Message #4235
From: John Bailey <jbaile2@rochester.rr.com>
Subject: FW: Re: Shortest solution for any dimension Rubik’s Cube.
Date: Fri, 11 Oct 2019 12:15:47 +0000
In case you missed this: [1]https://arxiv.org/abs/1106.5736 [2]
"In this paper, we show that the Rubik's Cube also has a rich<br> underlying algorithmic structure. Specifically, we show that the n x n<br> x n Rubik's Cube, as well as the n x n x 1 variant, has a "God's<br> Number" (diameter of the configuration space) of Theta(n^2/log n)."
When I passed this along to Melinda Green, I thought "n" included<br> higher dimensionality. It only refers to the number of cublets along<br> any edge but all in 3 dimensions.
In any case, I would think God's Number could be easily found by<br> establishing how many twists would be needed to reach any cube<br> configuration. Reverse that an that should be God's Number.
Regards
John Bailey
-----------------------------------------From: "Melinda Green" <br> To: "John Bailey"<br> Cc: <br> Sent: Thursday October 10 2019 6:46:30PM<br> Subject: Re: Shortest solution for any dimension Rubik's Cube.
Dear John,
I skimmed the article and it’s very interesting. Please consider
posting it to the mailing list where I’m sure several people will
really enjoy it and help the rest of us to understand it.
Best,
-Melinda
On 10/4/2019 11:35 AM, John Bailey wrote:
In case you missed this: [3]https://arxiv.org/abs/1106.5736 [4]
"In this paper, we show that the Rubik's Cube also has a rich<br> underlying algorithmic structure. Specifically, we show that the n x n<br> x n Rubik's Cube, as well as the n x n x 1 variant, has a "God's<br> Number" (diameter of the configuration space) of Theta(n^2/log n)."
Regards
John
Links:
——
[1] https://arxiv.org/abs/1106.5736
[2] https://arxiv.org/abs/1106.5736
[3] https://arxiv.org/abs/1106.5736
[4] https://arxiv.org/abs/1106.5736