Here I will present an approach to solve a scrambled 3x3x3x3 “Rubik’s type” puzzle that is based on the “Ultimate Solution to the Rubik’s Cube” by Philip Marshall. The goal here is to provide a straightforward and reasonably sized solution that will give those who have learned the 3D cube an opportunity to take it one step further.
Having been through the relatively long process of solving a 3^4 only a few times, this will be meant as a detailed outline. This means some of the nuances will be left out, but nonetheless my hope is that there will be more than enough information here to solve the hypercube. This solution will include the overall attack of the problem and descriptions of the sequences required.
I have decided to present this solution with specific reference to the user interface of MagicCube4D by Melinda Green, Don Hatch, and E. Jay Birkenbilt. Theirs is the most elegant and usable interface I have seen.
Before getting started, I recommend visiting the superliminal site and reading the introduction to this puzzle. Also, I would like to note that before tackling the 4D puzzle with this solution, you will most certainly need to understand Philip’s Rubik’s Cube solution (or a similar solution) and be able to solve a 3D cube using it. This hypercube solution was developed by extending the concepts Philip has already laid out, and so I am going to make references to his solution. This also means I may gloss over descriptions Philip has already taken the time to write out, so the better you know and understand his solution, the easier it will be to apply those ideas here.
One last thing. If you haven’t been exposed to four-dimensional concepts and right about now are thinking “4D what?”, I recommend the book The Fourth Dimension by Rudy Rucker.
Send any comments or suggestions for this solution to Roice Nelson, firstname.lastname@example.org
You may also want to consider joining the Rubik's hypercube discussion group.