# Fewest Moves To Solve Every 5x5x5 Center Arrangement for 2 Against 2



## unsolved (Mar 9, 2016)

My program finally finished solving the shortest solutions for every one of the 328 different ways to arrange 2 unsolved centers on the Top face against 2 unsolved centers of the Front face. It did each of the 32 cases for 1 vs. 1 first. It is now working on the 3 vs. 3 cases.

I'm not sure if this is the correct place for the announcement.

All solutions are 13 moves or less.

If anyone would like to see a specific solution, I can look up the result instantly now.


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## G2013 (Mar 9, 2016)

It's interesting, do you plan to name this alg-array after something?
Also, it's 2 unsolved center pieces (out of the 8 which are movable of each 5x5 center) from the U face and the F face?


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## unsolved (Mar 9, 2016)

G2013 said:


> It's interesting, do you plan to name this alg-array after something?
> Also, it's 2 unsolved center pieces (out of the 8 which are movable of each 5x5 center) from the U face and the F face?



I don't think it's in need of a name. I did index each of the positions for ease of reference.

If VisualCube was up I could show the diagrams. But here is a sample ASCII version from the text file it created (shown is the final position).


```
Omnia Obtorquebantur 5x5x5 Version 1.3.7, February 25, 2016. Copyright 2015 by Ed Trice.



                                   TOP
                                   -------------------------
                                  |####|####|####|####|####|
                                   -------------------------
                                  |####|####|####|####|####|
                                   -------------------------
                                  |####|####|####|####|####|
                                   -------------------------
                                  |####|####|OOOO|OOOO|####|
                                   -------------------------
                                  |####|####|####|####|####|
                                   -------------------------
      LEFT                         FRONT                        RIGHT                        BACK
      -------------------------    -------------------------    -------------------------    -------------------------
     |&&&&|&&&&|&&&&|&&&&|&&&&|   |OOOO|OOOO|OOOO|OOOO|OOOO|   |XXXX|XXXX|XXXX|XXXX|XXXX|   |^^^^|^^^^|^^^^|^^^^|^^^^|
      -------------------------    -------------------------    -------------------------    -------------------------
     |&&&&|&&&&|&&&&|&&&&|&&&&|   |OOOO|OOOO|OOOO|OOOO|OOOO|   |XXXX|XXXX|XXXX|XXXX|XXXX|   |^^^^|^^^^|^^^^|^^^^|^^^^|
      -------------------------    -------------------------    -------------------------    -------------------------
     |&&&&|&&&&|&&&&|&&&&|&&&&|   |OOOO|OOOO|OOOO|OOOO|OOOO|   |XXXX|XXXX|XXXX|XXXX|XXXX|   |^^^^|^^^^|^^^^|^^^^|^^^^|
      -------------------------    -------------------------    -------------------------    -------------------------
     |&&&&|&&&&|&&&&|&&&&|&&&&|   |OOOO|OOOO|####|####|OOOO|   |XXXX|XXXX|XXXX|XXXX|XXXX|   |^^^^|^^^^|^^^^|^^^^|^^^^|
      -------------------------    -------------------------    -------------------------    -------------------------
     |&&&&|&&&&|&&&&|&&&&|&&&&|   |OOOO|OOOO|OOOO|OOOO|OOOO|   |XXXX|XXXX|XXXX|XXXX|XXXX|   |^^^^|^^^^|^^^^|^^^^|^^^^|
      -------------------------    -------------------------    -------------------------    -------------------------

                                   BOTTOM
                                   -------------------------
                                  |~~~~|~~~~|~~~~|~~~~|~~~~|
                                   -------------------------
                                  |~~~~|~~~~|~~~~|~~~~|~~~~|
                                   -------------------------
                                  |~~~~|~~~~|~~~~|~~~~|~~~~|
                                   -------------------------
                                  |~~~~|~~~~|~~~~|~~~~|~~~~|
                                   -------------------------
                                  |~~~~|~~~~|~~~~|~~~~|~~~~|
                                   -------------------------

 
  Solutions To:   [02 vs. 02 Position # 0328]: Top Center Cubes 18-19 vs. Front Center Cubes 18-19
 
  Solution [0001] =  r  m' U  l'  [inside 06-TFS] --->  U' m  r' U  l  U'  @ 000000000217475 solved state checks [time = < 1 second]
  Solution [0002] =  r' m  F  l   [inside 06-TFS] --->  F' m' r  F  l' F'  @ 000000000268021 solved state checks [time = < 1 second]
```


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## G2013 (Mar 9, 2016)

Then it was just what I was thinking 

Anyway, that case is an easy one. 12 moves isn't it?


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## unsolved (Mar 10, 2016)

G2013 said:


> Then it was just what I was thinking
> 
> Anyway, that case is an easy one. 12 moves isn't it?



In reading the solution left to right, there are 10 moves. The program only had to generate 4 of them. Applying those 4 moves to the scrambled cube yielded a result in its database of 6-move solutions. To the left of "inside 06-TFS" is the "6 Turns From Solved" solution it encountered. For the price of looking up the result, it saves itself from having to generate 6 additional moves. This makes the program about 2.6 billion times faster.

Here is the solution in SiGN notation:

2R 3R U 2L' U' 3R' 2R' U 2L U' 

None of the arrangements require more than 13 moves. Here is the entry that was the hardest for the program to solve:

3R U' 2R U 3R' U' 2U2 2R' U2 2R 2U2 2R' U'


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