in step 5. If you have blue solved fully, four sides solved two-thirds of the way, and the edges involving green positioned with the green sides on the green face, you are done with step 4.

Step 5: In step 5, we are going to align the edges of the green face so that they line up with the colors on the sides of the faces. You may have 1, 2 or 4 of the top edges aligned correctly with colors on the sides (if you look at the picture above, you can rotate the upper face clockwise by 90 degrees to align the green and yellow face). If all 4 edge pieces are aligned correctly, skip step 5 and go directly to step 6.

If you find only one top edge aligned correctly, make that part of the front face, as shown in the picture below. You are now going to apply the algorithm below that will move the edge piece from the left face to the right face, the one on the right face to the back face, and the one on the back face to the left face. The piece on the front face does not move. So, it is an anticlockwise rotation of the edge pieces skipping the edge on the front face.
Edges before rotation
Step 5 Before

The algorithm is: R U R' U R U U R'.
Edges after rotation
Step 5 After

Since three of the edge pieces move when this algorithm is applied, if your cube already has two top edges aligned correctly, you may have to apply the algorithm multiple times to get all the edges aligned correctly. In the first application, you will end up destroying one or both of the original alignments, and then you can rebuild all of them by applying the algorithms a couple more times. Make sure you understand what changes the algorithm makes (anticlockwise rotation of the edges, skipping the front face), and you will have no trouble figuring out how best to use it.

Step 6: Step 6 is used to position the top corner pieces correctly. At this point, you only have 4 unsolved pieces in the cube (at most). These 4 pieces could be at the correct places, but wrongly oriented (in which case, skip to step 7). None of them may be in the right place (note that at this stage, you can not rotate the upper face because that will cause the edge pieces to get out of position), or 1 of them could be in the right place, but the other three are in the wrong corners.

If none of them are in their correct corners, you can apply the algorithm holding the cube with any of the sides (that is the faces other than blue and green in my case) as the front face. If one of the corner pieces is in the correct corner (don't worry about its orientation), make sure you hold the cube such that you place that piece in the front upper right corner of the cube (this is the only corner that is not going to move when you apply this algorithm).

The algorithm below causes the front upper left corner piece to move to the back upper right corner, the back upper right corner piece to move to the back upper left corner and the back upper left corner piece to move to the front upper left corner. It is an anticlockwise rotation of the corner pieces skipping the front upper right corner. You might have to apply it more than once to position all the corners correctly. Once again, understand what the algorithm does, and you will have no problem figuring out how to use it.

The algorithm is: U R U' L' U R' U' L.

Step 7: Now you have a cube in which all the top corners are positioned correctly, but one or more of them may be oriented wrongly. If you find that the cube is fully solved at the end of step 6 (that is, all the corners oriented themselves correctly while being placed in their correct spots), you are done. Congratulations! Otherwise, you will have to orient the corner pieces.

Now, step 7 is a little confusing. Not because the algorithm for it is complicated. Quite on the contrary: it is a very short algorithm. But throughout step 7, your front face is never changed. So, pick a front face right now. I have picked red in the pictures below. You can pick any, but it is not going to change as you progress through step 7.

Once you have picked a front face, bring a mis-oriented corner piece to the upper front right position by rotating the upper face of the cube. The mis-orientation may look like the picture below, in which the top color (green) is on the right face.
Corner with green on right
Step 7 Before, Option 1

In this case, apply the algorithm below twice to get the green side on the upper face: R' D' R D. After you do this, you may notice that your cube may look very scrambled. You may find blue pieces floating around, away from the bottom face where they belong. DO NOT PANIC. Between when you begin step 7 and when you complete step 7, you will find all kinds of weird changes in the cube that you just have to ignore.

Just make sure you get the green side of the corner cube to the upper face, and then rotate the upper face (only the upper face) of the cube to get the next mis-oriented corner piece in the front upper right corner of the cube. Make sure you continue to keep red (or whatever face you chose at the beginning of step 7) as the front face. You may then be faced with the following situation pictured below where the green is on the front face.
Green on front face
Step 7 Before, Option 2

Notice how the cube looks very scrambled. That is because we are in the middle of step 7. Don't worry. Just apply the same algorithm as before (R' D' R D), but 4 times to get the green side on the upper face. Continue turning the upper face and orienting each top corner piece so that the green is on the upper face. Do not worry about how bad the cube looks in the interim.

Once you are done with all four corners, and all of them are oriented properly, you may find that your cube looks as below:
Almost there
Almost done!

Now, all you have to do is rotate the upper and down faces of the cube a couple of times to line up all the colors, and you will have yourself a fully solved cube, as shown below:
All done
Fully done!

That is all there is to it! Two algorithms in step 3 (one of which is actually a variation of the other), and one algorithm each in steps 4 (two if you want to use a shortcut), 5, 6 and 7. A total of 6 or 7 algorithms, none of which are longer than 8 steps. That is all it takes to solve the cube! I told you it was easy. Try it and let me know how it works out. Good luck!

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