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---
If you are unfamiliar with cube terms such as "cubie", "corner", and "permutation", you can refer to the "3x3x3 Concepts" page for further information.
Each algorithm is numbered, allowing for later reference.
---
This solution guide consists of seven steps:
---
Most Rubik's Cube solution guides for beginners orient the puzzle so the white face is on top. However, most intermediate and advanced solutions recommend the white face be put on the bottom. This allows the solver to perform later steps without having to turn over the puzzle, which wastes time. This guide will keep the white face on the bottom for the entire solve.
We will use the white-orange edge as an example edge, but the same principles and algorithms apply to all the white edges. When solving the white-orange edge, orient the entire cube in your hands so that the white center is on the D face and the orange center is on the F face.
Sometimes a white edge might already be solved--in its correct place and oriented correctly--such as below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | |\G\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\_W_\___\ \|
| | O | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
Note that the orange sticker is adjacent to the orange center, and the white sticker is adjacent to the white center. If either sticker does not match the center adjacent to it, the edge is not solved!
The white edge might already be connected to orange center, but not the white center. An example is shown below, where the edge is in the middle layer (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | O |\ \
| | | |/B/| +---+---+---+W\ |
+---+---+---+W/ | | | | |\B\|
| | O | O |/ / +---+---+---+ \ | R
+---+---+---+ / \___\___\___\ \|
| | | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
In this case, we can solve the white edge using one move:
(1) F
Similarly, the following case--where the edge is in the U layer--can be solved in one move (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | O | |\
/ / W / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | O | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | | |\B\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\___\___\ \|
| | | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
(2) F2
However, sometimes the white edge is flipped. Specifically, the edge is in the middle or U layer, but the white sticker is adjacent to the orange face. This is shown below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+O/ | | | | |\B\|
| | O | W |/ / +---+---+---+ \ | R
+---+---+---+ / \___\___\___\ \|
| | | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
Because this edge is flipped, we need to flip it back before placing it. This can be done in four moves:
(3) R U R' F2
A similar algorithm solves a flipped edge located in the U layer (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / O / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | W | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | | |\B\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\___\___\ \|
| | | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
(4) R U' R' F
If the edge is in is place but flipped incorrectly, the following four moves will flip it back (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | | |/G/| +---+---+---+ \ |
+---+---+---+ / | | | W | |\B\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\_O_\___\ \|
| | W | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
(5) F' D R' D'
It might be necessary to turn the U face to move an edge above its correct place. An example is shown below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/_O_/ | | | | |\
/ / / /W/| +---+---+---+ \
+---+---+---+ / | R | | O | |\W\
| | | |/G/| +---+---+---+ \ |
+---+---+---+ / | | | | |\B\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\___\___\ \|
| | | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
Applying the following move will place the white-orange edge above the orange center. Note that when we do so, it will be flipped, so we will need to apply (4) to solve it.
U
Once we place one edge, we'll need to place the second edge. For example, the white-green edge might be ready next (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | G | G |\ \
| | | |/O/| +---+---+---+W\ |
+---+---+---+W/ | | | | |\O\|
| | G | G |/O/ +---+---+---+ \ | R
+---+---+---+ / \___\___\___\O\|
| | | |/ \___\_W_\_W_\ |
+---+---+---+ D \___\___\___\|
F
This can be solved using (1) above.
The algorithms above are constructed such that they will not displace edges that are already solved. For example, the second edge might be in the following configuration (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | G | W |\ \
| | | |/O/| +---+---+---+G\ |
+---+---+---+G/ | | | | |\O\|
| | G | W |/O/ +---+---+---+ \ | R
+---+---+---+ / \___\___\___\O\|
| | | |/ \___\_W_\_W_\ |
+---+---+---+ D \___\___\___\|
F
Applying (3) will solve the white-green edge, and the white-orange edge will remain solved as well.
There will be times when an incorrect edge is in another edge's spot. For example (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | | |/G/| +---+---+---+ \ |
+---+---+---+ / | | | R | |\B\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\_W_\___\ \|
| | R | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
We can fix this by moving the edge to the U layer. From there we can turn the U face to move the edge above its correct spot, re-orient the cube in our hands, then apply the appropriate algorithm to solve the edge. In the above example, simply applying (2) will move the edge to the U layer.
When solving the third and fourth edges, it might be the case that one of them is in the middle layer between two already-solved edges. An example is below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | G | W |\ \
| | | |/O/| +---+---+---+B\ |
+---+---+---+B/ | | | G | |\O\|
| | G | W |/O/ +---+---+---+ \ | R
+---+---+---+ / \___\_W_\___\O\|
| | G | |/ \___\_W_\_W_\ |
+---+---+---+ D \___\___\___\|
F
We can apply the following algorithm to remove the edge from the middle layer and keep the solved edges correct:
R U R'
Afterwards, solve the edge as normal.
Continue this process until all four white edges are solved. This will appear as follows (UFR and DBL visible):
____________ B
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | R | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | R | |\G\|
| | O | |/B/ +---+---+---+ \ | L
+---+---+---+ / \___\_W_\___\G\|
| | O | |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
---
After solving the white edges, we need to solve the four white corners. We will use the white-orange-green corner as an example corner, but the same principles and algorithms apply to all the white corners. When solving the white-orange-green corner, orient the entire cube in your hands so that the white center is on the D face and the orange center is on the F face.
Sometimes a white corner might already be solved, such as below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | O |\B\|
| | O | |/B/ +---+---+---+B\ | R
+---+---+---+B/ \___\_W_\_W_\B\|
| | O | O |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
Note that the white sticker is diagonally adjacent to the white center, the orange sticker is diagonally adjacent to the orange center, and the blue sticker is diagonally adjacent to the blue center. If two or more stickers do not match their diagonally-adjacent centers, the corner is not solved! (It is impossible for only one sticker to not match its adjacent center without tampering with the puzzle.)
More often, the desired corner will be somewhere in the U layer. Turn the U layer so that the corner is above its correct spot; then the corner will have one of three orientations.
The first orientation is the white sticker on the R face (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | O |\
/ / / B / /| +---+---+---+W\
+---+---+---+W/ | R | | O | |\ \
| | | O |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | |\B\|
| | O | |/B/ +---+---+---+ \ | R
+---+---+---+ / \___\_W_\___\B\|
| | O | |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
(6) R U R'
The second orientation is the white sticker on the F face (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | W |\
/ / / O / /| +---+---+---+B\
+---+---+---+B/ | R | | O | |\ \
| | | W |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | |\B\|
| | O | |/B/ +---+---+---+ \ | R
+---+---+---+ / \___\_W_\___\B\|
| | O | |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
(7) F' U' F
The third orientation is the white sticker on the U face (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | B |\
/ / / W / /| +---+---+---+O\
+---+---+---+O/ | R | | O | |\ \
| | | B |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | |\B\|
| | O | |/B/ +---+---+---+ \ | R
+---+---+---+ / \___\_W_\___\B\|
| | O | |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
(8) R U2 R' U' R U R'
The corner might already be in its correct place, but twisted incorrectly. An example is below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | O |\
/ / / / /| +---+---+---+W\
+---+---+---+ / | R | | O | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | W |\B\|
| | O | |/B/ +---+---+---+O\ | R
+---+---+---+O/ \___\_W_\_B_\B\|
| | O | W |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
Applying the following algorithm moves the corner into the U layer:
(9) R U R' U'
Afterward, we can use either (6) or (8) to solve the corner.
Sometimes an incorrect corner can be in another corner's spot (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | O |\
/ / / / /| +---+---+---+W\
+---+---+---+ / | R | | O | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | O | R |\B\|
| | O | |/B/ +---+---+---+G\ | R
+---+---+---+G/ \___\_W_\_W_\B\|
| | O | R |/ \_W_\_W_\_W_\ |
+---+---+---+ D \___\_W_\___\|
F
Applying (9) moves the corner into the U layer; from there we can turn U to move the corner above its correct spot, re-orient the cube in our hands, and use (6), (7) or (8) to solve the corner.
Continue this process until all four white corners are solved. This will solve the white face and the bottom equatorial layer of the cube. This will appear as follows (UFR and DBL visible):
____________ B
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | R | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ /B| | R | R | R |\G\|
| | O | |/B/ +---+---+---+G\ | L
+---+---+---+B/ \_W_\_W_\_W_\G\|
| O | O | O |/ \_W_\_W_\_W_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
---
The next step is to solve the middle edges of the cube.
Sometimes a middle edge will already be solved, as below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | O |\ \
| | | |/B/| +---+---+---+B\ |
+---+---+---+B/B| | O | O | O |\B\|
| | O | O |/B/ +---+---+---+B\ | R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
More often, the desired edge will be somewhere in the U layer. Turn the U layer so that the sticker not on the U face is connected to its center. There are two possible cases resulting from this.
The first case is that the edge connects to the center on the F face (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | O | |\
/ / B / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | O | |/B/| +---+---+---+ \ |
+---+---+---+ /B| | O | O | O |\B\|
| | O | |/B/ +---+---+---+B\ | R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
(10) U R U R' U' F' U' F
The second case is that the edge connects to the center on the R face (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/_O_/ | | | | |\
/ / / /B/| +---+---+---+ \
+---+---+---+ / | R | | O | |\B\
| | | |/B/| +---+---+---+ \ |
+---+---+---+ /B| | O | O | O |\B\|
| | O | |/B/ +---+---+---+B\ | R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
(11) U' F' U' F U R U R'
The edge might already be in its correct place, but flipped incorrectly. An example is below (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | B |\ \
| | | |/B/| +---+---+---+O\ |
+---+---+---+O/B| | O | O | O |\B\|
| | O | B |/B/ +---+---+---+B\ | R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
Applying the following algorithm moves the edge into the U layer:
(12) R U R' U' F' U' F
We can then use U2 to connect the orange-blue edge to the orange center, after which applying (10) will solve the edge.
Sometimes an incorrect edge can be in another edge's spot (UFR and DFR visible):
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | R |\ \
| | | |/B/| +---+---+---+G\ |
+---+---+---+G/B| | O | O | O |\B\|
| | O | R |/B/ +---+---+---+B\ | R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
Applying (12) moves the edge into the U layer; from there we can turn U to move the edge around, re-orient the cube in our hands, and use (10) or (11) to solve the edge.
Continue this process until all four middle edges are solved. This will solve the middle equatorial layer of the cube. This will appear as follows (UFR and DBL visible):
____________ B
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ /B| R | R | R | R |\ \
| | | |/B/| +---+---+---+G\ |
+---+---+---+B/B| | R | R | R |\G\|
| O | O | O |/B/ +---+---+---+G\G| L
+---+---+---+B/ \_W_\_W_\_W_\G\|
| O | O | O |/ \_W_\_W_\_W_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
---
We now have one equatorial layer and the yellow face to solve. The algorithms for these four steps become a little longer, as more pieces need to be returned to their correct places when we make changes to the U layer. Our first step on the U layer is to orient the yellow edges.
There are 4 possible edge orientations at the beginning of this step.
The first possibility is that all four edges are oriented correctly (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/_Y_/___/| +---+---+---+ | | | |
/_Y_/_Y_/_Y_/ | | | | |\ +---+---+---+---+---+
/ / Y / / /| +---+---+---+ \ | | | Y | | |
+---+---+---+ /B| R | R | R | R |\ \ +---+---+---+---+---+
| | | |/B/| +---+---+---+G\ | | | Y | Y | Y | | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | Y | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
The second possibility is that two adjacent edges are oriented correctly and the other two are not. Turn U so that the correctly-flipped edges are at UB and UL (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/_Y_/___/| +---+---+---+ | | | |
/_Y_/_Y_/___/ | | | | |\ +---+---+---+---+---+
/ / / /Y/| +---+---+---+ \ | | | Y | | |
+---+---+---+ /B| R | R | R | R |\ \ +---+---+---+---+---+
| | Y | |/B/| +---+---+---+G\ | | | Y | Y | | Y | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | Y | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
(13) R' U' F' U F R
The third possibility is that two opposite edges are oriented correctly and the other two are not. Turn U so that the correctly-flipped edges are at UF and UB (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/_Y_/___/| +---+---+---+ | | | |
/___/_Y_/___/ | | | | |\ +---+---+---+---+---+
/ / Y / /Y/| +---+---+---+ \ | | | Y | | |
+---+---+---+ /B| R | R | R | R |\Y\ +---+---+---+---+---+
| | | |/B/| +---+---+---+G\ | | Y | | Y | | Y | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | Y | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
(14) R' F' U' F U R
The fourth possibility is that all four edges are oriented incorrectly (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/___/___/| +---+---+---+ | | Y | |
/___/_Y_/___/ | | | Y | |\ +---+---+---+---+---+
/ / / /Y/| +---+---+---+ \ | | | | | |
+---+---+---+ /B| R | R | R | R |\Y\ +---+---+---+---+---+
| | Y | |/B/| +---+---+---+G\ | | Y | | Y | | Y | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | Y | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
Applying (14) flips the UF and UR edges. U2 moves these edges to UB and UL, allowing us to perform (13) and orient the remaining two edges.
---
All the yellow edges are now oriented such that the yellow stickers are adjacent to the yellow center. We now need to permute (swap around) the edges until they are completely solved.
Adjust the U layer until at least two edges are solved. In the examples below, we assume the yellow-orange edge is one of those two edges, but that won't always be the case.
There will be three possible permutations of the other edges.
The first permutation is that all four edges are solved (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/_Y_/___/| +---+---+---+ | | R | |
/_Y_/_Y_/_Y_/ | | | R | |\ +---+---+---+---+---+
/ / Y / /B/| +---+---+---+ \ | | | Y | | |
+---+---+---+ /B| R | R | R | R |\G\ +---+---+---+---+---+
| | O | |/B/| +---+---+---+G\ | | G | Y | Y | Y | B | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | Y | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | O | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
The second permutation requires swapping two adjacent edges. Rotate the entire cube in your hands so that the incorrect edges are in the UB and UL positions (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/_Y_/___/| +---+---+---+ | | G | |
/_Y_/_Y_/_Y_/ | | | G | |\ +---+---+---+---+---+
/ / Y / /B/| +---+---+---+ \ | | | Y | | |
+---+---+---+ /B| R | R | R | R |\R\ +---+---+---+---+---+
| | O | |/B/| +---+---+---+G\ | | R | Y | Y | Y | B | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | Y | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | O | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
Apply U, then perform:
(15) F2 U' R' L F2 L' R U' F2
The third permutation requires swapping two opposite edges. Rotate the entire cube in your hands so that the incorrect edges are in the UR and UL positions (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /___/_Y_/___/| +---+---+---+ | | R | |
/_Y_/_Y_/_Y_/ | | | R | |\ +---+---+---+---+---+
/ / Y / /G/| +---+---+---+ \ | | | Y | | |
+---+---+---+ /B| R | R | R | R |\B\ +---+---+---+---+---+
| | O | |/B/| +---+---+---+G\ | | B | Y | Y | Y | G | R
+---+---+---+B/ | | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | | | Y | | |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | | O | |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
Applying (15) changes the edges from the third permutation to the second permutation, with the UF and UR edges swapped. Rotate the entire cube in your hands so that the incorrect edges are in the UB and UL positions, then apply U and use (15) again to solve the edges.
At this point, all the edges of the cube are solved.
---
We need to orient the yellow corners correctly, without concern if they're in the correct place or not.
Sometimes a yellow corner will already be oriented correctly. This will appear as follows (UFR and DFR visible):
____________ F
U /___/_Y_/___/| +---+---+---+
/_Y_/_Y_/_Y_/ | | | O | |\
/ / Y / Y /B/| +---+---+---+ \
+---+---+---+ /B| R | O | O | O |\B\
| | O | |/B/| +---+---+---+B\ |
+---+---+---+B/B| | O | O | O |\B\|
| O | O | O |/B/ +---+---+---+B\B| R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
If any corners are incorrectly oriented, rotate the entire cube in your hands until one incorrectly-oriented corner is at UFR. The corner will be in one of two orientations.
The first orientation is that the yellow sticker is on the R face (UFR and DFR visible):
____________ F
U /___/_Y_/___/| +---+---+---+
/_Y_/_Y_/_Y_/ | | | O | |\
/ / Y / /B/| +---+---+---+Y\
+---+---+---+Y/B| R | O | O | O |\B\
| | O | |/B/| +---+---+---+B\ |
+---+---+---+B/B| | O | O | O |\B\|
| O | O | O |/B/ +---+---+---+B\B| R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
(16) R' D' R D R' D' R D
The second orientation is that the yellow sticker is on the F face (UFR and DFR visible):
____________ F
U /___/_Y_/___/| +---+---+---+
/_Y_/_Y_/_Y_/ | | | O | |\
/ / Y / /B/| +---+---+---+ \
+---+---+---+ /B| R | O | O | O |\B\
| | O | Y |/B/| +---+---+---+B\ |
+---+---+---+B/B| | O | O | O |\B\|
| O | O | O |/B/ +---+---+---+B\B| R
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_W_\_W_\_W_\B|
+---+---+---+ D \_W_\_W_\_W_\|
F
Apply (16) twice.
!!! NOTE !!!
After orienting the first yellow corner and before orienting the others, the bottom two equatorial layers and the white face will be messed up. DO NOT PANIC! As all the yellow corners are oriented, the bottom of the puzzle will fix itself--no need to solve anything a second time.
!!! NOTE !!!
Adjust the U layer until another incorrectly-oriented corner is in the UFR spot. Do NOT rotate the entire cube in your hands. Continue to apply (16) to each incorrectly-oriented corner until all four corners are correctly oriented.
Adjust the U layer so that the edges are solved again. After all four corners are oriented correctly, the cube will appear as follows (UFR and DBL):
____________ B
U /_Y_/_Y_/_Y_/| +---+---+---+
/_Y_/_Y_/_Y_/ | | | R | |\
/ Y / Y / Y /B/| +---+---+---+ \
+---+---+---+ /B| R | R | R | R |\G\
| | O | |/B/| +---+---+---+G\ |
+---+---+---+B/B| | R | R | R |\G\|
| O | O | O |/B/ +---+---+---+G\G| L
+---+---+---+B/ \_W_\_W_\_W_\G\|
| O | O | O |/ \_W_\_W_\_W_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
---
We're almost done! The last step is to permute the yellow corners in order to solve them.
There are five overall cases for the permutation of corners. The first case is that all corners are solved; two cases have one corner solved and three corners requiring permutation; and the final two cases have no corners solved.
In the cases that one corner is solved, the other three corners will need to be cycled. In the examples below, the yellow-orange-green corner is solved, but that won't always be the case.
The first case is that the other three corners will need to be cycled counterclockwise (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /_Y_/_Y_/_Y_/| +---+---+---+ | O | R | G |
/_Y_/_Y_/_Y_/R| | G | R | O |\ +---+---+---+---+---+
/ Y / Y / Y /B/| +---+---+---+B\ | B | Y | Y | Y | R |
+---+---+---+R/B| R | R | R | R |\G\ +---+---+---+---+---+
| O | O | B |/B/| +---+---+---+G\G| | G | Y | Y | Y | B | R
+---+---+---+B/B| | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | G | Y | Y | Y | R |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | O | O | B |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
(17) R' D' R U R' D R U R' D' R U2 R' D R
The second case is that the other three corners will need to be cycled clockwise (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /_Y_/_Y_/_Y_/| +---+---+---+ | B | R | B |
/_Y_/_Y_/_Y_/O| | B | R | B |\ +---+---+---+---+---+
/ Y / Y / Y /B/| +---+---+---+R\ | R | Y | Y | Y | O |
+---+---+---+G/B| R | R | R | R |\G\ +---+---+---+---+---+
| O | O | R |/B/| +---+---+---+G\G| | G | Y | Y | Y | B | R
+---+---+---+B/B| | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | G | Y | Y | Y | G |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | O | O | R |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
(18) R' D' R U2 R' D R U' R' D' R U' R' D R
In the cases that no corners are solved, either two pairs of adjacent corners will need to be swapped, or two pairs of opposite corners will need to be swapped.
In the first case, rotate the entire cube in your hands until the two pairs of corners to be swapped are UFR-UBR and UFL-UBL (UFR, DBL and U layer visible):
all corners swapped, case 1 (, then re-solve)
____________ B +---+---+---+
U /_Y_/_Y_/_Y_/| +---+---+---+ | G | R | B |
/_Y_/_Y_/_Y_/O| | B | R | G |\ +---+---+---+---+---+
/ Y / Y / Y /B/| +---+---+---+O\ | O | Y | Y | Y | O |
+---+---+---+R/B| R | R | R | R |\G\ +---+---+---+---+---+
| G | O | B |/B/| +---+---+---+G\R| | G | Y | Y | Y | B | R
+---+---+---+B/B| | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | R | Y | Y | Y | R |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | G | O | B |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
Apply (17) to solve the UBR corner. Rotate the entire cube in your hands until the solved corner is at UFL, then apply (18) to solve the remaining yellow corners.
In the second case, the cube will appear as below (UFR, DBL and U layer visible):
____________ B +---+---+---+
U /_Y_/_Y_/_Y_/| +---+---+---+ | O | R | O |
/_Y_/_Y_/_Y_/G| | O | R | O |\ +---+---+---+---+---+
/ Y / Y / Y /B/| +---+---+---+B\ | B | Y | Y | Y | G |
+---+---+---+G/B| R | R | R | R |\G\ +---+---+---+---+---+
| R | O | R |/B/| +---+---+---+G\B| | G | Y | Y | Y | B | R
+---+---+---+B/B| | R | R | R |\G\| +---+---+---+---+---+
| O | O | O |/B/ +---+---+---+G\G| L | B | Y | Y | Y | G |
+---+---+---+B/ \_W_\_W_\_W_\G\| +---+---+---+---+---+
| O | O | O |/ \_W_\_W_\_W_\G| | R | O | R |
+---+---+---+ D \_W_\_W_\_W_\| +---+---+---+
F F
Apply (17) to solve the UFR corner. Rotate the entire cube in your hands until the solved corner is at UFL, then apply (17) again to solve the remaining yellow corners.
At the point, all the yellow corners are solved, the yellow face is solved, the top equatorial layer is solved, all the corners are solved, and the entire cube is solved. Congratulations!
____________ B
U /_Y_/_Y_/_Y_/| +---+---+---+
/_Y_/_Y_/_Y_/B| | R | R | R |\
/ Y / Y / Y /B/| +---+---+---+G\
+---+---+---+B/B| R | R | R | R |\G\
| O | O | O |/B/| +---+---+---+G\G|
+---+---+---+B/B| | R | R | R |\G\|
| O | O | O |/B/ +---+---+---+G\G| L
+---+---+---+B/ \_W_\_W_\_W_\G\|
| O | O | O |/ \_W_\_W_\_W_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
An example solve using this method can be found below:
3x3x3 Layer-by-layer Example Solve
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[Last updated: 2023-04-20]