5×5 L2C: Does anyone know an algorithm for this configuration?

[Skywalker2026]

Hi everyone,

I have been studying the last two centers (L2C) of the 5×5 cube and came across the following configuration.

Orange center
OOO
OOO
OOG
Green center
GGG
GGO
GGG
For convenience, I refer to this as a BM configuration, since the only misplaced pieces are the Bottom (B) piece of the right column on the orange center and the Middle (M) piece of the right column on the green center.
Similarly, if the misplaced piece on the green center were the Top (T) piece instead of the middle piece, I would refer to that configuration as BT.
Does anyone know a direct algorithm for solving this L2C case?
Alternatively,

• Is this BM configuration known to be unreachable?
• Has anyone seen it discussed in the literature or existing methods?

Any references or insights would be greatly appreciated.

Thank you!

 

[Martyt7777]

Hi everyone,

I have been studying the last two centers (L2C) of the 5×5 cube and came across the following configuration.

Orange center
OOO
OOO
OOG
Green center
GGG
GGO
GGG
For convenience, I refer to this as a BM configuration, since the only misplaced pieces are the Bottom (B) piece of the right column on the orange center and the Middle (M) piece of the right column on the green center.
Similarly, if the misplaced piece on the green center were the Top (T) piece instead of the middle piece, I would refer to that configuration as BT.
Does anyone know a direct algorithm for solving this L2C case?
Alternatively,

• Is this BM configuration known to be unreachable?
• Has anyone seen it discussed in the literature or existing methods?

Any references or insights would be greatly appreciated.

Thank you!

How do you have 5 green corner centers???

 

[Skywalker2026]

I only showed the internal 3x3 green center, ignoring the outer layer.

 

[Martyt7777]

I only showed the internal 3x3 green center, ignoring the outer layer.

Yes, but your diagram appears to have 5 green corner centers (the ones diagonal to the middle center). Since a normal 5x5 only has 4 of these, your 5x5 (if I'm reading the diagram correctly) is unsolvable.

 

[Skywalker2026]

Thanks, Marty! I think you have answered my question.

You are absolutely right. I was concentrating on the O/G pattern and overlooked the physical constraint that a 5×5 has only four green center pieces of this corner type. My proposed BM configuration would require four of them on the green center plus one on the orange center — five in total — so the configuration is indeed unreachable.

This is especially helpful because, under rotation, the BM configuration is equivalent to the TM configuration that I had also been investigating. Your observation therefore appears to explain why I have never been able to produce any of these configurations on a real cube.

Thank you very much for taking the time to draw the cube and point this out. I learned something important from your explanation!

 

[Skywalker2026]

View attachment 50748
Yes, but your diagram appears to have 5 green corner centers (the ones diagonal to the middle center). Since a normal 5x5 only has 4 of these, your 5x5 (if I'm reading the diagram correctly) is unsolvable.

Hi Marty,

I would like to sincerely thank you again for your kind help and encouragement when I joined the SpeedSolving.com community. Your suggestions and willingness to share your cubing knowledge were very helpful to me.

I have recently completed two new notebooks (#6 and #7) focusing on understanding the Last Two Centers (L2C) of the 5×5 Rubik’s Cube. If you have time, I would be very happy if you could take a look and share any comments or suggestions.

Here are the links:

https://ltwang888.github.io/resources/LT_Wang_Notebook_6_August_15_2026_v1.0.pdf

https://ltwang888.github.io/resources/LT_Wang_Notebook_7_August_15_2026_v1.0.pdf

I also wanted to share the acknowledgment section in #6 with you. I included your name as a small way to express my appreciation for your help and for the supportive spirit you represent in the cubing community.

Acknowledgments

The author gratefully acknowledges Marty Kelsey (Martyt7777) for his valuable insights and helpful discussions on center-solving algorithms, which helped inspire the systematic study of the 5×5 last-two-center cases presented in this notebook. The author also thanks members of the SpeedSolving.com community who generously shared references, links, technical comments, and their cubing experience during the development of this work.

Thank you again for your kindness. It is wonderful to see how cubers of different backgrounds can learn from and help each other through this community.