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Introduction
Sarah's Advanced consists of two steps:
What do the 4-movers do?
Both sledge and hedge swap the U and F centers, and the R and L centers. Since they have the same effect on the centers, they are interchangeable when considering the centers solution, so the only reason to use one over the other will be their differing effects on the corners. Sledge twists the front two corners counterclockwise and the back two corners clockwise, whereas hedge does the opposite.
These are the cases that sledge and hedge solve, respectively.
Solving the centers
A non-U center that needs to move to an adjacent location not in U is called a bad center, because such a center cannot be solved in one 4-mover, and a single 4-mover can only eliminate one bad center. Therefore, the number of 4-movers required to solve the centers is at least the number of bad centers plus one.
To solve the centers, first eliminate all the bad centers. The only way to eliminate a bad center is to place it in the front and do a 4-mover to bring it to the top. However, do not eliminate a bad center if the center on the top is the opposite color, because doing a 4-mover will create another bad center. If this is the case, eliminate a different bad center first. (You can completely ignore that 4-movers swap the R and L centers during this step if you're not thinking ahead. At this stage, the only relevant center swap is the U-F center swap.)
Once all the bad centers are eliminated, you can end up with one of three centers cases: Single 4-mover (U-F and R-L swap), U-perm (U -> F -> B -> U cycle), and H-perm (L-R and F-B swap).
From left to right: Single 4-mover, U perm (4-mover y2 4-mover), H perm (4-mover y2 U-perm). You will encounter H perm very rarely, that is, only when solving the layer immediately results in it.
Solving the corners with the centers
How do you determine which 4-movers to use in the centers solution such that the corners also get solved?
This table shows which corner cases can be reached by doing a 4-mover and then a y/y' rotation starting from each case:
* For H-perm and vertical U-perm, the next sledge will be a y2 away. Therefore, what would normally result in Misaligned Pi actually results in Aligned Pi and vice versa. Choose Option 1 in these cases.
It turns out that to maximize the chances of solving the corners with the centers, or at the very least, ending with a double sledge, choose the 4-mover that corresponds with Option 1 while there are at least two bad centers, and choose Option 2 otherwise.
To determine which 4-mover to use to achieve the desired result, note that the direction of the first move of the 4-mover is the direction that the front two corners will twist. For example, if you have a Peanut case where the FL corner needs to twist clockwise, but you want to get to Aligned Pi, the first move should go counterclockwise, which means you should do a sledge.
Twisting the corners
Usually, the corners will be solved with the centers. If they aren't, all that is left will be to twist the corners in place. There are two such cases:
Left: Pure Pi - set the headlights on left and do a double sledge.
Right: Pure Peanut - place the corner that needs to twist CCW in UFL or UFR then execute double sledge to reduce to Pure Pi
Special cases (optional)
Example L2L with detailed explanations:
Example 1 - One bad center
Example 2 - Two bad centers
Example 3 - Three bad centers
Example 4 - H perm centers
Example 5 - Pure twist ending
Introduction
Sarah's Advanced consists of two steps:
- Solve a layer
- Solve the rest (134 cases)
What do the 4-movers do?
Both sledge and hedge swap the U and F centers, and the R and L centers. Since they have the same effect on the centers, they are interchangeable when considering the centers solution, so the only reason to use one over the other will be their differing effects on the corners. Sledge twists the front two corners counterclockwise and the back two corners clockwise, whereas hedge does the opposite.
These are the cases that sledge and hedge solve, respectively.
Solving the centers
A non-U center that needs to move to an adjacent location not in U is called a bad center, because such a center cannot be solved in one 4-mover, and a single 4-mover can only eliminate one bad center. Therefore, the number of 4-movers required to solve the centers is at least the number of bad centers plus one.
To solve the centers, first eliminate all the bad centers. The only way to eliminate a bad center is to place it in the front and do a 4-mover to bring it to the top. However, do not eliminate a bad center if the center on the top is the opposite color, because doing a 4-mover will create another bad center. If this is the case, eliminate a different bad center first. (You can completely ignore that 4-movers swap the R and L centers during this step if you're not thinking ahead. At this stage, the only relevant center swap is the U-F center swap.)
Once all the bad centers are eliminated, you can end up with one of three centers cases: Single 4-mover (U-F and R-L swap), U-perm (U -> F -> B -> U cycle), and H-perm (L-R and F-B swap).
From left to right: Single 4-mover, U perm (4-mover y2 4-mover), H perm (4-mover y2 U-perm). You will encounter H perm very rarely, that is, only when solving the layer immediately results in it.
Solving the corners with the centers
How do you determine which 4-movers to use in the centers solution such that the corners also get solved?
This table shows which corner cases can be reached by doing a 4-mover and then a y/y' rotation starting from each case:
| Starting Corners Case | Option 1 | Option 2 |
| Oriented (L5C) | Misaligned Pi* | |
| Misaligned Pi (headlights on F/B) | Peanut | |
| Peanut (2 unsolved corners) | Peanut | Aligned Pi* |
| Aligned Pi (Headlights on L/R) | Misaligned Pi* | Oriented |
* For H-perm and vertical U-perm, the next sledge will be a y2 away. Therefore, what would normally result in Misaligned Pi actually results in Aligned Pi and vice versa. Choose Option 1 in these cases.
It turns out that to maximize the chances of solving the corners with the centers, or at the very least, ending with a double sledge, choose the 4-mover that corresponds with Option 1 while there are at least two bad centers, and choose Option 2 otherwise.
To determine which 4-mover to use to achieve the desired result, note that the direction of the first move of the 4-mover is the direction that the front two corners will twist. For example, if you have a Peanut case where the FL corner needs to twist clockwise, but you want to get to Aligned Pi, the first move should go counterclockwise, which means you should do a sledge.
Twisting the corners
Usually, the corners will be solved with the centers. If they aren't, all that is left will be to twist the corners in place. There are two such cases:
Left: Pure Pi - set the headlights on left and do a double sledge.
Right: Pure Peanut - place the corner that needs to twist CCW in UFL or UFR then execute double sledge to reduce to Pure Pi
Special cases (optional)
- If there are three bad centers, there are two options to eliminate a bad center. Choose the option that solves the current U center, because this requires four 4-movers and the other option requires five.
- If there are one or two bad centers and the corners are solved, Sarah's beginner method is more efficient: If the U center is unsolved, solve it by placing it in the back and doing a U perm. Then, rotate and finish with a U perm.
- For cases with 2 bad centers, an unsolved U center, and Aligned Pi, Sarah's intermediate method is more efficient: Place the U center in the front and do a 4-mover that oriented the corners. Then, rotate and finish with a U perm.
- If there are only three unsolved centers all around the same corner, you can rotate such that the U and F centers are opposite and do a 4-mover. Both the standard centers solution and this solution require three 4-movers, but for the Pi cases, only one of them also solves the corners in three 4-movers.
- If the centers form a U-perm where the top center is solved, there are two options to eliminate a bad center. The option that places a solved center in the back requires four 4-movers, and the option that places it on the side requires three. Both options are sometimes useful.
Example L2L with detailed explanations:
Example 1 - One bad center
Example 2 - Two bad centers
Example 3 - Three bad centers
Example 4 - H perm centers
Example 5 - Pure twist ending
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