Thread: "n^6 Formula Found"

Hi everyone,

I have derived a formula for the upper bound of an n^6 Rubik's Cube! I was=
able to do so after discovering a general method that will allow me to fin=
d a formula for any specific dimension. Because of this, I now believe tha=
t it will not be long before a formula is found for all dimensions! The me=
thod makes clear that there are many patterns hidden in the formulas, and i=
n fact the formulas are very much recursive! Here is the n^6 formula:

http://www.gravitation3d.com/david/n%5E6_Cube.pdf

Also, I have reformulated my n^5 formula to match the method I am now using=
. Here it is:

http://www.gravitation3d.com/david/n%5E5_Cube.pdf

These formulas build on each other, and already I can see how I will go abo=
ut finding the n^d formula.

I am leaving for vacation today, and will not be able to reply or work on t=
he general formula until next Friday. Thanks everyone, and I'll talk to yo=
u when I get back.

All the best,
David

--- In 4D_Cubing@yahoogroups.com, "David Smith" wrote:
>
> Hi everyone,
>=20
> I have derived a formula for the upper bound of an n^6 Rubik's Cube! I w=
as able to do so after discovering a general method that will allow me to f=
ind a formula for any specific dimension. Because of this, I now believe t=
hat it will not be long before a formula is found for all dimensions! The =
method makes clear that there are many patterns hidden in the formulas, and=
in fact the formulas are very much recursive! Here is the n^6 formula:
>=20
> http://www.gravitation3d.com/david/n%5E6_Cube.pdf
>=20
> Also, I have reformulated my n^5 formula to match the method I am now usi=
ng. Here it is:
>=20
> http://www.gravitation3d.com/david/n%5E5_Cube.pdf
>=20
> These formulas build on each other, and already I can see how I will go a=
bout finding the n^d formula.
>=20
> I am leaving for vacation today, and will not be able to reply or work on=
the general formula until next Friday. Thanks everyone, and I'll talk to =
you when I get back.
>=20
> All the best,
> David
>
That's really impressive!! But if you actually calculate it, the computer w=
ould... well, you would need a computer with a huge processor.