Difference between revisions of "3-Color Method"

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==Steps==
 
==Steps==
There are 2 steps for a 3-Color Cube and 4 steps for a 6-Color Cube with the same [https://mfeather1.github.io/3ColorCube/quick.html list of solving sequences] (for detailed explanation see the [[3-Color_Method#External_Links|External Links]] section below).
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There are 2 steps for a 3-Color Cube and 4 steps for a 6-Color Cube with the same [https://mfeather1.github.io/3ColorCube/quick.html list of solving sequences] (for detailed explanation see the [[3-Color_Method#Example_Solves|Example Solves]] and [[3-Color_Method#External_Links|External Links]] sections below).
  
 
'''Solving the corners'''
 
'''Solving the corners'''

Revision as of 21:44, 8 March 2021

3-Color method
3-Color-Method.png
Information about the method
Proposer(s): Michael Feather
Proposed: 1980
Alt Names:
Variants:
No. Steps: 4
No. Algs: 12
Avg Moves: 75 ± 2
Purpose(s):


The 3-Color Method is a unique solving method developed completely independently by Michael Feather in 1980. The method name is derived from the 3-Color Cube, which is a Rubik's Cube having tri-color scheme that uses the same color on opposite faces.

Steps

There are 2 steps for a 3-Color Cube and 4 steps for a 6-Color Cube with the same list of solving sequences (for detailed explanation see the Example Solves and External Links sections below).

Solving the corners

1. Orient corners. Either think of the puzzle as a 3-Color Cube (i.e. Red=Orange, Blue=Green, Yellow=White in case of BOY color scheme) and solve corners as such, or think of the puzzle as a 6-Color Cube and orient all corner stickers in a way that they are matching either the center color or that of the opposite face.

2. Permute corners on a 6-Color Cube, three possible cases can be reached using half turns only:

2a. Corners can be solved in both layers.

2b. Corners can be solved in one layer, diagonal swap of corners is required in the other layer.

2c. Corners can be solved in neither layers.

Convert 2b or 2c to 2a using an algorithm (Michael Feather calls them Waterwheel Sequence for 2b and Parallel Sequence for 2c), then continue by solving the edges (or apply 2a first and continue by solving the edges).

Solving the edges

3. Orient edges. Either think of the puzzle as a 3-Color Cube and solve edges as such, or think of the puzzle as a 6-Color Cube and orient all edge stickers in a way that they are matching either the center color or that of the opposite face.

Use only half turns and/or cube rotations as setup moves between all solving sequences.

After finishing this step, a 3-Color Cube will be solved and a 6-Color Cube will be solvable using half turns only.

4. On a 6-Color Cube, restore corners and permute edges.

Pros

  • Low number of algorithms
  • Short algorithms; average number of moves per algorithm: 5.7 in STM
  • Room for improvement of a move count; current average move count in STM for step 1 ~ 14, for step 2 ~ 9 (or ~ 12 with applying 2a), for step 3 ~ 31, for step 4 ~ 17

Cons

  • Thinking of a 6-Color Cube as a 3-Color Cube could seem rather unintuitive at first
  • It's not always possible to exactly match the setup for a solving sequence
  • Not suitable for speed solving

Example Solves

Similarities with Human Thistlethwaite Algorithm (HTA)

While the 3-Color Method is very different from HTA, there are some obvious similarities in that both start by solving as a 3-Color Cube and both finish by reaching a configuration that can be solved with half turns only. The 3-Color Method can be modified to work a bit more like HTA by doing the following.

After solving the corners on two opposite faces (like the 3-Color Starter Cube), instead of solving the corners on the remaining faces, solve the edges on the two faces with the solved corners.

An advantage of doing it this way is that after solving the corners & edges on two opposite faces (as 3-Color Cube) the setups for the 3-color edge sequences can always be matched exactly when solving the rest of the cube, no need to make partial matches where only some of the misplaced facelets/stickers get fixed. Another advantage is that the cases in which no misplaced facelets can be fixed are avoided.

One other difference is with the solve order of 6-color corners in relation to 3-color edges. When solving this way, the corners should only be solved after the edges otherwise the above advantages have exceptions.

See also

External Links