Message #3647

From: Christopher Locke <project.eutopia@gmail.com>
Subject: Re: [MC4D] Re: Physical 4D puzzle achieved
Date: Sun, 12 Feb 2017 15:35:32 -0800

Matt,

>First of all, I think that taking a 2x2x1 block from one end and
putting at the other end is a valid maneuver, a 4D rotation which will
allow blue/red pieces to mix with other colours and to fully scramble
the 2^4.

It is possible to swap two 2x2x1 blocks, if you are careful to keep the
orientations correct. For instance swapping the two topmost 2x2x1
blocks (as demonstrated in Melinda’s video) is a 180 degree rotation of
the +z face about the y axis (it moves cubies of +z face, keeps +z
stickers on +z face, +y stickers on +y face, and swaps the +/-w
(red/blue) sticker positions and the +/-x positions). Similarly,
swapping the front face of the physical puzzle is a 180 degree rotation
of the +x face about the y axis.

However, red/blue (w-face) stickers are always pointing "outwards",
while the x, y, z colors are pointing towards the 2x2x2 cube-half faces,
so these moves do not mix up red/blue with the others.

Melinda,

Could you elaborate on what kind of move you are describing? I cannot
visualize it very well.

Also, I don’t think there is a need to make the puzzle transparent, as
all 4 stickers attached to each cubie are always visible (one on the
outward facing corner, and three touching 2x2x2 cube face centers).

By the way, looking at the video again, the move at 23:30
(https://youtu.be/Asx653BGDWA?t=1410) could be a valid remixing of the
red/blue. It is hard to check by hand by just looking at the video
though, as I cannot easily enumerate how each piece changed. It is
definitely not a single 90 degree twist, but it could be a combination
of twists which would open the possibility of having all permutations
available. My rough feeling by looking at it is that it is doing a "90
degree" twist of the top and bottom, "90 degree" twist of the front and
back, and "90 degree" twist through the inside/outside faces and the
red/blue w-faces. It could of course be an illegal position due to
parity or something, but that would require deeper investigation.
Probably the easiest way would be to put the positions into MagicCube4D
and then try to solve it from that configuration :D

Best regards,
Chris

On 2017年02月12日 14:53, Melinda Green melinda@superliminal.com [4D_Cubing]
wrote:
>
> In my last message I mentioned that it appears that moving both end
> caps to opposite sides (as opposed to "ends") works. That looks to be
> a 90 degree rotation of the central black face, and exchanges red-blue
> stickers with other colors. Can someone confirm or refute that? What
> surprises me is just how scrambled the puzzle looks after just one of
> these moves. It clearly makes the puzzle much more difficult. It also
> suggests that to solve it, you’ll probably need to frequently examine
> the interior. If so, perhaps the ultimate version would involve
> transparent materials such as colored glass, or perhaps clear cubes
> with four colored corners. It also makes the current bandaged version
> look not so bad. I suspect a natural solution would first position and
> orient all the red and blue stickers and then solve the bandaged form.
>
> -Melinda
>
> On 2/12/2017 12:44 PM, damienturtle@hotmail.co.uk [4D_Cubing] wrote:
>> I’ve looked at this a little more today, and have a correction to
>> make to my previous message.
>>
>> >First of all, I think that taking a 2x2x1 block from one end and
>> putting at the other end is a valid maneuver, a 4D rotation which
>> will allow blue/red pieces to mix with other colours and to fully
>> scramble the 2^4.
>>
>> Nope, sadly it is not quite that simple. I’m now convinced that there
>> is no simple maneuver which will do a 4D rotation to put some other
>> pair of colours in place of blue/red, or a twist which mixes red/blue
>> stickers with other colours. There are of course ways to achieve
>> these, but they require several steps and I’m not yet sure what the
>> easiest/shortest one would be, or how best to describe any such
>> maneuver. I’ll post an update if I find a good answer, unless someone
>> else figures it out first.
>>
>> Matt
>
>