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Hey everyone!
I've been working on the random-state scrambler/solver and discussing
things with Marc over the past few days, and I've come up with some things
that I think are worth sharing.
Notation
I've yet to see a proper compendium of notation for the 2^4, so here's my
proposal for moves in the horizontal orientation:
- A face *R*, *L*, *I*, or *O*, followed by one of the following:
- Any letter *r*, *l*, *u*, *d*, *f*, *b*, *x*, *y*, *z* (plus an
optional *'* or *2*).
- A pair of square brackets containing any sequence of 3D moves
on a 2x2x2.
- Most of the time, of course, these moves should be 0-mod-4.
- The moves *U2*, *D2*, *F2*, and *B2*.
- The full puzzle rotations *x*, *x'*, *x2*, *y2*, and *z2*.
- The stacking moves *M*, *M'*, *M2*, *E*, and *S*.
- *M* moves the right endcap over to the left of the puzzle; *M'* does
the opposite, and *M2* swaps the left and right halves of the puzzle.
- *E* swaps the top and bottom halves of the puzzle.
- *S* swaps the front and back halves of the puzzle.
- *z clam* and *z' clam*.
- *z clam* is a *z* rotation followed by a clamshell move.
- *z' clam* is a *z'* rotation followed by a clamshell move.
- *z clam* and *z' clam* are inverses.
- Parentheses can be used for grouping, and numbers can follow
parentheses to repeat a sequence.
- Commutator notation
is allowed when useful.
The use of lowercase letters in moves like *Rr* may be controversial; if
they are deemed confusing, *R[R]* could be encouraged instead.
Here's an equivalent of Melinda's original gyro sequence in this notation:
*M E z' clam (x z' clam)2 *
I'll briefly digress to discuss a WCA-inspired
orientation" that Marc and I have been using. WCA regulations state that
white face should be on top (Y axis) and the green face should be on the
front (Z axis). On a standard NxNxN, this will result in the red face on
the right (X axis). If the X, Y, and Z axes are aligned in this manner on
the 2^4, here is the result:
[image: image.png]
Metric
As for counting numbers of moves, I'd like to propose the "snap" metric.
Each separation and reattachment of pieces is a single move. This can be
very dependent on how a move is executed, but I think it makes the most
sense for the purpose of solving and speedsolving.
A single move like *Iy* could be executed in three snaps as *M Ry M'* or in
just two snaps by rearranging the right and left endcaps around the *I* layer.
A sequence like *x' Rz Lz' M2* may seem like a lot of moves, but it can be
executed in one snap. (The *x'* is actually zero snaps, regardless of
context.) The sequence *z' clam* is two snaps, while the equivalent *Rx2 U2
(R[x2 y'] Ly)* is three snaps. *Ix* can be executed as three snaps with *M
Rx M'*, two snaps with *Rr Ll' x'*, or one snap by holding the endcaps with
one hand and rotating the *I* layer with the other. (In an actual solve,
the two-snap method is probably fastest.) While *Rr* is pretty clearly one
snap, *Ru* could be executed in two snaps (by separating the left and right
halves, performing *Ru*, and then reattaching them) or one snap (by
removing the four pieces of *Ru* directly, rotating them, and replacing
them).
I'd love to hear all your opinions on these things! - Andy
--
"Machines take me by surprise with great frequency." - Alan Turing
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everyone!
everyone!
ms, sans-serif">
=3D"trebuchet ms, sans-serif">I've been working on the random-state scr=
ambler/solver and discussing things with Marc over the past few days, and I=
've come up with some things that I think are worth sharing.v>
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div>serif">--
ambler/solver and discussing things with Marc over the past few days, and I=
've come up with some things that I think are worth sharing.v>
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t ms, sans-serif">Notation
ace=3D"trebuchet ms, sans-serif">I've yet to see a proper compendium of=
notation for the 2^4, so here's my proposal for moves in the horizonta=
l orientation:
notation for the 2^4, so here's my proposal for moves in the horizonta=
l orientation:
- =3D"trebuchet ms, sans-serif">A face R, L, I, or O<=
/b>, followed by one of the following: - "trebuchet ms, sans-serif">Any letter=C2=A0r, l,=C2=A0u>,=C2=A0d,=C2=A0f,=C2=A0b,=C2=A0x,=C2=A0y>,=C2=A0z=C2=A0(plus an optional '=C2=A0or 2).nt>
- A pair of square bracke=
ts containing any sequence of index.php/Notation" target=3D"_blank">3D moves that are valid on a 2x2x=
2. - Most of the t=
ime, of course, these moves should be 0-mod-4.
/b>, and=C2=A0B2.- s-serif">The full puzzle rotations x, x', x2, y=
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=C2=A0does the opposite, and M2=C2=A0swaps the left and right halves=
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halves of the puzzle.- -serif">z clam and z' clam.
- =3D"trebuchet ms, sans-serif">z clam=C2=A0is a=C2=A0z=C2=A0ro=
tation followed by a clamshell move. - ms, sans-serif">z' clam=C2=A0is a z'=C2=A0rotation f=
ollowed by a clamshell move. - s-serif">z clam=C2=A0and z' clam=C2=A0are inverses.>
- Parentheses can be u=
sed for grouping, and numbers can follow parentheses to repeat a sequence.<=
/font> - ww.speedsolving.com/wiki/index.php/Commutators_and_Conjugates" target=3D"_b=
lank">Commutator notation is allowed when useful.
=
The use of lowercase letters in mov=
es like Rr=C2=A0may be controversial; if they are deemed confusing,=
=C2=A0R[R]=C2=A0could be encouraged instead.
The use of lowercase letters in mov=
es like Rr=C2=A0may be controversial; if they are deemed confusing,=
=C2=A0R[R]=C2=A0could be encouraged instead.
face=3D"trebuchet ms, sans-serif">
chet ms, sans-serif">Here's an equivalent of Melinda's original gyr=
o sequence in this notation:
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trebuchet ms, sans-serif">I'll briefly digress to discuss a https://www.worldcubeassociation.org/regulations/#4d1" target=3D"_blank" st=
yle=3D"">WCA-inspired "standard orientation" that Marc and I =
have been using. WCA regulations state that white face should be on top (Y =
axis) and the green face should be on the front (Z axis). On a standard NxN=
xN, this will result in the red face on the right (X axis). If the X, Y, an=
d Z axes are aligned in this manner on the 2^4, here is the result:<=
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" width=3D"224" height=3D"126">
yle=3D"">WCA-inspired "standard orientation" that Marc and I =
have been using. WCA regulations state that white face should be on top (Y =
axis) and the green face should be on the front (Z axis). On a standard NxN=
xN, this will result in the red face on the right (X axis). If the X, Y, an=
d Z axes are aligned in this manner on the 2^4, here is the result:<=
/div>
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if" size=3D"4">Metric
if">As for counting numbers of moves, I'd like to propose the "sna=
p" metric. Each separation and reattachment of pieces is a single move=
. This can be very dependent on how a move is executed, but I think it make=
s the most sense for the purpose of solving and speedsolving.
<=p" metric. Each separation and reattachment of pieces is a single move=
. This can be very dependent on how a move is executed, but I think it make=
s the most sense for the purpose of solving and speedsolving.
div>
e=3D"trebuchet ms, sans-serif">A single move like Iy=C2=A0could be e=
xecuted in three snaps as M Ry M'=C2=A0or in just two snaps by r=
earranging the right and left endcaps around the I=C2=A0layer. A seq=
uence like x' Rz Lz' M2=C2=A0may seem like a lot of moves, b=
ut it can be executed in one snap. (The x'=C2=A0is actually zero=
snaps, regardless of context.) The sequence z' clam=C2=A0is two=
snaps, while the equivalent Rx2 U2 (R[x2 y'] Ly)=C2=A0is three =
snaps. Ix=C2=A0can be executed as three snaps with M Rx M'>, two snaps with Rr Ll' x', or one snap by holding the endc=
aps with one hand and rotating the I=C2=A0layer with the other. (In =
an actual solve, the two-snap method is probably fastest.) While Rr=
=C2=A0is pretty clearly one snap, Ru=C2=A0could be executed in two s=
naps (by separating the left and right halves, performing Ru, and th=
en reattaching them) or one snap (by removing the four pieces of Ru=
=C2=A0directly, rotating them, and replacing them).
xecuted in three snaps as M Ry M'=C2=A0or in just two snaps by r=
earranging the right and left endcaps around the I=C2=A0layer. A seq=
uence like x' Rz Lz' M2=C2=A0may seem like a lot of moves, b=
ut it can be executed in one snap. (The x'=C2=A0is actually zero=
snaps, regardless of context.) The sequence z' clam=C2=A0is two=
snaps, while the equivalent Rx2 U2 (R[x2 y'] Ly)=C2=A0is three =
snaps. Ix=C2=A0can be executed as three snaps with M Rx M'>, two snaps with Rr Ll' x', or one snap by holding the endc=
aps with one hand and rotating the I=C2=A0layer with the other. (In =
an actual solve, the two-snap method is probably fastest.) While Rr=
=C2=A0is pretty clearly one snap, Ru=C2=A0could be executed in two s=
naps (by separating the left and right halves, performing Ru, and th=
en reattaching them) or one snap (by removing the four pieces of Ru=
=C2=A0directly, rotating them, and replacing them).
div>
I'd love to hear all y=
our opinions on these things! - Andy
our opinions on these things! - Andy
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ce, monospace" size=3D"1">"Machines take me by surprise with great fre=
quency." - Alan Turing
quency." - Alan Turing
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