Message #394

From: markoram109 <>
Subject: One way to solve the 5-D cube
Date: Tue, 07 Aug 2007 15:23:06 -0000

To anyone contemplating an assault on the 5-D cubes, these following
points may be useful.

Firstly, the one thing you will need is patience (and/or an
understanding partner!). It took me many months from start to
finish, and my wife was amazing in her support for me in all this.
[I owe her so much in even being able to complete the cube, and
write this summary of my experience. So thank-you sweetheart for

I couldn’t have tackled the 5-D cube without feeling at least a
little familiar with the 4-D version, and this in turn I could never
have conquered without Roice’s excellent step-by-step solution at

So as a warm-up I suggest first working through Roice’s solution
step by step. (This will also extend the 4-D Hall of Fame list as

Second, two invaluable features of the 5-D cube are the means to
hide and show each hyperface, and also the means to highlight the 2-
sided up to the 5-sided hypercubies. I ended up hiding the +U, -U
and +V faces, and setting the parameters of the 5-D version to give
a representation similar to the 4-D cube projection. This I found
workable, whereas other settings made everything too confusing.

I also spent several weeks trying twists along different axes, to
get familiar with where things move to when a hyperface is turned.
Generally the X-Y-Z directions made sense, but I never quite felt
the U-V directions were as easy to follow. Still, it turned out this
was not essential.

For the solution itself, my approach was to start with just the 2-
sided pieces visible, and start by trying to correctly house these.
Again, experience with Roice’s solution paid off, and this step was
fairly smooth. (It is also a huge confidence boost :)

Next, I could then ‘turn off’ the 2-sided pieces, and highlight just
the 3-sided pieces. This approach made it easy to work on each set
of pieces one by one i.e. 2-, then 3-, then 4- then 5-sided pieces;
each as a separate problem.

I ended up making some macros for the 3-sided pieces, and I stumbled
on these more or less by accident. I am very embarrassed to admit I
didn’t write anything down at this stage, but if it is possible to
access the individual moves in the saved macro (is it Roice?) I will
happily forward these. Anyway, I had macros that would move three
pieces around, or flip 2 or 3 at a time: these I called a ‘minimal
toolkit’, and one by one it proved possible to house all the 3-sided
hypercubies using the toolkit in this way. Again, patience proved to
be essential here.

By chance, none of the macros moved any pieces in the +U and -U
hyperfaces, so my strategy then became to first house all the 3-
sided pieces in the red hyperface, and then the green hyperface
(opposite the red one). Once these were complete, I moved them into
the +U and -U positions and `forgot’ about them while I worked on
the rest of the pieces.

It then proved possible to adapt the 3-sided piece macros to move 2
or 3 of the 4-sided pieces, while leaving everything else intact.
For the 4-sided pieces I followed the same approach as with the 3-
sided pieces i.e. I completed the red then the green faces, and
moved them into the +U/-U positions to finish off the remaining 4-
sided pieces in the other hyperfaces.

The final set of macros I developed allowed me to rotate and/or flip
3 of the 5-sided corners. By now each set of macros was built on
ones from the previous ‘level’, and so these had become very big
sequences: there would even be a delay of a few seconds while the
software worked its way through the (? many hundreds of) individual
moves. Still, all this ended up with every piece correctly housed,
but right at the end I had a single 5-sided piece flipped. Clearly
this needed to be corrected for the cube to be completed.

There is a message that pops up once the cube is solved, and this is
a lovely touch. Perhaps I won’t expand on what it says here (I don’t
want to spoil the surprise after all) but to the author of that
message (Roice again): excellent job!

I am happy to expand on any of these points if anyone is interested,
and then all that this leaves for me to say is Good Luck!