Thread: "2x2x2x2: a few algs and an example solve"

Hi gang!   I'm back to studying the physical 2^4, after a 6 month
break.   You know what that means:  lots of little YouTube videos with
no production values whatsoever!  I've uploaded six videos to the new
YouTube channel I've created for my puzzle stuff.   Five short videos
describe the move set I'm using and a few algorithms, then I give a 10
minute solution video to put me on the HOF list.

Probably the most generally interesting of these videos is the third,
#23 in my numbering sequence, showing how to perform a 180 degree twist
on a single piece (in 30 moves using ROIL Zero).   I shorten this to 10
moves in the case of orienting two opposite faces only, in video #24.  I
used the shortened version in my example solve at this point 6m45s in:  
https://youtu.be/N4lqDkDJ4Yo?t=6m45s

21 ROIL Zero moveset     1m11s   https://youtu.be/hOt5DnDNibg
22 Sune+Antisune+twist2    3m17s   https://youtu.be/R9DQhB88yMY
23 Doubletwist algorithm    2m17s    https://youtu.be/Io4rN080V7c
24 Doubletwist, align two faces only, shorter, 3 cases    2m59s
https://youtu.be/wmdbYPiegqQ
25 Alg for final U2 on R cube   1m16s   https://youtu.be/K2d01CMqtgw
26 Example solve    10m42s    https://youtu.be/N4lqDkDJ4Yo


Just now, I tried an additional goofy experiment:  a wildly different
solution method where I permute all pieces first, then orient them
afterwards!   It only took half an hour or so.   It was a hoot, try
it!   I'm fascinated by the 12 orientations of these 4d puzzle pieces,
and the second half of this method is a way to focus in on orientation
exclusively.


Cheers
Marc

--------------8A29C263D73FB72752A552C6
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: quoted-printable

That's so cool, Marc! Best of all it puts you among the first 10 official s=
olvers at number 8. And so much goodness within these videos. I love your s=
ingle piece flip and the way you so casually perform twists in the spooky p=
rojection &t=3D4m4s> which hurts my brain. I'm also curious about that crazy solve yo=
u did where you placed all the pieces and then oriented them all in place a=
nd hope you'll make a video walk through of that method. It may not be a us=
eful solution method but it's certainly a good exercise of a handy techniqu=
e.

In unrelated news, a crazy YouTube celebrity Miguel Gimenez in Spain bought=
a puzzle and made a wonderful video introduction in Spanish outube.com/watch?v=3DKjHC6iR_DUM>. I had seen his work before but didn't re=
alize this was him until he told me about his new video. He has an astoundi=
ng 1.2 million subscribers and his video already has over 100,000 views and=
1,000 comments! He appears to have done a very careful job though I can't =
tell how accurate it is. If one of you understands the puzzle and also spea=
ks Spanish, please let me know what you think. He told me he plans to allow=
community subtitle submissions, so if anyone wants to attempt that, please=
let him know, and of course let us know because I'm eager to read it mysel=
f.

Now back to Marc with congratulations on securing his prime spot in the 2x2=
x2x2 HOF! Very nicely done, Marc!

Happy puzzling!
-Melinda

On 7/12/2018 6:51 PM, Marc Ringuette ringuette@solarmirror.com [4D_Cubing] =
wrote:
> Hi gang!=C2=A0=C2=A0 I'm back to studying the physical 2^4, after a 6 mon=
th
> break.=C2=A0=C2=A0 You know what that means:=C2=A0 lots of little YouTube=
videos with
> no production values whatsoever!=C2=A0 I've uploaded six videos to the ne=
w
> YouTube channel I've created for my puzzle stuff.=C2=A0=C2=A0 Five short =
videos
> describe the move set I'm using and a few algorithms, then I give a 10
> minute solution video to put me on the HOF list.
>
> Probably the most generally interesting of these videos is the third,
> #23 in my numbering sequence, showing how to perform a 180 degree twist
> on a single piece (in 30 moves using ROIL Zero). =C2=A0 I shorten this to=
10
> moves in the case of orienting two opposite faces only, in video #24.=C2=
=A0 I
> used the shortened version in my example solve at this point 6m45s in:
> https://youtu.be/N4lqDkDJ4Yo?t=3D6m45s
>
> 21 ROIL Zero moveset=C2=A0=C2=A0=C2=A0=C2=A0 1m11s=C2=A0=C2=A0 https://yo=
utu.be/hOt5DnDNibg
> 22 Sune+Antisune+twist2=C2=A0=C2=A0=C2=A0 3m17s=C2=A0=C2=A0 https://youtu=
.be/R9DQhB88yMY
> 23 Doubletwist algorithm=C2=A0=C2=A0=C2=A0 2m17s=C2=A0=C2=A0=C2=A0 https:=
//youtu.be/Io4rN080V7c
> 24 Doubletwist, align two faces only, shorter, 3 cases=C2=A0=C2=A0=C2=A0 =
2m59s
> https://youtu.be/wmdbYPiegqQ
> 25 Alg for final U2 on R cube=C2=A0=C2=A0 1m16s=C2=A0=C2=A0 https://youtu=
.be/K2d01CMqtgw
> 26 Example solve=C2=A0=C2=A0=C2=A0 10m42s =C2=A0=C2=A0 https://youtu.be/N=
4lqDkDJ4Yo
>
>
> Just now, I tried an additional goofy experiment:=C2=A0 a wildly differen=
t
> solution method where I permute all pieces first, then orient them
> afterwards!=C2=A0=C2=A0 It only took half an hour or so. =C2=A0 It was a =
hoot, try
> it!=C2=A0=C2=A0 I'm fascinated by the 12 orientations of these 4d puzzle =
pieces,
> and the second half of this method is a way to focus in on orientation
> exclusively.
>
>
> Cheers
> Marc
>
>
>
> ------------------------------------
> Posted by: Marc Ringuette
> ------------------------------------
>
>
> ------------------------------------
>
> Yahoo Groups Links
>
>
>
>


--------------8A29C263D73FB72752A552C6
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: quoted-printable



">


That's so cool, Marc! Best of all it puts you among the first 10
official solvers at number 8. And so much goodness within these
videos. I love your single piece flip and the way you so casually
perform href=3D"https://www.youtube.com/watch?v=3DN4lqDkDJ4Yo&feature=3Dyoutu.b=
e&t=3D4m4s">twists
in the spooky projection which hurts my brain. I'm also
curious about that crazy solve you did where you placed all the
pieces and then oriented them all in place and hope you'll make a
video walk through of that method. It may not be a useful solution
method but it's certainly a good exercise of a handy technique.



In unrelated news, a crazy YouTube celebrity Miguel Gimenez in Spain
bought a puzzle and made href=3D"https://www.youtube.com/watch?v=3DKjHC6iR_DUM">a wonderful
video introduction in Spanish. I had seen his work before but
didn't realize this was him until he told me about his new video. He
has an astounding 1.2 million subscribers and his video already has
over 100,000 views and 1,000 comments! He appears to have done a
very careful job though I can't tell how accurate it is. If one of
you understands the puzzle and also speaks Spanish, please let me
know what you think. He told me he plans to allow community subtitle
submissions, so if anyone wants to attempt that, please let him
know, and of course let us know because I'm eager to read it myself.>


Now back to Marc with congratulations on securing his prime spot in
the 2x2x2x2 HOF! Very nicely done, Marc!



Happy puzzling!

-Melinda

cite=3D"mid:f771b287-fcc3-c33a-4c8d-d1762b66df52@solarmirror.com">

Hi gang!=C2=A0=C2=A0 I'm back to studying the physical=
 2^4, after a 6 month=20
break.=C2=A0=C2=A0 You know what that means:=C2=A0 lots of little YouTube v=
ideos with=20
no production values whatsoever!=C2=A0 I've uploaded six videos to the new=
=20
YouTube channel I've created for my puzzle stuff.=C2=A0=C2=A0 Five short vi=
deos=20
describe the move set I'm using and a few algorithms, then I give a 10=20
minute solution video to put me on the HOF list.

Probably the most generally interesting of these videos is the third,=20
#23 in my numbering sequence, showing how to perform a 180 degree twist=20
on a single piece (in 30 moves using ROIL Zero). =C2=A0 I shorten this to 1=
0=20
moves in the case of orienting two opposite faces only, in video #24.=C2=A0=
 I=20
used the shortened version in my example solve at this point 6m45s in:=C2=
=A0=C2=A0=20
=3D6m45s">https://youtu.be/N4lqDkDJ4Yo?t=3D6m45s

21 ROIL Zero moveset=C2=A0=C2=A0=C2=A0=C2=A0 1m11s=C2=A0=C2=A0 moz-txt-link-freetext" href=3D"https://youtu.be/hOt5DnDNibg">https://youtu.=
be/hOt5DnDNibg
22 Sune+Antisune+twist2=C2=A0=C2=A0=C2=A0 3m17s=C2=A0=C2=A0 -txt-link-freetext" href=3D"https://youtu.be/R9DQhB88yMY">https://youtu.be/=
R9DQhB88yMY
23 Doubletwist algorithm=C2=A0=C2=A0=C2=A0 2m17s=C2=A0=C2=A0=C2=A0 =3D"moz-txt-link-freetext" href=3D"https://youtu.be/Io4rN080V7c">https://yo=
utu.be/Io4rN080V7c
24 Doubletwist, align two faces only, shorter, 3 cases=C2=A0=C2=A0=C2=A0 2m=
59s=20
ht=
tps://youtu.be/wmdbYPiegqQ
25 Alg for final U2 on R cube=C2=A0=C2=A0 1m16s=C2=A0=C2=A0 -txt-link-freetext" href=3D"https://youtu.be/K2d01CMqtgw">https://youtu.be/=
K2d01CMqtgw
26 Example solve=C2=A0=C2=A0=C2=A0 10m42s =C2=A0=C2=A0 link-freetext" href=3D"https://youtu.be/N4lqDkDJ4Yo">https://youtu.be/N4lqD=
kDJ4Yo


Just now, I tried an additional goofy experiment:=C2=A0 a wildly different=
=20
solution method where I permute all pieces first, then orient them=20
afterwards!=C2=A0=C2=A0 It only took half an hour or so. =C2=A0 It was a ho=
ot, try=20
it!=C2=A0=C2=A0 I'm fascinated by the 12 orientations of these 4d puzzle pi=
eces,=20
and the second half of this method is a way to focus in on orientation=20
exclusively.


Cheers
Marc



------------------------------------
Posted by: Marc Ringuette :ringuette@solarmirror.com"><ringuette@solarmirror.com>
------------------------------------


------------------------------------

Yahoo Groups Links

<*> To visit your group on the web, go to:
    p/4D_Cubing/">http://groups.yahoo.com/group/4D_Cubing/

<*> Your email settings:
    Individual Email | Traditional

<*> To change settings online go to:
    p/4D_Cubing/join">http://groups.yahoo.com/group/4D_Cubing/join
    (Yahoo! ID required)

<*> To change settings via email:
    ahoogroups.com">4D_Cubing-digest@yahoogroups.com=20
    ured@yahoogroups.com">4D_Cubing-fullfeatured@yahoogroups.com

<*> To unsubscribe from this group, send an email to:
    ibe@yahoogroups.com">4D_Cubing-unsubscribe@yahoogroups.com

<*> Your use of Yahoo Groups is subject to:
    /us/yahoo/utos/terms/">https://info.yahoo.com/legal/us/yahoo/utos/terms/>

--------------27C2C0EC02BAE9390861A29E
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit

Hi, Andy,

That 8 move U2 parity algorithm is so much better than the 18 move one
that I had come up with, thanks!  And it is easy to tweak to maximize
cancellations as below.

Your idea of coming up with a complete list of "PBL plus parity" algs,
to avoid ever inserting an explicit parity step, is pretty fancy.   In
lieu of the fancy approach, I think I'll use this method when I'm trying
to minimize moves:

(1) Solve each subcube to "1 turn away from solved" counting parity of each.
(2) Mentally find the shortest solution to the full puzzle ignoring
parity.   It will be a trivial solution of <=4 moves.   Count parity of
that solution.
(3) If parity would be off, insert a variant of the parity algorithm
(either R2 F2 R2 U' R2 F2 R2 U', or R2 F2 R2 U R2 F2 R2 U, or U' R2 F2
R2 U' R2 F2 R2) on one of the subcubes now, cancelling the last move of
the parity algorithm with the first move of the computed solution
whenever possible.
(4) Finish the solution.


Cheers
Marc


On 7/13/2018 8:11 PM, Andy F legomany3448@gmail.com [4D_Cubing] wrote:
> ... As for solving the U2 parity ...
> (R2 F2 R2 U')2
>
>
>
> On 7/12/2018 6:51 PM, Marc Ringuette ringuette@solarmirror.com
> [4D_Cubing] wrote:
>> 25 Alg for final U2 on R cube (18 moves)   1m16shttps://youtu.be/K2d01CMqtgw
>>


--------------27C2C0EC02BAE9390861A29E
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: 8bit






Hi, Andy,



That 8 move U2 parity algorithm is so much better than the 18 move
one that I had come up with, thanks!  And it is easy to tweak to
maximize cancellations as below.



Your idea of coming up with a complete list of "PBL plus parity"
algs, to avoid ever inserting an explicit parity step, is pretty
fancy.   In lieu of the fancy approach, I think I'll use this method
when I'm trying to minimize moves:



(1) Solve each subcube to "1 turn away from solved" counting parity
of each.

(2) Mentally find the shortest solution to the full puzzle ignoring
parity.   It will be a trivial solution of <=4 moves.   Count
parity of that solution.

(3) If parity would be off, insert a variant of the parity algorithm
(either R2 F2 R2 U' R2 F2 R2 U', or R2 F2 R2 U R2 F2 R2 U, or U' R2
F2 R2 U' R2 F2 R2) on one of the subcubes now, cancelling the last
move of the parity algorithm with the first move of the computed
solution whenever possible.

(4) Finish the solution.





Cheers

Marc





On 7/13/2018 8:11 PM, Andy F legomany3448@gmail.com [4D_Cubing]
wrote:

cite="mid:CAC1m+CGKa2hdnTMZxFTSAa4hCgXWbS=B=ZP9y=kfxEz5WHr=EQ@mail.gmail.com">

 

... As for solving the U2 parity ...

(R2 F2 R2 U')2

style="border-left:1px #ccc solid;">

id="m_8177238700915352477m_5523283801066067593ygrp-mlmsg">
id="m_8177238700915352477m_5523283801066067593ygrp-msg">
id="m_8177238700915352477m_5523283801066067593ygrp-text">

class="m_8177238700915352477m_5523283801066067593moz-cite-prefix">On
7/12/2018 6:51 PM, Marc
Ringuette class="m_8177238700915352477m_5523283801066067593moz-txt-link-abbreviated"
href="mailto:ringuette@solarmirror.com" target="_blank"
moz-do-not-send="true">ringuette@solarmirror.com
[4D_Cubing] wrote:

id="m_8177238700915352477m_5523283801066067593ygrp-mlmsg">
id="m_8177238700915352477m_5523283801066067593ygrp-msg">
id="m_8177238700915352477m_5523283801066067593ygrp-text">

25 Alg for final U2 on R cube (18 moves)   1m16s   https://youtu.be/K2d01CMqtgw

--0000000000002faa380570fae0c7
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Well that was fun!

NCM =3D Net (modulus) Clockwise Movement* before* executing the algorithm.
After executing the correct algorithm, NCM will be zero.

While HTM is the standard
for (l>3)^n, I think ATM =
is
more appropriate for 2^n, so that's what I've used here.

Hopefully the formatting holds up.

PBL Case NCM Algorithm Move count Explanation

skip
0 solved 0
2 (R2 F2 R2 U')2 8

ADJ swap
(UBL =E2=86=94 UBR)
1 (U) (R' L') U2 R U R' U2 L U' R 10 inverse Ja permutation
3 R' U L' U2 R U' R' U2 (R L) (U') 10 Ja permutation

OPP swap
(UFR =E2=86=94 UBL)
1 y [alg below without AUF] (U') 13
3 R' U L' U2 R U' x' U L' U2 R U' L (U) 13 Nb permutation

double OPP swap
0 (U') R2 F2 R2 (U') 5 standard Ortega alg cancels completely with skip-2
2 R2 F2 R2 3 standard Ortega alg

double ADJ swap
(BL =E2=86=94 BR)
0 R2 U' F2 U2 R2 D' R2 7 standard Ortega alg
2 y R2 F2 U' F2 U2 R2 D' R2 8 R2 F2 R2 rotates case while solving parity;
cancels nicely with alg above

hybrid swap
(UFR =E2=86=94 UFL; DFR =E2=86=94 DBL)
0 (D) [alg below] (D) 9
2 L' U R' D2 R U' L 7 standard Ortega alg (half Aa permutation)

This algset has an average movecount of 7.75 including AUF; pure Ortega,
taking the shortest algorithm from each pair above plus a 50% chance of
U2P, yields 6.83+(8/2)=3D10.83. PBL-P saves an average of ~3 moves per solv=
e.

So that covers U2P, but Marc also mentioned corner twists between faces
that manifest during Ortega. I would think this is a significant issue,
happening 2/3 of the time, so here's a crazy idea to remedy that:

Use PBL-P only for solving the second half. If there's a +2 NCM during PBL
on the first half, carry it over when solving the second half. For the
first half, we'd need variants of OCLL and PBL that do the following:
OCLL-[something] - Orient corners of last layer, but "solve" (into some
consistent position) a badly oriented corner in the process. These
algorithms would be strictly 3D, and would have to be executed on both
halves. They might require some lookahead into PBL. I don't know how large
they would have to be, but ignoring permutation leaves 10 additional cases
over OCLL by my count (only 5 unique cases due to symmetry).
PBL-[something] - Permute both layers of one half while exchanging a corner
twist with the opposite half. These algorithms would be 4D, and I have no
idea how many there would be or how difficult they would be to execute.

A simpler, less glamorous solution is to simply solving the corner twist
before doing either Ortega half. Recognizing a twisted corner isn't too
difficult on an n^3, even when scrambled, especially if one is already
familiar with the seven OCLLs. This is the 4D equivalent of step 4 in
the Guimond
Beginner Method
Method>.
Here's a short alg for a solving a clockwise twist on R: I[y2] R[U' R' U' R
U2] I[y2] (Brackets indicate ROIL-style 3D moves -- let me know if my
notation is difficult to understand.)

But what if we could solve the twisted corner *and* OLL of both halves all
at the same time? There are only a few possibilities there:
No corner parity:
Mirror OLLs - 7 cases; execute 3D algorithm using 4D twists
Non-mirror OLLs - 21 unique cases (26 including mirrors; like
sune/antisune); can use specialized 4D algorithms or two separate OCLLs
Corner parity:
6 cases for clockwise half * 6 cases for counterclockwise half =3D 36 cases=
;
must use specialized 4D algorithms

Most, if not all, of these specialized 4D algorithms would probably consist
of the "Orient All" stage of the 2^3 SOAP method
(algorithms here
) sandwiched by
I[y2]s.

Using I[y2] like this gave me an idea for a 3-stage method, after 4D
orientation/separation:
1. Solve one face of each half (strictly 3D; just like Ortega)
2.1. Orient the L and R halves so that their unsolved layers are in LI and
RO respectively
2.2. Perform I[y2]
2. 3D-orient all pieces on the R half (strictly 3D; perhaps using something
akin to Guimond >
)
3. Solve PBL on both faces

Here's another crazy idea to go along with the above proposition: PBBL
(permute both "both layers"s). These would be 4D algorithms that solve PBL
on both halves of the puzzle at once. I think there would only be 10 unique
cases, not counting those with one half solved (i.e. normal PBL) or where
both halves have the same case (for these, execute the normal PBL algorithm
using the 4D subset ). This set might not be too useful in physical
solves using Marc's moveset, where 3D algs are easy, but in a virtual solve
it may be worth considering. Those 10 unique cases are:

- ADJ swap + OPP swap
- ADJ swap + double OPP swap
- ADJ swap + double ADJ swap
- ADJ swap + hybrid swap
- OPP swap + double OPP swap
- OPP swap + double ADJ swap
- OPP swap + hybrid swap
- double OPP swap + double ADJ swap
- double OPP swap + hybrid swap
- double ADJ swap + hybrid swap

I hope this gave you all something to think about, and I might start to
look for PBBL algorithms (especially some that would be easy to perform on
the physical puzzle).

- Andy


On Fri, Jul 13, 2018 at 11:11 PM, Andy F wrote:

> Hey all!
>
> I haven't been keeping up with the activity here, but I thought I'd give
> my thoughts on Marc's solve anyway.
>
> The double Ortega method makes a lot of sense, so I just tried it on a
> virtual 2^4 since I don't have a physical puzzle yet. It took 132 moves,
> which was on-par with my 130-move first-layer/OLL/PLL (FLOP?) solve.
> Instead of using the subset for permuting the first layer (PFL?), I
> used , which cut the move count on that step by half at the cost
> since the opposite layer's permutation didn't matter.
>
> As for solving the U2 parity, I was introduced to a much shorter algorith=
m
> at a recent 3D competition:
>
> (R' L' U2 R L U')2
>
> This can be adapted to an even shorter 2^n algorithm, which is quite
> ergonomic on a 2^3:
>
> (R2 F2 R2 U')2
>
> Since PBL is so small, I think it may even be possible to combine PBL wit=
h
> U2 parity (U2P? Am I going too crazy with these acronyms?). I'll start
> looking through the PBL algs
> and see if I can put
> together a PBL-P set.
>
> - Andy
>
> On Fri, Jul 13, 2018 at 12:42 PM, Ty Jones whotyjones@gmail.com
> [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>
>>
>>
>> Wow! That's exciting that someone with so many subscribers got a hold of
>> your puzzle!
>>
>> On Fri, Jul 13, 2018 at 12:32 AM Melinda Green melinda@superliminal.com
>> [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>>
>>>
>>>
>>> That's so cool, Marc! Best of all it puts you among the first 10
>>> official solvers at number 8. And so much goodness within these videos.=
I
>>> love your single piece flip and the way you so casually perform twists
>>> in the spooky projection
>>> m4s>
>>> which hurts my brain. I'm also curious about that crazy solve you did w=
here
>>> you placed all the pieces and then oriented them all in place and hope
>>> you'll make a video walk through of that method. It may not be a useful
>>> solution method but it's certainly a good exercise of a handy technique=
.
>>>
>>> In unrelated news, a crazy YouTube celebrity Miguel Gimenez in Spain
>>> bought a puzzle and made a wonderful video introduction in Spanish
>>> . I had seen his work
>>> before but didn't realize this was him until he told me about his new
>>> video. He has an astounding 1.2 million subscribers and his video alrea=
dy
>>> has over 100,000 views and 1,000 comments! He appears to have done a ve=
ry
>>> careful job though I can't tell how accurate it is. If one of you
>>> understands the puzzle and also speaks Spanish, please let me know what=
you
>>> think. He told me he plans to allow community subtitle submissions, so =
if
>>> anyone wants to attempt that, please let him know, and of course let us
>>> know because I'm eager to read it myself..
>>>
>>>
>>> Now back to Marc with congratulations on securing his prime spot in the
>>> 2x2x2x2 HOF! Very nicely done, Marc!
>>>
>>> Happy puzzling!
>>> -Melinda
>>>
>>>
>>>
>>> On 7/12/2018 6:51 PM, Marc Ringuette ringuette@solarmirror.com
>>> [4D_Cubing] wrote:
>>>
>>> Hi gang! I'm back to studying the physical 2^4, after a 6 month
>>> break. You know what that means: lots of little YouTube videos with
>>> no production values whatsoever! I've uploaded six videos to the new
>>> YouTube channel I've created for my puzzle stuff. Five short videos
>>> describe the move set I'm using and a few algorithms, then I give a 10
>>> minute solution video to put me on the HOF list.
>>>
>>> Probably the most generally interesting of these videos is the third,
>>> #23 in my numbering sequence, showing how to perform a 180 degree twist
>>> on a single piece (in 30 moves using ROIL Zero). I shorten this to 10
>>> moves in the case of orienting two opposite faces only, in video #24. =
I
>>> used the shortened version in my example solve at this point 6m45s in: =
https://youtu.be/N4lqDkDJ4Yo?t=3D6m45s
>>>
>>> 21 ROIL Zero moveset 1m11s https://youtu.be/hOt5DnDNibg
>>> 22 Sune+Antisune+twist2 3m17s https://youtu.be/R9DQhB88yMY
>>> 23 Doubletwist algorithm 2m17s https://youtu.be/Io4rN080V7c
>>> 24 Doubletwist, align two faces only, shorter, 3 cases 2m59s https:/=
/youtu.be/wmdbYPiegqQ
>>> 25 Alg for final U2 on R cube 1m16s https://youtu.be/K2d01CMqtgw
>>> 26 Example solve 10m42s https://youtu.be/N4lqDkDJ4Yo
>>>
>>>
>>> Just now, I tried an additional goofy experiment: a wildly different
>>> solution method where I permute all pieces first, then orient them
>>> afterwards! It only took half an hour or so. It was a hoot, try
>>> it! I'm fascinated by the 12 orientations of these 4d puzzle pieces,
>>> and the second half of this method is a way to focus in on orientation
>>> exclusively.
>>>
>>>
>>> Cheers
>>> Marc
>>>
>>>
>>>
>>> ------------------------------------
>>> Posted by: Marc Ringuette irror.com>
>>> ------------------------------------
>>>
>>>
>>> ------------------------------------
>>>
>>> Yahoo Groups Links
>>>
>>>
>>>
>>>
>>>=20
>>
>
>
>
> --
>
> "Engineers like to solve problems. If there are no problems handily
> available, they will create their own problems." - Scott Adams
>



--=20

"Engineers like to solve problems. If there are no problems handily
available, they will create their own problems." - Scott Adams

--0000000000002faa380570fae0c7
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable