My name is Anthony Deschamps. I am 17 years old and living in Windsor, Ont=
ario, Canada. I am in my last year of high school, and next year I plan to=
study physics, chemistry or something in between. I recently became the 2=
0th person to solve the 3^5 cube and I thought I'd explain the general stra=
tegy that I used to solve it. This isn't a complete description of my solu=
tion, but rather a description of the concepts I used to come up with the s=
olution.
I think the biggest challenge when solving higher dimensional cubes is real=
izing that the fourth dimension and beyond are really no different from the=
first three that we are so familiar with. Most, if not all of the same al=
gorithms you would use in 3D still apply and are quite useful.
It also helps if your solution to the 3D cube is more logic based rather th=
an consisting of memorized sequences. I use a number of algorithms that ar=
e based on the same idea: Pick a side of the cube and do whatever you need=
to do in order to manipulate one or two pieces while leaving the rest of t=
he side untouched. Now you can turn that side and perform everything you j=
ust did in reverse, which will restore any damage you did to the rest of th=
e cube. Now turn that side back to where it was and you're done. This met=
hod can be used to swap two pairs of corners/edges or to rotate one corner =
clockwise and another counter clockwise.
If you don't solve the 3D cube like this (I know there are faster ways, lik=
e the Fridrich method) I would recommend trying it in order to get the hang=
of it. It gives you a finer degree of control. Besides, it's useful for =
making patterns on the cube, if you enjoy that sort of thing.
Moving on to the 5D cube, my solution went something like this: I divided =
the cube into three layers (starting with blue, out of habit) and for each =
one I started from the inside and worked my way out, from 2 coloured pieces=
to 5 coloured. I would first move all the relevant pieces to the layer I =
was working on and ensure that they were orientated properly, then I'd move=
them around on that side to get the right permutation. For the first laye=
r, you can use the method I described above throughout. However, the next =
two layers force an important restriction on you. If you are using the sam=
e algorithms you use in 3D to manipulate pieces on the side in the center o=
f the screen (that's the -V side), they will also affect all the pieces alo=
ng the U and V axis with the same XYZ coordinates in the same way. In orde=
r to avoid the 3D algorithms affecting the other layers, I used a modified =
strategy.
Let's say you're performing an algorithm on the side you see in the center =
(-V). You can use your normal 3D algorithms by twisting the surrounding si=
des (X Y Z). However, this will also affect +V and +-U. So instead of usi=
ng X Y Z to manipulate the -V side, you restrict yourself to only twisting =
two opposing sides (say, +-X) When you'd normally twist the Z or Y sides, =
instead you rotate -V such that you can perform your desired moves using +-=
X. This will minimalize the effects on the rest of the cube (if anything i=
s messed up, you can fix it by turning one or two sides).
When you get to the 5 coloured pieces, you have to get even more creative, =
but the strategy I used for them was really just an extension of what I exp=
lained (hopefully clearly) above.
I hope I did a decent job of explaining how I went about solving this monst=
er. If anybody has any questions, feel free to ask and I'll hopefully be a=
ble to clarify further.