Thread: "Physical 2^4 puzzle: the ROIL moveset"

From: Marc Ringuette <ringuette@solarmirror.com>
Date: Wed, 9 Aug 2017 13:57:07 -0700
Subject: Physical 2^4 puzzle: the ROIL moveset



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Hi, physical 2^4 puzzlers,

Extending Michael Gottlieb's RIL idea from last week, I present to you
... the ROIL moveset.

I think ROIL will be a very nice and useful way of manipulating the
puzzle. Also, I've found a straightforward version of FOro, our key
full-puzzle rotation, that fits right into the ROIL scheme. Somebody
will need to fill in a bit of theoretical work to systematize all of
this a bit better, but I think it's a winner.

I've made five videos, the first three of which are less than 5 minutes
total and give the high points of ROIL. I'd recommend having a look
and skimming or skipping the rest of the explanatory text below.

12 ROIL moveset intro 2m14s https://youtu.be/oYeh5fK8LCI
13 ROIL version of FOro 1m10s https://youtu.be/3gvrda5fMto
14 ROIL scrambling 1m17s https://youtu.be/ymnvMzypUp8
15 ROIL strict subset vs macro equivalents 3m37s
https://youtu.be/Iu7MKzD4yq0
16 ROIL meaning of junctions out positions 2m54s
https://youtu.be/xN_vn-6RnV8

For those who don't wish to watch the videos, the main idea is: starting
at the usual home position for the puzzle, shift the 4-piece right end
cap all the way to the left, and then take apart the puzzle into its new
left and right subcubes. You are now holding all pieces of the In face
in your right hand, and the Out face in your left hand. Perform any 3D
rotation on either or both of the I and O faces, trying not to freak out
about the fact that you are looking at the puzzle in an inside-out
"junctions out" projection. Put the subcubes back together, and shift
the left end cap to the right, to return to the normal "corners out"
projection. Continue as normal. Any I and O face turns you have just
done will either be one-click MC4D moves, or macros of around length 9
(in the cases of the I and O face moves, such as Ix and Oz, that make an
odd number of 90 degree turns around the x or the z axis).

Michael already gave us the key two macro sequences last week:

> Iy (physical) == IU' RO2 IF RO2 IU RO2 IF' RO2 IU (virtual)
>
> IU (virtual) == Iy' Rx2 Iz Rx2 Iy Rx2 Iz' Rx2 Iy (physical)
>

With these, and some (admittedly fairly major) bookkeeping work but no
new research, we should be able to complete a proof that the set of ROIL
states is identical to the set of virtual 2^4 states, by providing
macros in each puzzle for all moves in the "other" puzzle, so that each
puzzle can "follow along" with any moves made on the other puzzle.


Or, if you prefer to solve the physical 2^4 puzzle using a strict MC4D
subset -- only moves that have one-click equivalents in MC4D -- you can
add only the new FOro physical "macro" sequence, as a unitary move, to
the common-subset moves that are identical and length-1 in both puzzles.

FOro == Iy Oy' RO2 BO2 UO2 RO2

You'll note that this FOro sequence begins with a pair of opposite I and
O moves, a rotation of sorts, followed by four cleanup moves.

If you're concerned about my slab moves UO2, DO2, FO2, BO2, a set of
strict ROIL substitutions are:
UO2 == Rz' Lz Iy2 Rz Lz'
DO2 == Rz Lz' Iy2 Rz' Lz
FO2 == Ry Ly' Iz2 Ry' Ly
BO2 == Ry' Ly Iz2 Ry Ly'
and of course RO2 == Rx2. Sorry about the still-unsettled mix of
virtual and physical notations.


Cheers
Marc


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Hi, physical 2^4 puzzlers,



Extending Michael Gottlieb's RIL idea from last week, I present to
you ... the ROIL moveset. 



I think ROIL will be a very nice and useful way of manipulating the
puzzle.   Also, I've found a straightforward version of FOro, our
key full-puzzle rotation, that fits right into the ROIL scheme.  
Somebody will need to fill in a bit of theoretical work to
systematize all of this a bit better, but I think it's a winner.



I've made five videos, the first three of which are less than 5
minutes total and give the high points of ROIL.   I'd recommend
having a look and skimming or skipping the rest of the explanatory
text below.



12 ROIL moveset intro   2m14s href="https://youtu.be/oYeh5fK8LCI">https://youtu.be/oYeh5fK8LCI


13 ROIL version of FOro   1m10s href="https://youtu.be/3gvrda5fMto">https://youtu.be/3gvrda5fMto


14 ROIL scrambling   1m17s href="https://youtu.be/ymnvMzypUp8">https://youtu.be/ymnvMzypUp8


15 ROIL strict subset vs macro equivalents   3m37s class="moz-txt-link-freetext" href="https://youtu.be/Iu7MKzD4yq0">https://youtu.be/Iu7MKzD4yq0


16 ROIL meaning of junctions out positions   2m54s class="moz-txt-link-freetext" href="https://youtu.be/xN_vn-6RnV8">https://youtu.be/xN_vn-6RnV8




For those who don't wish to watch the videos, the main idea is: 
starting at the usual home position for the puzzle, shift the
4-piece right end cap all the way to the left, and then take apart
the puzzle into its new left and right subcubes.  You are now
holding all pieces of the In face in your right hand, and the Out
face in your left hand.   Perform any 3D rotation on either or both
of the I and O faces, trying not to freak out about the fact that
you are looking at the puzzle in an inside-out "junctions out"
projection.   Put the subcubes back together, and shift the left end
cap to the right, to return to the normal "corners out" projection. 
Continue as normal.  Any I and O face turns you have just done will
either be one-click MC4D moves, or macros of around length 9 (in the
cases of the I and O face moves, such as Ix and Oz, that make an odd
number of 90 degree turns around the x or the z axis).



Michael already gave us the key two macro sequences last week:






Iy (physical) == IU' RO2 IF RO2 IU RO2 IF'
RO2 IU (virtual)

IU (virtual) == Iy' Rx2 Iz Rx2 Iy Rx2 Iz' Rx2 Iy
(physical)








With these, and some (admittedly fairly major) bookkeeping work but
no new research, we should be able to complete a proof that the set
of ROIL states is identical to the set of virtual 2^4 states, by
providing macros in each puzzle for all moves in the "other" puzzle,
so that each puzzle can "follow along" with any moves made on the
other puzzle.





Or, if you prefer to solve the physical 2^4 puzzle using a strict
MC4D subset -- only moves that have one-click equivalents in MC4D --
you can add only the new FOro physical "macro" sequence, as a
unitary move, to the common-subset moves that are identical and
length-1 in both puzzles.



      FOro == Iy Oy' RO2 BO2 UO2 RO2



You'll note that this FOro sequence begins with a pair of opposite I
and O moves, a rotation of sorts, followed by four cleanup moves.  




If you're concerned about my slab moves UO2, DO2, FO2, BO2, a set of
strict ROIL substitutions are:

    UO2 == Rz' Lz Iy2 Rz Lz'

    DO2 == Rz Lz' Iy2 Rz' Lz

    FO2 == Ry Ly' Iz2 Ry' Ly

    BO2 == Ry' Ly Iz2 Ry Ly'

and of course RO2 == Rx2.  Sorry about the still-unsettled mix of
virtual and physical notations.





Cheers

Marc






--------------49919558E9CAA88198E3DC14--



From: "Eduard Baumann" <ed.baumann@bluewin.ch>
Date: Thu, 10 Aug 2017 12:48:21 +0200
Subject: Re: [MC4D] Physical 2^4 puzzle: the ROIL moveset



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Thanks, very clear and nice instructions!
Kind regards
Ed


----- Original Message -----=20
From: Marc Ringuette ringuette@solarmirror.com [4D_Cubing]=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Wednesday, August 09, 2017 10:57 PM
Subject: [MC4D] Physical 2^4 puzzle: the ROIL moveset


=20=20=20=20
Hi, physical 2^4 puzzlers,

Extending Michael Gottlieb's RIL idea from last week, I present to you ..=
. the ROIL moveset.=20=20

I think ROIL will be a very nice and useful way of manipulating the puzzl=
e. Also, I've found a straightforward version of FOro, our key full-puzzl=
e rotation, that fits right into the ROIL scheme. Somebody will need to f=
ill in a bit of theoretical work to systematize all of this a bit better, b=
ut I think it's a winner.

I've made five videos, the first three of which are less than 5 minutes t=
otal and give the high points of ROIL. I'd recommend having a look and sk=
imming or skipping the rest of the explanatory text below.

12 ROIL moveset intro 2m14s https://youtu.be/oYeh5fK8LCI=20
13 ROIL version of FOro 1m10s https://youtu.be/3gvrda5fMto=20
14 ROIL scrambling 1m17s https://youtu.be/ymnvMzypUp8=20
15 ROIL strict subset vs macro equivalents 3m37s https://youtu.be/Iu7MK=
zD4yq0=20
16 ROIL meaning of junctions out positions 2m54s https://youtu.be/xN_vn=
-6RnV8=20

For those who don't wish to watch the videos, the main idea is: starting=
at the usual home position for the puzzle, shift the 4-piece right end cap=
all the way to the left, and then take apart the puzzle into its new left =
and right subcubes. You are now holding all pieces of the In face in your =
right hand, and the Out face in your left hand. Perform any 3D rotation o=
n either or both of the I and O faces, trying not to freak out about the fa=
ct that you are looking at the puzzle in an inside-out "junctions out" proj=
ection. Put the subcubes back together, and shift the left end cap to the=
right, to return to the normal "corners out" projection. Continue as norm=
al. Any I and O face turns you have just done will either be one-click MC4=
D moves, or macros of around length 9 (in the cases of the I and O face mov=
es, such as Ix and Oz, that make an odd number of 90 degree turns around th=
e x or the z axis).

Michael already gave us the key two macro sequences last week:



Iy (physical) =3D=3D IU' RO2 IF RO2 IU RO2 IF' RO2 IU (virtual)=20
IU (virtual) =3D=3D Iy' Rx2 Iz Rx2 Iy Rx2 Iz' Rx2 Iy (physical)


With these, and some (admittedly fairly major) bookkeeping work but no ne=
w research, we should be able to complete a proof that the set of ROIL stat=
es is identical to the set of virtual 2^4 states, by providing macros in ea=
ch puzzle for all moves in the "other" puzzle, so that each puzzle can "fol=
low along" with any moves made on the other puzzle.


Or, if you prefer to solve the physical 2^4 puzzle using a strict MC4D su=
bset -- only moves that have one-click equivalents in MC4D -- you can add o=
nly the new FOro physical "macro" sequence, as a unitary move, to the commo=
n-subset moves that are identical and length-1 in both puzzles.

FOro =3D=3D Iy Oy' RO2 BO2 UO2 RO2

You'll note that this FOro sequence begins with a pair of opposite I and =
O moves, a rotation of sorts, followed by four cleanup moves.=20=20=20

If you're concerned about my slab moves UO2, DO2, FO2, BO2, a set of stri=
ct ROIL substitutions are:
UO2 =3D=3D Rz' Lz Iy2 Rz Lz'
DO2 =3D=3D Rz Lz' Iy2 Rz' Lz
FO2 =3D=3D Ry Ly' Iz2 Ry' Ly
BO2 =3D=3D Ry' Ly Iz2 Ry Ly'
and of course RO2 =3D=3D Rx2. Sorry about the still-unsettled mix of vir=
tual and physical notations.


Cheers
Marc



=20=20
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charset="UTF-8"
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=EF=BB=BF




Thanks, very clear and nice=20
instructions!

Kind regards

Ed

 

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:=20
href=3D"mailto:ringuette@solarmirror.com [4D_Cubing]">Marc Ringuette=20
ringuette@solarmirror.com [4D_Cubing]
To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>
Sent: Wednesday, August 09, 2017 1=
0:57=20
PM

Subject: [MC4D] Physical 2^4 puzzl=
e: the=20
ROIL moveset


 =20

Hi, physical 2^4 puzzlers,

Extending Michael Gottlieb's RIL ide=
a=20
from last week, I present to you ... the ROIL moveset. 

I th=
ink=20
ROIL will be a very nice and useful way of manipulating the=20
puzzle.   Also, I've found a straightforward version of FOro, o=
ur=20
key full-puzzle rotation, that fits right into the ROIL scheme.  =20
Somebody will need to fill in a bit of theoretical work to systematize al=
l of=20
this a bit better, but I think it's a winner.

I've made five video=
s,=20
the first three of which are less than 5 minutes total and give the high=
=20
points of ROIL.   I'd recommend having a look and skimming or=20
skipping the rest of the explanatory text below.

12 ROIL moveset=20
intro   2m14s href=3D"https://youtu.be/oYeh5fK8LCI">https://youtu.be/oYeh5fK8LCI R>13=20
ROIL version of FOro   1m10s href=3D"https://youtu.be/3gvrda5fMto">https://youtu.be/3gvrda5fMto R>14=20
ROIL scrambling   1m17s href=3D"https://youtu.be/ymnvMzypUp8">https://youtu.be/ymnvMzypUp8 R>15=20
ROIL strict subset vs macro equivalents   3m37s class=3Dmoz-txt-link-freetext=20
href=3D"https://youtu.be/Iu7MKzD4yq0">https://youtu.be/Iu7MKzD4yq0 R>16=20
ROIL meaning of junctions out positions   2m54s class=3Dmoz-txt-link-freetext=20
href=3D"https://youtu.be/xN_vn-6RnV8">https://youtu.be/xN_vn-6RnV8=20


For those who don't wish to watch the videos, the main idea is:&n=
bsp;=20
starting at the usual home position for the puzzle, shift the 4-piece rig=
ht=20
end cap all the way to the left, and then take apart the puzzle into its =
new=20
left and right subcubes.  You are now holding all pieces of the In f=
ace=20
in your right hand, and the Out face in your left hand.   Perfo=
rm=20
any 3D rotation on either or both of the I and O faces, trying not to fre=
ak=20
out about the fact that you are looking at the puzzle in an inside-out=20
"junctions out" projection.   Put the subcubes back together, and sh=
ift=20
the left end cap to the right, to return to the normal "corners out"=20
projection.  Continue as normal.  Any I and O face turns you ha=
ve=20
just done will either be one-click MC4D moves, or macros of around length=
9=20
(in the cases of the I and O face moves, such as Ix and Oz, that make an =
odd=20
number of 90 degree turns around the x or the z axis).

Michael alr=
eady=20
gave us the key two macro sequences last week:





Iy (physical) =3D=3D IU' RO2 IF RO2 IU RO2 IF' RO2 =
IU=20
(virtual)=20

IU (virtual) =3D=3D Iy' Rx2 Iz Rx2 Iy Rx2 Iz' Rx2 Iy=20
(physical)


With these, and some=20
(admittedly fairly major) bookkeeping work but no new research, we should=
be=20
able to complete a proof that the set of ROIL states is identical to the =
set=20
of virtual 2^4 states, by providing macros in each puzzle for all moves i=
n the=20
"other" puzzle, so that each puzzle can "follow along" with any moves mad=
e on=20
the other puzzle.


Or, if you prefer to solve the physical 2^4=
=20
puzzle using a strict MC4D subset -- only moves that have one-click=20
equivalents in MC4D -- you can add only the new FOro physical "macro"=20
sequence, as a unitary move, to the common-subset moves that are identica=
l and=20
length-1 in both puzzles.

      FOro =3D=3D Iy=
Oy' RO2=20
BO2 UO2 RO2

You'll note that this FOro sequence begins with a pair=
of=20
opposite I and O moves, a rotation of sorts, followed by four cleanup=20
moves.  

If you're concerned about my slab moves UO2, D=
O2,=20
FO2, BO2, a set of strict ROIL substitutions are:
    U=
O2 =3D=3D=20
Rz' Lz Iy2 Rz Lz'
    DO2 =3D=3D Rz Lz' Iy2 Rz'=20
Lz
    FO2 =3D=3D Ry Ly' Iz2 Ry' Ly
  &nbs=
p; BO2 =3D=3D=20
Ry' Ly Iz2 Ry Ly'
and of course RO2 =3D=3D Rx2.  Sorry about the=
=20
still-unsettled mix of virtual and physical=20
notations.


Cheers
Marc




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