Message #3694

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Physical 4D puzzle V2
Date: Thu, 27 Apr 2017 18:00:05 -0700

The new arrangement of magnets allows every valid orientation of pieces. The only invalid ones are those where the diagonal lines cutting each cube’s face cross each other rather than coincide. In other words, you can assemble the puzzle in all ways that preserve the overall diamond/harlequin pattern. Just about every move you can think of on the whole puzzle is valid though there are definitely invalid moves that the magnets allow. The most obvious invalid move is twisting of a single end cap.

I think your description of the center face is not correct though. Twists of the outer faces cause twists "through" the center face, not "of" that face. Twists of the outer faces are twists of those faces themselves because they are the ones not changing, just like the center and outer faces of MC4D when you twist the center face. The only direct twist of the center face that this puzzle allows is a 90 degree twist about the outer axis. That happens when you simultaneously twist both end caps in the same direction.

Yes, it’s quite straightforward reorienting the whole puzzle to put any of the four axes on the outside. This is a very nice improvement over the first version and should make it much easier to solve. You may be right that we just need to find the right way to think about the outside faces. I’ll leave it to the math geniuses on the list to figure that out.

-Melinda

On 4/27/2017 10:31 AM, Joel Karlsson joelkarlsson97@gmail.com [4D_Cubing] wrote:
>
> Hi Melinda,
>
> I do not agree with the criticism regarding the white and yellow stickers touching each other, this could simply be an effect of the different representations of the puzzle. To really figure out if this indeed is a representation of a 2x2x2x2 we need to look at the possible moves (twists and rotations) and figure out the equivalent moves in the MC4D software. From the MC4D software, it’s easy to understand that the only moves required are free twists of one of the faces (that is, only twisting the center face in the standard perspective projection in MC4D) and 4D rotations swapping which face is in the center (ctrl-clicking in MC4D). The first is possible in your physical puzzle by rotating the white and yellow subcubes (from here on I use subcube to refer to the two halves of the puzzle and the colours of the subcubes to refer to the "outer colours"). The second is possible if it’s possible to reach a solved state with any two colours on the subcubes that still allow you
> to perform the previously mentioned twists. This seems to be the case from your demonstration and is indeed true if the magnets allow the simple twists regardless of the colours of the subcubes. Thus, it is possible to let your puzzle be a representation of a 2x2x2x2, however, it might require that some moves that the magnets allow aren’t used.
>
> Best regards,
> Joel
>
> 2017-04-27 3:09 GMT+02:00 Melinda Green melinda@superliminal.com <mailto:melinda@superliminal.com> [4D_Cubing] <4D_Cubing@yahoogroups.com <mailto:4D_Cubing@yahoogroups.com>>:
>
> Dear Cubists,
>
> I’ve finished version 2 of my physical puzzle and uploaded a video of it here:
> https://www.youtube.com/watch?v=zqftZ8kJKLo <https://www.youtube.com/watch?v=zqftZ8kJKLo>
> Again, please don’t share these videos outside this group as their purpose is just to get your feedback. I’ll eventually replace them with a public video.
>
> Here is an extra math puzzle that I bet you folks can answer: How many families of states does this puzzle have? In other words, if disassembled and reassembled in any random configuration the magnets allow, what are the odds that it can be solved? This has practical implications if all such configurations are solvable because it would provide a very easy way to fully scramble the puzzle.
>
> And finally, a bit of fun: A relatively new friend of mine and new list member, Marc Ringuette, got excited enough to make his own version. He built it from EPP foam and colored tape, and used honey instead of magnets to hold it together. Check it out here: http://superliminal.com/cube/dessert_cube.jpg <http://superliminal.com/cube/dessert_cube.jpg> I don’t know how practical a solution this is but it sure looks delicious! Welcome Marc!
>
> -Melinda
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