Message #3818

From: Eduard Baumann <ed.baumann@bluewin.ch>
Subject: Re: [MC4D] Melinda’s physical 2^4 puzzle, Marc’s videos 1-6
Date: Thu, 16 Nov 2017 23:22:36 +0100

Hi,

Since a few days I have my "physical 2^4" ! :-)

Here are some considerations.

Each cubicle has 4 colors. These are chosen from 8 colors. You have 8 over 4 = 70 possibilities. You must take away those combinations where a opposing color pair is present. You are left with 16 combinations. One combination has two mirrored realisations. You must chose the right one. There are 4 opposing color pairs.

The standard arrangement of the phys 2^4 has 8 octahedra. Only one is complet. Five are splitted in two halfs and two are "inverted" (on the corners of a supercube). All splitted octahedra can with a simple operation be placed in the middle but NOT the two inverted ones !

So you can turn each octahedron (except two) in 24 manners after having placed it in the middle. The unsetting must follow.

Each turn corresponds to a turn (twist) in the virtual 2^4.

BIG question. Is it possible to change the two "inverted" colors by simple moves?

So far I was forced for this to do an assembling from scratch !!! All four pairs of opponing colors can be in the "inverted" position and nothing else.

Kind regards
Ed

—– Original Message —–
From: Marc Ringuette ringuette@solarmirror.com [4D_Cubing]
To: 4D_Cubing@yahoogroups.com
Sent: Saturday, June 10, 2017 9:50 PM
Subject: [MC4D] Melinda’s physical 2^4 puzzle, Marc’s videos 1-6

Hi, mc4d list! It’s Marc, a friend of Melinda’s in the SF Bay Area,
here to report on my progress so far in figuring out her physical 2^4
puzzle and its correspondence with mc4d.

I found it expedient to record a series of brief videos, upload them to
YouTube, and link to them here. They’re intended to be viewed in
sequence, but if you’re pressed for time or not sure you’re interested,
I’d recommend videos 1 and 3 as being the shortest and most lively 5.5
minutes out out of the total of 32 minutes.

1 marc’s physical puzzles 1m32s https://youtu.be/cMH6N2PK6GE
2 over the shoulder intro v3 6m40s https://youtu.be/_rXJr4SokC0
3 special rotations FUro and FOro 3m58s https://youtu.be/htTTn7qY35M
4 overlap of natural moves 6m58s https://youtu.be/Dsu-5TTDNbM
5 quarter puzzle moves 5m38s https://youtu.be/VULJgClg-5g
6 solution sketch partition+ortega 7m30s https://youtu.be/pKHU5sFaGvY

I have marked these videos as "unlisted" on YouTube, since Melinda has
asked me not to broadcast in wide-open forums until she is more ready to
release the puzzle out into the world beyond the mc4d list. So, to
find them again, use the links from this message, or bookmarks, not my
YouTube channel.

I’m using my own simple move-naming system, because it seems very
natural to me and I couldn’t make it through Joel’s stuff (sorry Joel).
Hopefully it will be clear to you.

After verifying to my own satisfaction that they’re equivalent puzzles,
I’ve moved on (a bit prematurely) to the projects I’m most excited
about: defining a good move set for the physical puzzle (easy to use,
sufficiently powerful that solves are not excruciatingly long,
preserving the equivalence of the puzzles, and generally pleasing and
tasteful); and then figuring out how to solve the puzzle using that move
set.

I’m sure that many people here will need more time to go over (and over)
the question of equivalence. That’s OK. I wanted to forge ahead and
give you an idea of the direction I’m pushing, so you can either give me
some feedback, or take it and run with it.

C’mon, gang, get building your own puzzles! I’m having a huge amount
of fun with it, but it would be even more fun with company.

Cheers
Marc Ringuette
Pacifica, CA