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