Efficient 3-color cube example solve thread

[bcube]

Hi,

the Rubik's Cube can be simplified by using only 3 colors instead of usual 6 colors. Generally, opposite faces would share the same color. I am wondering whether method developers can come up with a linear method which would consistently solve the 3-color cube in 20 moves or less (although 25 moves seem to be more realistic)? Then I would consider this thread a success. Feel free to post your example solves if a solution is at most 30 moves long in STM.

Scramble: F2 R U2 R U' L F U L' U2 F' L' B2 F' L' F' U' D F D' L B2 D R2 F'



Roux method:
1-5: First block
6-15: Second block
16-24: CMLL
25-30: LSE

The same solution on a 6-color cube:



Next scramble: D B U R D R B2 L' B2 F2 U' L' U2 B D F R B' D U

 

[Deleted member 36445]

human thwistlewaite/kociemba or domino reduction?

there must be a super simple OO way to reach that state.

check this: https://www.speedsolving.com/wiki/index.php?title=Domino_Reduction

 

[Silky]

human thwistlewaite/kociemba or domino reduction?

there must be a super simple OO way to reach that state.

check this: https://www.speedsolving.com/wiki/index.php?title=Domino_Reduction

I think their looking for a human version of Feather's Algorithm. DR/HTR is obviously a subset of this so it would be an expansion on those ideas. I believe you would need to come up with a system of solving parity while finishing from a 3-colour state. HTR is basically solving this parity beforehand - at least to my understanding.

 

[bcube]

Next scramble: D B U R D R B2 L' B2 F2 U' L' U2 B D F R B' D U

HTA method, kind of:
1-4: EO
5-7: placing edges
8-21: orienting corners
22-24: solving corners
25-29: solving edges

Next scramble: B' L R' B F' L2 R U' R B2 U' D2 B U B L' R2 B' R L D2 F' L2 R' F

I think their looking for a human version of Feather's Algorithm. DR/HTR is obviously a subset of this so it would be an expansion on those ideas. I believe you would need to come up with a system of solving parity while finishing from a 3-colour state. HTR is basically solving this parity beforehand - at least to my understanding.

Actually, I am only looking for an efficient method for the 3-color cube (i.e. a simplified Rubik´s cube). No 6-color cube involved.

human thwistlewaite/kociemba or domino reduction?

there must be a super simple OO way to reach that state.

By a linear method I meant a method only going forward concerning solving. I can think of either a simple method with a high move count, or a method with a very low move count which needs going back and forth (using NISS, checking different EO/DR, or using other techniques from FMC).

 

[bcube]

@crystalcuber, as a cuber having experience with the ZZ, Roux and RUbar methods, can you please make a comparison/estimate regarding the move count in STM for these methods being optimized to solve a 3-color cube?

I am very interested in the RUbar method being optimized for a 3-color cube (and how can method steps be simplified), could you please make an example solve?

 

[bcube]

Next scramble: B' L R' B F' L2 R U' R B2 U' D2 B U B L' R2 B' R L D2 F' L2 R' F

This method:
1-6: EO
7-12: CO (7-8: orienting 3 red corners on one side, then orienting remaining corners on the other side while preserving EO - avoid F/F' and B/B' moves by making E/E' moves and y/y' cube rotation)
13-15: solving 2 E-slice edges while preserving CO
16-20: solving remaining 2 E-slice edges while preserving CO
21-24: solving edges
25-27: solving corners


Next scramble: L R2 U L F' U' B2 L R2 U2 F U2 L2 B2 R2 F L' B' D B D2 R' U D' R'

 

[bcube]

Next scramble: L R2 U L F' U' B2 L R2 U2 F U2 L2 B2 R2 F L' B' D B D2 R' U D' R'

Corners-first method:
1-2: orienting blue corner stickers
3-5: orienting red corner stickers
6-8: orienting UL & UR edges
9-12: orienting UL & UR edges
13-17: orienting UL & UR edges
18-21: solving edges in top and bottom layer
22-28: solving edges in E-slice

Next scramble: D F' B U' D' L' B L2 B D2 B2 D B2 U2 R' D L B' F U' L2 D2 R' D2 F'

 

[bcube]

Next scramble: D F' B U' D' L' B L2 B D2 B2 D B2 U2 R' D L B' F U' L2 D2 R' D2 F'

My first FMC attempt ever, it took me 30 minutes (only 1 virtual cube was used, paper & pen were not used)

1-4: EO
5-10: DR
11-14: orienting red corner stickers (normal continuation would be D2 L)
14: realizing F2 is leading to a shorter finish
15-17: finish

Next scramble: R D2 L' D2 F2 U2 D2 L2 D2 F2 B2 U' F2 B2 L' R U' R' U' L2 F2 U2 L F2 D

 

[bcube]

Next scramble: R D2 L' D2 F2 U2 D2 L2 D2 F2 B2 U' F2 B2 L' R U' R' U' L2 F2 U2 L F2 D

This method:
1-2: orienting red corner stickers
3: matching setup
4-6: applying sequence
7-8: matching setup
9-11: applying sequence
12-13: orienting blue corner stickers (matching setup and applying sequence would be L L2 U2 L)
14: matching setup
15-17: applying sequence
18: adjusting L layer

Next scramble: L F L2 D' U L R2 F2 B' U' R' D R L' D2 B' R' B2 F U' D2 R2 U' B U2

---

I made a little research on what Human Kociemba method refers to. Thom Barlow came up with that term in 2010. He later changed the name to Redux, and in 2011 changed the name again to Actual Human Kociemba. They are all the same, the intermediate state being a solved 3-color cube. Since Thom was a Roux user, he used to use the Roux method to get to that intermediate state (see example solve #1 in this thread or the video below). A 3-color cube reduction is known at least since 1980.

 

[bcube]

Next scramble: L F L2 D' U L R2 F2 B' U' R' D R L' D2 B' R' B2 F U' D2 R2 U' B U2

Method: God´s algorithm (hopefully)



Next scramble: R2 D2 B2 U2 R2 U2 B D2 F R2 B2 R' B2 R' D B' F D L' F2

 

[bcube]

Next scramble: R2 D2 B2 U2 R2 U2 B D2 F R2 B2 R' B2 R' D B' F D L' F2

Method: God´s algoritm (hopefully)



Next scramble: U L2 B2 U2 F2 D B2 L2 U' L2 U2 R' F' L D2 L F L D F' R2

 

[bcube]

Next scramble: U L2 B2 U2 F2 D B2 L2 U' L2 U2 R' F' L D2 L F L D F' R2

1-4: yellow faces
5-8: red faces

Next scramble: B' U R2 B R2 F' B' U2 R D B2 D L2 B2 L2 B2 U R2 D'

 

[Renslay]

Next scramble: B' U R2 B R2 F' B' U2 R D B2 D L2 B2 L2 B2 U R2 D'

I hope I'm doing this right.



Next: U' L' R' B2 R2 F2 L B2 R' F2 U2 R U' L2 D' F2 L2 F' U' L'

 

[bcube]

I hope I'm doing this right.

Looks right to me . What method did you use? Must have been some 6-color based one as I can solve your scramble with just 8 moves (5 moves for yellow faces, 3 moves for blue faces).

Next: U' L' R' B2 R2 F2 L B2 R' F2 U2 R U' L2 D' F2 L2 F' U' L'

1-15: yellow faces
16-18: solving corners
19-21: solving 4 edges
22-26: solving 2 edges

Next scramble: R' F2 L' D2 L' U2 L F2 L2 D2 B2 U' R B F2 D2 L2 D' L' R D2

 

[bcube]

Next scramble: R' F2 L' D2 L' U2 L F2 L2 D2 B2 U' R B F2 D2 L2 D' L' R D2

1-5: white/yellow faces
6-9: green/blue faces

Next scramble: D' L2 R2 U2 F2 D' L2 D R2 D L2 F R2 U B F' L' F R' B' F2

 

[Renslay]

1-5: white/yellow faces
6-9: green/blue faces

Next scramble: D' L2 R2 U2 F2 D' L2 D R2 D L2 F R2 U B F' L' F R' B' F2

To me it shows a 6-colored cube.

Also, what does it depend on whenever you solve a 3-colored 3x3 or 2x2?

 

[bcube]

Next scramble: D' L2 R2 U2 F2 D' L2 D R2 D L2 F R2 U B F' L' F R' B' F2

1-4: red/orange faces
5-6: blue/green faces
switching to 6-color cube
7-8: HTR finish

Next scramble: F2 U2 F2 L2 F2 D' F2 U' R2 B2 U L' B' U' F' U R D R2 F D'

Since God´s number for 3-color 2x2x2 cube is 9, it´s nice to see I seem to find sub God´s number solution most of the time (if that makes sense)

To me it shows a 6-colored cube.

I figured that´s the way how the guys saw it back in 1980s and how most of today´s cubers can simulate a 3-color cube. For instance, I don´t own a physical 3-color cube at all. What you see as an end-state still represents a solved 3-color cube.

Also, what does it depend on whenever you solve a 3-colored 3x3 or 2x2?

There are no rules regarding scrambles and cubes. Feel free to solve any cube size you want with any scramble you want. If you like Twizzle as a simulator, go ahead and use that if you want - there is no simulator limitation either.
Personally, I solve whatever cube size I like more at the moment

 

[bcube]

Next scramble: F2 U2 F2 L2 F2 D' F2 U' R2 B2 U L' B' U' F' U R D R2 F D'

1-4: yellow faces
5-8: red faces

Next scramble: D2 R' D2 R' B2 F2 R F2 D2 U2 L' F D2 F D U' B U2 B2 D'

Since God´s number for 3-color 2x2x2 cube is 9, it´s nice to see I seem to find sub God´s number solution most of the time (if that makes sense)

Not so fast, me. It is probably caused by a poor quality of scrambles when applying a 6-color 3x3x3 scrambling sequence to a 3-color 2x2x2 cube.

 

[bcube]

Next scramble: D2 R' D2 R' B2 F2 R F2 D2 U2 L' F D2 F D U' B U2 B2 D'

1-3: white/yellow faces
4-8: blue/green faces (3-color cube solved)
switching to 6-color cube
9-18: half-turn reduction

Next scramble: F2 D2 F2 L2 B' R2 B D2 F' D2 L2 D' L R' B' F' D' U B L2 D'

 

[bcube]

Next scramble: F2 D2 F2 L2 B' R2 B D2 F' D2 L2 D' L R' B' F' D' U B L2 D'

1-4: blue/green faces
5-9: red/orange faces (3-color cube solved)
switching to 6-color cube
10-12: HTR finish

Next scramble: U B' L' U' D L2 B' R2 F2 B L D2 F D2 B R2 F B2 R2 L2 F'