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Still working on putting my thoughts into order re: avoiding situations wit=
h single pieces that have their orientations flipped, but I've at least had=
a chance to find an expression in Roice's notation of my 16-twist sequence=
for cycling through three of the 4-color pieces. I've also found an expre=
ssion of my own 8-twist sequence for cycling through three 3-color pieces, =
which differs from Roice's published sequences.
I arrived at these sequences after studying the same 3^3 solution sequences=
by Phillip Marshall that Roice adapted his own sequences from. I took a s=
lightly different tack in developing my own sequences, though. The key to =
their development was in treating one of the 3-D "faces" of the 3^4 puzzle =
exactly as though it were a standard 3^3 cube, and performing Marshall's se=
quences on that "face" to cycle through its edges or corners. This works b=
ecause of the highly symmetrical structure of Marshall's sequences. I perf=
orm alternating twists of two 3-D "faces" in my sequences: one 3-D "face" t=
hat I treat as the standard 3-D puzzle, and one neighboring 3-D "face" that=
I use to perform twists on the 2-D faces of that 3-D puzzle. I'll call th=
ese two 3-D faces "Cube" and "Neighbor" for the moment. I start by identif=
ying which face of "Cube" I want to twist first in order to perform a parti=
cular Marshall sequence on "Cube." I set "Neighbor" as the 3-D "face" of t=
he 3^4 puzzle that shares that 2-D face with "Cube." After beginning the M=
arshall sequence on "Cube" by twisting "Neighbor" in the appropriate direct=
ion to achieve that effect, I then twist "Cube" so that the next face of it=
that I wish to twist in that Marshall sequence is presented to "Neighbor."=
I continue through the Marshall sequence in this manner, each time using =
"Neighbor" to twist the appropriate face of "Cube", then perform a final tw=
ist to return "Cube" to its starting orientation in the sequence. Because =
of the symmetry of the Marshall sequences, "Neighbor" performs an equal num=
ber of clockwise and counterclockwise twists on "Cube" throughout this proc=
edure, which allows this technique to work without disturbing the rest of t=
he 4-D puzzle.
Okay, enough background explanations. Here are my 3-color and 4-color sequ=
ences in Roice's notation. In both sequences, the face I designate as "Cub=
e" is in the position Roice calls "Top". In my 3-color sequence, "Neighbor=
" is "Front"; in the 4-color sequence, "Neighbor" is "Upper". This is to p=
reserve the sense of the Marshall sequences as presented on his site.
My 3-color sequence:
Front 5 Right
Top 11 Right
Front 5 Left
Top 11 Left
Front 5 Left
Top 11 Right
Front 5 Right
Top 11 Left
My 4-color sequence:
Upper 11 Right
Top 5 Left
Upper 11 Right
Top 5 Right
Upper 11 Left
Top 5 Right
Upper 11 Left
Top 5 Left
Upper 11 Right
Top 5 Left
Upper 11 Left
Top 5 Right
Upper 11 Left
Top 5 Right
Upper 11 Right
Top 5 Left
These can be reversed (right twists becoming left twists and vice-versa) to=
perform mirror images of the Marshall sequences, just as in Marshall's ori=
ginal technique. You can treat any face you want as "Cube" and "Neighbor",=
of course; notating it as above was simply for convenience's sake.
More hopefully to follow, on the tactical use of these sequences to solve t=
he 3^4 puzzle without creating situations where a single puzzle piece is in=
the correct position but incorrect orientation. Time to rest the brain fo=
r a while.
--Matt Young
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