# Every Possible 5x5x5 Center Alg Solved

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#### unsolved

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I wrote code to solve every possible center exchange between two adjacent faces and two opposite faces on the 5x5x5 for those who use the Reduction Method.

Example: Every trade of 1 center on the top face vs. 1 center on the front face, every trade of 1 center on the top face vs. 1 center on the bottom face, 2 against 2, 3 against 3...8 against 8.

The Algs do not disturb any other centers, other than the ones being solved.

The question is: How do I organize it and make it available? Right now it's just a text file of ASCII diagrams and the solutions to go along with it.

Anyone with 8 GB of RAM can run the program as well.

#### cmhardw

I wrote code to solve every possible center exchange between two adjacent faces and two opposite faces on the 5x5x5 for those who use the Reduction Method.

Example: Every trade of 1 center on the top face vs. 1 center on the front face, every trade of 1 center on the top face vs. 1 center on the bottom face, 2 against 2, 3 against 3...8 against 8.

The Algs do not disturb any other centers, other than the ones being solved.
Do you mean that on an otherwise solved cube that there does not appear to be any other change to the centers? For the cases that swap one center from each of two faces, swapping exactly two centers in either center orbit would have permutation parity changing effects on other piece orbits. 3 swapping with 3 cases should also have the same issue.

The question is: How do I organize it and make it available? Right now it's just a text file of ASCII diagrams and the solutions to go along with it.

Anyone with 8 GB of RAM can run the program as well.
I think ASCII is fine, as long as you think it's readable. Thanks for doing this, I'd be curious to look through these cases.

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#### AlexMaass

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maybe just organize them by how many moves it takes to optimally solve the case? so easiest cases first to hardest cases last

#### unsolved

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This might explain it better. Here is a case of 5 vs. 5 from the top/front. All other centers are preserved while these 10 centers get to the correct faces. Edges/corners are ignored because this is the first stage of reduction.

https://alg.cubing.net/?type=alg&puzzle=5x5x5&alg=U_2R_U-_3R_U_3R-_U-_2R2_F-_2R

And a short video clip...

[video]https://youtu.be/reN8RN9EsxM[/video]

maybe just organize them by how many moves it takes to optimally solve the case? so easiest cases first to hardest cases last
Amazingly, none took longer than 11 moves. Most were 9 and 10 moves and some much shorter.

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#### 00

##### Member
Amazingly, none took longer than 11 moves. Most were 9 and 10 moves and some much shorter.
What are all of the 11 move cases?

#### unsolved

##### Member
The first one in the text file is for a 3 vs. 3 case, top/front exchange:

2R U2 2L' U 2R' 3F R2 3F' 2L2 F 2L'

https://alg.cubing.net/?type=alg&puzzle=5x5x5&alg=2R_U2_2L-_U_2R-_3F_R2_3F-_2L2_F_2L-

And for a 4 vs. 4 case:

2R 3R U 3R' U' 2R2 F 2L 2R F 2L'

https://alg.cubing.net/?type=alg&puzzle=5x5x5&alg=2R_3R_U_3R-_U-_2R2_F_2L_2R_F_2L-

A 5 vs. 5 case:

2R U 2R' U2 2L' 3F U2 3F' 2L2 F 2L'

https://alg.cubing.net/?type=alg&puzzle=5x5x5&alg=2R_U_2R-_U2_2L-_3F_U2_3F-_2L2_F_2L-

A 6 vs. 6 case:

2R U2 2R2 2U' 3R' 2D R2 2D' 3R 2U 2R

https://alg.cubing.net/?type=alg&puzzle=5x5x5&alg=2R_U2_2R2_2U-_3R-_2D_R2_2D-_3R_2U_2R

Edit: This is too laborious to do on my iPhone, but you get the idea.

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