Thread: "Magic Cube 6^5 Solved"

Well, it was a lengthy journey, but after 24 days (avg 6 hrs/day) and=20
1.9 million twists, the 7^5 is the only peak left unclaimed. After=20
scaling the 6^5, I'm intimidated by the magnitude of the next summit.=20
I doubt I'll attempt a single uninterupted solution to the 7^5=20
anytime soon.=20

I didn't experience any "parity" errors. I don't think they're even=20
possible on m^n puzzles with n>=3D4, and m =3D even. The stickers that=20
gave me the most trouble were the final 64 3C's. I think the 2C and=20
1C's were simple because there were so many identical pieces they=20
were easy to place. I think the 4C and 5C weren't too bad either,=20
simply because there were so few pieces they were over and done with=20
so quickly. Based on my experiences, I think the worst pieces on a=20
MC6D would be the 4C's...=20

I'm going to make another claim in this post. I think I've developed=20
a solution to the m^n puzzle. It requires only seven algoriths. I'm=20
in the process of typing it up, and I'll post it if there's interest.=20
I have minimal formal math training, so I don't have the knowledge to=20
prove it is a complete solution. I just have a very strong gut=20
feeling.

The basic ideas of my solution to the 6^5, and also the m^n, is as=20
follows:

Solve the pieces with the most stickers first, and work your way down=20
to the single sticker pieces.=20

While solving each of these, align one set of all the opposing face=20
stickers at a time (i.e. red and green).=20

Once these are aligned, position each of the remaining stickers on=20
these pieces, once again aligning one set of all the opposing face=20
stickers at the same time. (These steps are recursive.)

There's a little more to it than that, but you get the idea.=20

I'd also like to warn you that spending so much continuous time=20
working on one of these puzzles has almost a narcotic effect. Over=20
the last couple of days, I think I've experienced some withdrawal. I=20
almost found myself starting the 7^5 just to relieve it! Don't worry,=20
I stopped myself! ;-)

I haven't posted anything about myself to the group yet, so I'll tack=20
on a little right here. Some of my personal interests include=20
juggling and triathlon. I'm a member of the US Navy, currently=20
stationed in Washington state. My wife and home are back in St. Paul,=20
MN, which is where I will return to when my current tour is up. I'm=20
planning on attending the U of MN, majoring in a branch of science or=20
engineering. I think I'll minor in math as well. A large part of my=20
renewed interest in math stems from this group (thanks, Melinda,=20
Roice, Don and everyone else!)

I'd like to close this message with some congratulations. First of=20
all to Melinda, for solving the evil puzzle of her own creation. We=20
all knew you could do it! Second to Noel for managing the 120 cell.=20
Enough said. Finally, David, thank you for the work on all the=20
formulas for these puzzles. Your latest for permutations of an n^5 is=20
almost scarier than my first glimpse of a MC5D puzzle!

-Levi

Congratulations!! 1.9 million twists - incredible!

Also, great to hear about your solution to the m^n puzzle; I'm
definitely interested in hearing more about it. About parity errors,
forgive my ignorance, but I'm not even certain what counts as a
parity error when solving a cube. I know the basic idea is
correcting the parity of pieces, but I believe that could apply
to the corners on a 4D cube, which obviously do not count, so I'm not
sure. I am certain you are correct in your assertion though given
the fact that you are typing up a solution! If you want, I could
send you information on all of the orientation possibilities on
an m^n cube, but it sounds like you've got that covered.

Once again, great job on solving this puzzle! And thanks for your
appreciation of my formulas and your description of the n^5 one as
frightening! :) Your solution is a great achievement and
contribution.

David

--- In 4D_Cubing@yahoogroups.com, "rev_16_4" wrote:
>
> Well, it was a lengthy journey, but after 24 days (avg 6 hrs/day) and=20
> 1.9 million twists, the 7^5 is the only peak left unclaimed. After=20
> scaling the 6^5, I'm intimidated by the magnitude of the next summit.=20
> I doubt I'll attempt a single uninterupted solution to the 7^5=20
> anytime soon.=20
>=20
> I didn't experience any "parity" errors. I don't think they're even=20
> possible on m^n puzzles with n>=3D4, and m =3D even. The stickers that=20
> gave me the most trouble were the final 64 3C's. I think the 2C and=20
> 1C's were simple because there were so many identical pieces they=20
> were easy to place. I think the 4C and 5C weren't too bad either,=20
> simply because there were so few pieces they were over and done with=20
> so quickly. Based on my experiences, I think the worst pieces on a=20
> MC6D would be the 4C's...=20
>=20
> I'm going to make another claim in this post. I think I've developed=20
> a solution to the m^n puzzle. It requires only seven algoriths. I'm=20
> in the process of typing it up, and I'll post it if there's interest.=20
> I have minimal formal math training, so I don't have the knowledge to=20
> prove it is a complete solution. I just have a very strong gut=20
> feeling.
>=20
> The basic ideas of my solution to the 6^5, and also the m^n, is as=20
> follows:
>=20
> Solve the pieces with the most stickers first, and work your way down=20
> to the single sticker pieces.=20
>=20
> While solving each of these, align one set of all the opposing face=20
> stickers at a time (i.e. red and green).=20
>=20
> Once these are aligned, position each of the remaining stickers on=20
> these pieces, once again aligning one set of all the opposing face=20
> stickers at the same time. (These steps are recursive.)
>=20
> There's a little more to it than that, but you get the idea.=20
>=20
> I'd also like to warn you that spending so much continuous time=20
> working on one of these puzzles has almost a narcotic effect. Over=20
> the last couple of days, I think I've experienced some withdrawal. I=20
> almost found myself starting the 7^5 just to relieve it! Don't worry,=20
> I stopped myself! ;-)
>=20
> I haven't posted anything about myself to the group yet, so I'll tack=20
> on a little right here. Some of my personal interests include=20
> juggling and triathlon. I'm a member of the US Navy, currently=20
> stationed in Washington state. My wife and home are back in St. Paul,=20
> MN, which is where I will return to when my current tour is up. I'm=20
> planning on attending the U of MN, majoring in a branch of science or=20
> engineering. I think I'll minor in math as well. A large part of my=20
> renewed interest in math stems from this group (thanks, Melinda,=20
> Roice, Don and everyone else!)
>=20
> I'd like to close this message with some congratulations. First of=20
> all to Melinda, for solving the evil puzzle of her own creation. We=20
> all knew you could do it! Second to Noel for managing the 120 cell.=20
> Enough said. Finally, David, thank you for the work on all the=20
> formulas for these puzzles. Your latest for permutations of an n^5 is=20
> almost scarier than my first glimpse of a MC5D puzzle!
>=20
> -Levi
>

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I think the lack of experienced parity problems is likely due to the
solution method (corners-in instead of centers-out). In Noel's
writeup about higher dimensional
parities,
he described the issues like this:

"When the puzzle is simplified to a 3x3, it will have configurations that
are normally impossible in a standard 3x3."

But with a corners-in approach, the cube is never reduced to a 3x3 to
be solved as that simpler puzzle. If I were a betting man, and occasionally
I am, I'd wager Levi's general solution approach avoids parities even on a
4^3 puzzle.

My congratulations to Levi too! And my empathy for the addiction :)

Roice


On 1/26/09, rev_16_4 wrote:
>
> Well, it was a lengthy journey, but after 24 days (avg 6 hrs/day) and
> 1.9 million twists, the 7^5 is the only peak left unclaimed. After
> scaling the 6^5, I'm intimidated by the magnitude of the next summit.
> I doubt I'll attempt a single uninterupted solution to the 7^5
> anytime soon.
>
> I didn't experience any "parity" errors. I don't think they're even
> possible on m^n puzzles with n>=4, and m = even. The stickers that
> gave me the most trouble were the final 64 3C's. I think the 2C and
> 1C's were simple because there were so many identical pieces they
> were easy to place. I think the 4C and 5C weren't too bad either,
> simply because there were so few pieces they were over and done with
> so quickly. Based on my experiences, I think the worst pieces on a
> MC6D would be the 4C's...
>
> I'm going to make another claim in this post. I think I've developed
> a solution to the m^n puzzle. It requires only seven algoriths. I'm
> in the process of typing it up, and I'll post it if there's interest.
> I have minimal formal math training, so I don't have the knowledge to
> prove it is a complete solution. I just have a very strong gut
> feeling.
>
> The basic ideas of my solution to the 6^5, and also the m^n, is as
> follows:
>
> Solve the pieces with the most stickers first, and work your way down
> to the single sticker pieces.
>
> While solving each of these, align one set of all the opposing face
> stickers at a time (i.e. red and green).
>
> Once these are aligned, position each of the remaining stickers on
> these pieces, once again aligning one set of all the opposing face
> stickers at the same time. (These steps are recursive.)
>
> There's a little more to it than that, but you get the idea.
>
> I'd also like to warn you that spending so much continuous time
> working on one of these puzzles has almost a narcotic effect. Over
> the last couple of days, I think I've experienced some withdrawal. I
> almost found myself starting the 7^5 just to relieve it! Don't worry,
> I stopped myself! ;-)
>
> I haven't posted anything about myself to the group yet, so I'll tack
> on a little right here. Some of my personal interests include
> juggling and triathlon. I'm a member of the US Navy, currently
> stationed in Washington state. My wife and home are back in St. Paul,
> MN, which is where I will return to when my current tour is up. I'm
> planning on attending the U of MN, majoring in a branch of science or
> engineering. I think I'll minor in math as well. A large part of my
> renewed interest in math stems from this group (thanks, Melinda,
> Roice, Don and everyone else!)
>
> I'd like to close this message with some congratulations. First of
> all to Melinda, for solving the evil puzzle of her own creation. We
> all knew you could do it! Second to Noel for managing the 120 cell.
> Enough said. Finally, David, thank you for the work on all the
> formulas for these puzzles. Your latest for permutations of an n^5 is
> almost scarier than my first glimpse of a MC5D puzzle!
>
> -Levi
> .
>
>
>

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