Hello! I hope you enjoyed my 2x2x2 solution. Now it's time for my 3x3x3 solution. You will b using the same principles as the 2x2x2 and only some new formulas. The notation remains the same except for the addition of MH (Middle Horizontal), MV (Middle Vertical), and MS (Middle Sides, the new middle if you rotate the cube 90 degrees downwards). Then I will just say "MVD if I want you to rotate the Vertical Middle in a Downwardly direction or MVU for said layer in an upwardly direction. HML and HMR dictate to move the Horizontal Middle to the Left and Right respectively. MS and MS' mean the Side Vetical middles to go either clockwise or counterclockwise. Let me know if you have better terms as I am not the most creative.
To start, do the white corners as you did with the 2x2x2: using a (R'/D/R) or (L/D'/L') formula. The center bits are done using the same "bottom layer as transport layer" theory: if you have a center piece out of place, rotate the bottom layer so that the piece in question is directly below the target. If you see that the white color is on the side portion (on the bottom layer but white is facing towards you if the white face is on top), then execute (D/MVD/D'/MVU). If the white piece is on the bottom, simply rotate it to a place that is below the target place and execute (MVD/B2/MVU). If thesituation arises where the white piece in question is on the side of one of the faces, bring it to a pisition where it is on the same slice (Left or Right) as the target. If the two are on the right slice of a face, execute (MHL/R'/MHR/R). If it is on the left, mirror this executing (MHR/L/MHL/L'). Using these formulae you should be able to get the white face and layer solved.
The next step is to solve the four pieces that are on the MH slice. To do this, turn the cube upside-down. There is one universal formula for that and it is as follows: (R/U/R'/U'/F'/U'/F). Before executing this, find a middle (two-color) piece that has tow colors on it that are NOT the bottom color (bottom being the color opposite that which you started with) (if yellow is the bottom than an example would be R/G). Find the two center pieces that correspond with the colors that are on this piece and hold the cube so that these center pieces are both facing you (cube should be on an angle), then rotate it (the whole cube) so that the leftmost center piece is facing you. turn the targeted piece to a UL position by turning the new U layer x amount of times then check your positioning by looking to see if the uppermost color of the piece is the same color as the color on the right-hand side of the cube. Then execute the aforementioned formula. If the pieces are NOT the same color, turn the U layer so that the piece is at a UB position then execute said formula. That will flip the piece so you can properly place it. If you can't find a piece that doesn't have two non-bottom colors, execute the formula at random and that will turn up a piece. If a piece needs to be flipped in place, execute the formula, execute (U'), then do the formula again.
To solve the last layer, flip the cube back to its original position. Solve the corners in the same way as was done for the 2x2x2, then look at the bottom. If there are two flipped and moved pieces then orient the cube so that they are at DB and DR positions then execute the following: (MVD/D/MVU/D2/MVD/D/MVU). This works if there are four flipped pieces as well. If there are three pieces that need to be rotated but not flipped, look for a piece that needs to jump directly across the cube (I'll call this a "jumping" piece). When you find this piece, hold the cube so that the side that corresponds with the "jumping" color is facing you then execute (MVD/D or D' [turn the D layer towards the "solved" side]/MVU/D in the same direction as before/MVD/D2/MVU/D in the same direction as before/MVD/D in the same direction as before/MVU/D2. This works for a situation where there are four that need to be moved as well (perform at random).
To start, do the white corners as you did with the 2x2x2: using a (R'/D/R) or (L/D'/L') formula. The center bits are done using the same "bottom layer as transport layer" theory: if you have a center piece out of place, rotate the bottom layer so that the piece in question is directly below the target. If you see that the white color is on the side portion (on the bottom layer but white is facing towards you if the white face is on top), then execute (D/MVD/D'/MVU). If the white piece is on the bottom, simply rotate it to a place that is below the target place and execute (MVD/B2/MVU). If thesituation arises where the white piece in question is on the side of one of the faces, bring it to a pisition where it is on the same slice (Left or Right) as the target. If the two are on the right slice of a face, execute (MHL/R'/MHR/R). If it is on the left, mirror this executing (MHR/L/MHL/L'). Using these formulae you should be able to get the white face and layer solved.
The next step is to solve the four pieces that are on the MH slice. To do this, turn the cube upside-down. There is one universal formula for that and it is as follows: (R/U/R'/U'/F'/U'/F). Before executing this, find a middle (two-color) piece that has tow colors on it that are NOT the bottom color (bottom being the color opposite that which you started with) (if yellow is the bottom than an example would be R/G). Find the two center pieces that correspond with the colors that are on this piece and hold the cube so that these center pieces are both facing you (cube should be on an angle), then rotate it (the whole cube) so that the leftmost center piece is facing you. turn the targeted piece to a UL position by turning the new U layer x amount of times then check your positioning by looking to see if the uppermost color of the piece is the same color as the color on the right-hand side of the cube. Then execute the aforementioned formula. If the pieces are NOT the same color, turn the U layer so that the piece is at a UB position then execute said formula. That will flip the piece so you can properly place it. If you can't find a piece that doesn't have two non-bottom colors, execute the formula at random and that will turn up a piece. If a piece needs to be flipped in place, execute the formula, execute (U'), then do the formula again.
To solve the last layer, flip the cube back to its original position. Solve the corners in the same way as was done for the 2x2x2, then look at the bottom. If there are two flipped and moved pieces then orient the cube so that they are at DB and DR positions then execute the following: (MVD/D/MVU/D2/MVD/D/MVU). This works if there are four flipped pieces as well. If there are three pieces that need to be rotated but not flipped, look for a piece that needs to jump directly across the cube (I'll call this a "jumping" piece). When you find this piece, hold the cube so that the side that corresponds with the "jumping" color is facing you then execute (MVD/D or D' [turn the D layer towards the "solved" side]/MVU/D in the same direction as before/MVD/D2/MVU/D in the same direction as before/MVD/D in the same direction as before/MVU/D2. This works for a situation where there are four that need to be moved as well (perform at random).
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