Okay, let's get started. The first cube I'm going to explain is the 2x2x2. Available at many toy stores, this is a good place to start to get you comfortable with the principles involved.
The notation I will be using is mostly universal for cubes: T for the Top, or starting color (this will generally be white because I usually start with this color), D for the Bottom, L for the Left, R for the Right, F for the Front, and B for the back. This will change as you re-orient the puzzle, but whatever you do TRY TO KEEP THE PUZZLE ORIENTED THE SAME WAY THROUGHOUT THE ALGORITHM'S EXECUTION. That is to say, don't change the way you hold the puzzle, at least unless I tell you to. For formulae, a letter on its own means to turn that layer clockwise as if you're looking at that layer. If that letter has ' beside it, turn that layer counterclockwise as if looking at that layer. A 2 means to turn the layer twice (in any direction, it doesn't matter) Now let's get started.
The first thing that we're going to do is solve the first face and layer. In figure 1, the first face and layer are composed of the White face, plus the halves of Green, Red, Yellow (hidden) and Orange (hidden) that connect to white (in this case, these halves are the horizontal upper halves). Many of you can figure out how to solve the first face and layer by logic, but for those who can't I will outline it.
Our base cubie (or cubelet) is going to be the one with the Rubik's logo that is generally present. In my case it is the WYO (White, Yellow, Orange) cubie. What we want to do is get the cubies that have two of the same colors on them right beside it. In my case, these two cubies are WRY and WGO. The common colors are W and Y as well as W and O (respectively). The process of doing this is repeated until the first F+L are solved
To actually begin, find the cubie with the logo on it. This will be your base cubie. If a logo cubie does not exist, just choose a random cubie as base (for your own convenience this should be white as this is the color that will be used as an example). Then find a cubie that has two of the same colors on it. This cubie could be anywhere on the cube, but the most common ways that it will be oriented are with the white on the bottom layer (with figures 2 and 3 being the 2 possible different situations). If the cubie is oriented as in figure 2, bring it to the position described in figure 4 by turning the B layer as many times as necessary. Once you have this situation, turn the B layer once to the right, then bring the L layer (with the white base cubie) down, then the B layer to the Right, then the L layer back up, bringing the desired cubie with it. The formula for this is (D/L/D'/L'). If the two secondary colors (in this case orange and orange) are not touching like they are in figure four, your situation is likely more similar to that of figure 3. If this occurs, mirror the patterns that I described (that is to say, bring the cubie in question to a BFR position with the base cubie at a UBR position, then execute (D'/R'/D/R). If you find that the cubie color in question is on the bottom, simply bring it to a position that is under the target spot (where you want the color to go then execute (R'/D/R/D'/F/D'/F') to bring it to the correct position. Using various combinations of these algorithms, you can eventually solve the top face and layer.
Now to solve the bottom. To begin, find two adjacent cubies that have a color (other than the top or bottom color) in common. In my example I chose BRY and OBY, with the bottom color being blue and the common color being yellow. To demonstrate this, I turned the cube on its side. Don't do this. Keep it the way it was before. Notice how I also brought the cubies to a position where they match up with the first layer color (the color that is directly above them, in this case Yellow). Please do this by turning the bottom layer. Now look at the 3rd color on the selected cubie (The color that is not the selected color nor the bottom color [orange, for demo purposes]). They should match up with the color that is adjacent to the selected color. For example, if your selected color is Yellow, look to the left side on the top layer. Then look at the "extra" color on the cubie directly below (I repeat, orange in my case). If you notice that the two are not the same, (as in my example) the cubies need to be switched. The formula for this is (R'/D'/R/F/D/F'/R'/D/R/D2). This brings them to the right position. Then do the same on the opposite side if necessary.
Finally, you need to rotate the corners. There are two formulae for this; they are the same but mirrored. These formulae rotate three cubies while leaving another untouched. For now, just perform them at random until you find three that need to be rotated and one that is solved. With experience, you will recognize what formula needs to be used for what situation. If there are three that need to be rotated clockwise, hold the cube so that the solved cubie is on the right hand side of the cube, then execute (L/D/L'/D/L/D2/L'/B2). If three need to be rotated counterclockwise, hold the cube so that the solved cubie is on the left then execute ( R'/D'/R/D'/R'/D2/R/D2). Thus, the cube is solved. Practise these formulae as they will be used in the 3x3x3 solution.
The notation I will be using is mostly universal for cubes: T for the Top, or starting color (this will generally be white because I usually start with this color), D for the Bottom, L for the Left, R for the Right, F for the Front, and B for the back. This will change as you re-orient the puzzle, but whatever you do TRY TO KEEP THE PUZZLE ORIENTED THE SAME WAY THROUGHOUT THE ALGORITHM'S EXECUTION. That is to say, don't change the way you hold the puzzle, at least unless I tell you to. For formulae, a letter on its own means to turn that layer clockwise as if you're looking at that layer. If that letter has ' beside it, turn that layer counterclockwise as if looking at that layer. A 2 means to turn the layer twice (in any direction, it doesn't matter) Now let's get started.
The first thing that we're going to do is solve the first face and layer. In figure 1, the first face and layer are composed of the White face, plus the halves of Green, Red, Yellow (hidden) and Orange (hidden) that connect to white (in this case, these halves are the horizontal upper halves). Many of you can figure out how to solve the first face and layer by logic, but for those who can't I will outline it.
Our base cubie (or cubelet) is going to be the one with the Rubik's logo that is generally present. In my case it is the WYO (White, Yellow, Orange) cubie. What we want to do is get the cubies that have two of the same colors on them right beside it. In my case, these two cubies are WRY and WGO. The common colors are W and Y as well as W and O (respectively). The process of doing this is repeated until the first F+L are solved
To actually begin, find the cubie with the logo on it. This will be your base cubie. If a logo cubie does not exist, just choose a random cubie as base (for your own convenience this should be white as this is the color that will be used as an example). Then find a cubie that has two of the same colors on it. This cubie could be anywhere on the cube, but the most common ways that it will be oriented are with the white on the bottom layer (with figures 2 and 3 being the 2 possible different situations). If the cubie is oriented as in figure 2, bring it to the position described in figure 4 by turning the B layer as many times as necessary. Once you have this situation, turn the B layer once to the right, then bring the L layer (with the white base cubie) down, then the B layer to the Right, then the L layer back up, bringing the desired cubie with it. The formula for this is (D/L/D'/L'). If the two secondary colors (in this case orange and orange) are not touching like they are in figure four, your situation is likely more similar to that of figure 3. If this occurs, mirror the patterns that I described (that is to say, bring the cubie in question to a BFR position with the base cubie at a UBR position, then execute (D'/R'/D/R). If you find that the cubie color in question is on the bottom, simply bring it to a position that is under the target spot (where you want the color to go then execute (R'/D/R/D'/F/D'/F') to bring it to the correct position. Using various combinations of these algorithms, you can eventually solve the top face and layer.
Now to solve the bottom. To begin, find two adjacent cubies that have a color (other than the top or bottom color) in common. In my example I chose BRY and OBY, with the bottom color being blue and the common color being yellow. To demonstrate this, I turned the cube on its side. Don't do this. Keep it the way it was before. Notice how I also brought the cubies to a position where they match up with the first layer color (the color that is directly above them, in this case Yellow). Please do this by turning the bottom layer. Now look at the 3rd color on the selected cubie (The color that is not the selected color nor the bottom color [orange, for demo purposes]). They should match up with the color that is adjacent to the selected color. For example, if your selected color is Yellow, look to the left side on the top layer. Then look at the "extra" color on the cubie directly below (I repeat, orange in my case). If you notice that the two are not the same, (as in my example) the cubies need to be switched. The formula for this is (R'/D'/R/F/D/F'/R'/D/R/D2). This brings them to the right position. Then do the same on the opposite side if necessary.
Finally, you need to rotate the corners. There are two formulae for this; they are the same but mirrored. These formulae rotate three cubies while leaving another untouched. For now, just perform them at random until you find three that need to be rotated and one that is solved. With experience, you will recognize what formula needs to be used for what situation. If there are three that need to be rotated clockwise, hold the cube so that the solved cubie is on the right hand side of the cube, then execute (L/D/L'/D/L/D2/L'/B2). If three need to be rotated counterclockwise, hold the cube so that the solved cubie is on the left then execute ( R'/D'/R/D'/R'/D2/R/D2). Thus, the cube is solved. Practise these formulae as they will be used in the 3x3x3 solution.
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