CSP
Cubeshape Parity
For this guide, I am assuming black top / white bottom and an otherwise standard color scheme.
- Orientation refers to the color on U or D (black or white),
- Color refers to the color on rest of the piece (green, orange, blue, or red), and
- Type refers to whether it is an edge or a corner.
- Orientation refers to the color on U or D (black or white),
- Color refers to the color on rest of the piece (green, orange, blue, or red), and
- Type refers to whether it is an edge or a corner.
Shapes
24 general shapes
29 total shapes (i.e. mirrored shapes count seperately)
How it Works:
- Purple: Starting position (start/continue tracing at this piece, going clockwise)
- Red: Odd-numbered edge positions (if it's the same type, include the purple piece)
- Cyan: Odd-numbered corner positions (if it's the same type, include the purple piece)
Keep in mind that these are the tracing positions that make the most sense to me, but if you don't like them, feel free to choose a new one. Just remember to check the solutions with that shape in them to see if the odd/even solutions switched or not!
- Purple: Starting position (start/continue tracing at this piece, going clockwise)
- Red: Odd-numbered edge positions (if it's the same type, include the purple piece)
- Cyan: Odd-numbered corner positions (if it's the same type, include the purple piece)
Keep in mind that these are the tracing positions that make the most sense to me, but if you don't like them, feel free to choose a new one. Just remember to check the solutions with that shape in them to see if the odd/even solutions switched or not!
0 Edges
Star
2 Edges
Pair
(Paired edges)
(Paired edges)
L
(Perpendicular edges)
(Perpendicular edges)
I
(Parallel edges)
(Parallel edges)
4 Edges
Scallop
Shield
Barrel
Square
Kite
Paw
(Pawn)
(Pawn)
Left Paw
Right Paw
Right Paw
Muffin
(Mushroom)
(Mushroom)
Fist
Left Fist
Right Fist
Right Fist
6 Edges
2-2-2
3-3
House
3-1-2
3-2-1
3-2-1
4-2
Left 4-2
Right 4-2
Right 4-2
4-1-1
5-1
Left 5-1
Right 5-1
Right 5-1
6
8 Edges
8
7-1
6-2
5-3
4-4
Tracing
Start your parity count at 0.
1. White Edge Color Parity
You are going to observe the first 3 white edges of the cubeshape (i.e. starting from the purple piece of the first layer listed in the case), and reduce it to 2.
If a color is followed by its opposite, remove the opposite.
If there are no opposite colors adjacent to each other, ignore the first color.
Consider the two remaining colors.
If they are Blue and Orange or Red and Green, +1 to parity count.
Otherwise, add nothing.
If a color is followed by its opposite, remove the opposite.
Example: Green, Blue, Red would be reduced to Green, Red.
When tracing, I usually think of nothing instead of the opposite color to make it easier.
So, I would think "Green, ..., Red", which reduces to Green, Red.
When tracing, I usually think of nothing instead of the opposite color to make it easier.
So, I would think "Green, ..., Red", which reduces to Green, Red.
If there are no opposite colors adjacent to each other, ignore the first color.
Example: Blue, Orange, Green would be reduced to Orange, Green.
When tracing, once I notice that Blue and Orange are not opposites, when I see Green is the last color (not the opposite of Orange), I forget about Blue, leaving me with only Orange, Green.
When tracing, once I notice that Blue and Orange are not opposites, when I see Green is the last color (not the opposite of Orange), I forget about Blue, leaving me with only Orange, Green.
Consider the two remaining colors.
If they are Blue and Orange or Red and Green, +1 to parity count.
Otherwise, add nothing.
2. Black Edge Color Parity
Same as above, but with the black edges.
3. White Corner Color Parity
Same as above, but with the white corners.
The color you should be considering is the counter-clockwisemost color on the corner.
The color you should be considering is the counter-clockwisemost color on the corner.
4. Black Corner Color Parity
Same as above, but with the black corners.
5. Edge Position Parity
Consider the orientation of the edges in the odd-numbered edge positions (i.e the red pieces), including the purple piece if it is an edge.
If there are an odd amount of black edges in these positions, +1 to parity count.
Otherwise, add nothing.
If there are an odd amount of black edges in these positions, +1 to parity count.
Otherwise, add nothing.
6. Corner Position Parity
Same as above, but instead consider the orientation of the corners in the odd-numbered corner positions (i.e the cyan pieces), including the purple piece if it is a corner.
Once you finish those 6 steps, your parity count being odd or even (i.e. the parity of the number) determines the solution!
Solution
65 general cases
78 distinct cases (i.e. horizontally mirrored cubeshapes with different solutions count separately)
How it Works:
For the general cubeshape X/Y, start tracing from the starting position (i.e. the purple piece) of X, even if it is on the bottom layer.
If a case is in an orange box you will have to +1 extra to your parity count before determining your solution.
These solutions are written as reductions to 3-slicers (which you should already know optimally) and should work from any angle.
The cases below are listed in order of most to least probable, according to Hashtag Cuber's website. It is recommended to learn them in this order, but I also have my own order of learning cases which is only slightly different (where cases and case sets are roughly organized by similarity to each other, probability, and simplicity):
For the general cubeshape X/Y, start tracing from the starting position (i.e. the purple piece) of X, even if it is on the bottom layer.
Example:
For the case 8/Star, start tracing from the purple piece of the 8.
If it is on the bottom, I like to do a z2 rotation and trace from there.
If a case is in an orange box you will have to +1 extra to your parity count before determining your solution.
These solutions are written as reductions to 3-slicers (which you should already know optimally) and should work from any angle.
The cases below are listed in order of most to least probable, according to Hashtag Cuber's website. It is recommended to learn them in this order, but I also have my own order of learning cases which is only slightly different (where cases and case sets are roughly organized by similarity to each other, probability, and simplicity):
Left 4-2/Pair
Right 4-2/Pair
Odd:
- Shield/Shield
- Solve
- Shield/Shield
- Solve
Even:
- Scallop/Scallop
- Solve
- Scallop/Scallop
- Solve
4-1-1/Pair
Odd:
- Opposite Paw/Paw (by connecting Pair to 4-1-1's clockwise-most L) - Solve
- Opposite Paw/Paw (by connecting Pair to 4-1-1's clockwise-most L) - Solve
Even:
- Opposite Paw/Paw (by connecting Pair to 4-1-1's counterclockwise-most L) - Solve
- Opposite Paw/Paw (by connecting Pair to 4-1-1's counterclockwise-most L) - Solve
3-3/Pair
Odd:
- Shield/Muffin (by connecting 3-3's I to the Pair's clockwise-most edge) - Scallop/Kite
- Solve
- Shield/Muffin (by connecting 3-3's I to the Pair's clockwise-most edge) - Scallop/Kite
- Solve
Even:
- Shield/Muffin (by connecting 3-3's I to the Pair's counterclockwise-most edge) - Scallop/Kite
- Solve
- Shield/Muffin (by connecting 3-3's I to the Pair's counterclockwise-most edge) - Scallop/Kite
- Solve
House/Pair
Odd:
- House/L
- Shield/Square
- Solve
- House/L
- Shield/Square
- Solve
Even:
- 5-1/Pair
- Scallop/Kite
- Solve
- 5-1/Pair
- Scallop/Kite
- Solve
Scallop/Shield
Odd:
- 4-2/Pair (by slicing across Shield's counterclockwise-most Pair) - Scallop/Scallop
- Solve
- 4-2/Pair (by slicing across Shield's counterclockwise-most Pair) - Scallop/Scallop
- Solve
Even:
- 4-2/Pair (by slicing across Shield's clockwise-most Pair) - Scallop/Scallop
- Solve
- 4-2/Pair (by slicing across Shield's clockwise-most Pair) - Scallop/Scallop
- Solve
Scallop/Left Fist
Scallop/Right Fist
Odd:
- Left 5-1/Pair
- Scallop/Kite
- Solve
- Left 5-1/Pair
- Scallop/Kite
- Solve
Even:
- Right 5-1/Pair
- Scallop/Kite
- Solve
- Right 5-1/Pair
- Scallop/Kite
- Solve