Message #3637

From: Melinda Green <>
Subject: Re: [MC4D] Re: Physical 4D puzzle achieved
Date: Thu, 09 Feb 2017 16:46:40 -0800

Hello Matt,

Great to hear from you again! For the newer members, Matt currently holds the record for the shortest 3^4 solution with 227 twists.

Good question regarding orientations. No, it hasn’t come up yet, and I feel a little embarrassed for not considering it more closely in light of the red-blue problem, but then that’s what the preview video is for! No, you can’t arbitrarily place any piece in any orientation. With this arrangement of magnets, each of the red or blue corners can be placed in any of the 3 orientations that leave it in the outer corner position, but no others. I guess that means the problem is unsolvable with this arrangement of magnets.

If I had used the "other" natural arrangement, it would also be possible to achieve 3 more orientations by turning a red or blue sticker all the way around and sticking it into the center of its 2x2x2 cube. That would be interesting, but would be a completely invalid orientation, leaving a 3-sticker junction sticking out of the corner and with the patterns of adjacent pieces not matching at all. By that I mean that the diagonal lines between colors on a piece would meet adjacent pieces in an ‘X’ configuration rather than matching diagonals. In other words, you could get a mixing of the the normal view with the crazy inside-out views you see in the video, but I don’t think it would be helpful. Those 3 inverted piece orientations are not among the 12 tetrahedral orientations that you are talking about however. They are from the additional 12 orientations of the cubic pieces, but it is an interesting aside.

Thanks Matt!

On 2/9/2017 3:19 PM, [4D_Cubing] wrote:
> Very impressive Melinda!
> Just a quick reply for now, I’ll try to find time to think about this in more detail. I may have missed this in the video, so apologies if this has been addressed already, but have you checked that each piece works in each of the 12 possible orientations with the arrangement of magnets? I’m hoping there’s some simple way to allow the puzzle to fully scramble.
> Matt