# Message #618

From: rev_16_4 <rev_16_4@yahoo.com>

Subject: Magic Cube 6^5 Solved

Date: Tue, 27 Jan 2009 04:48:27 -0000

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