Message #672

From: matthewsheerin <damienturtle@hotmail.co.uk>
Subject: Re: My solution
Date: Thu, 21 May 2009 18:02:35 -0000

— In 4D_Cubing@yahoogroups.com, "Kyle Headley" <kygron@…> wrote:
>
> In that case my solution was not unique at all. Any hints on getting corners to line up nicely? I was working to systematize the solution using 3d techniques, but I think I’m just trying to hard and frustrating myself.
>
> I’m also looking forward to seeing what the additional freedom of movement allows in the 5d version, but I just can’t make use of the control scheme in MC5D. Are you able to freely rearrange the stickies? I guess that requires a (3+)^5.
>
> — In 4D_Cubing@yahoogroups.com, "Anthony" <anthony.deschamps@> wrote:
> >
> > — In 4D_Cubing@yahoogroups.com, "Kyle Headley" <kygron@> wrote:
> > >
> > > Hi! I was #93 on the 3^4 solution list, and I was told I had a unique solution, so I wanted to let you all know what I did. Sorry for the delay, there was some confusion about me getting on this group.
> > >
> > > For an analogy, take a regular 3^3 (3d cube) and orient it so you’ve got a top and bottom and sides. Now rotate any sides 180 at a time. If you notice the center slice of the cube, it behaves exactly as a 3^2 puzzle, the 2d analog. If you also allow turning that center slice (reorienting the 3^2) you’ll find that you only need to turn one face of the 3^3.
> > >
> > > When you get to 4d, the extra freedom of movement makes this technique even more useful, as not only the center slice, but the top and bottom slices can be manipulated in the same way, as long as the top (and bottom) stickies are the same color.
> > >
> > > It gets a bit more complicated than that, but overall, if you’re willing to let your turn counter rise a bit, you can solve about 90% of the 3^4 not with analogous techniques, but with IDENTICAL techniques as the 3^3. If some visual and control issues are resolved (especially with the 5d), this should make it much easier for people to get started solving these puzzles.
> > >
> > > Kyle
> > >
> >
> >
> > That sounds vey similar to my solution. I began by making one side of the 3^4 a solid colour, without paying attention to the anything but the 2C pieces, then I did the same with the opposite side. From then on, it was like solving three 3^3 cubes, but restricting myself to only using one working side and reorienting the "middle slice"(although you can use the opposite side as a working side as well without mixing anything up)
> >
> > In the end you might end up with some situations that you would not get on a normal 3^3, such as a single disoriented edge. However, the problems always happen in pairs, so it is easy to correct at the very end.
> >
>

Hi,
hate to say it but I’ve also thought of that trick, though it did take a few attempts to figure out how to achieve it. It can’t be a bad way to solve it, it let me set the fewest moves record for the 2^4 just there to 75. I prefer to just use it on the last face though.

It can be applied to the 5D hypercubes too, but be warned, it is very tricky to work. I used to for all the corner algs I have recorded, and it took a fair few attempts to manage it correctly. Also, I believe the ‘additional freedom of movement’ maybe just makes the puzzle 100 times harder. I could also argue that the vast number of pieces moved with one turn actually hinders movement!

If you get stuck (which is unlikely given you have got this far already on your own) feel free to ask for a tip or two.

Good luck with the other hypercubes, it’s good to hear from others finding similar strategies to these monsters!

Matthew