# Message #620

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] Magic Cube 6^5 Solved

Date: Tue, 27 Jan 2009 12:11:04 -0600

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<http://games.groups.yahoo.com/group/4D_Cubing/message/522>,

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

> .

>

>

>