Thread: "ZZ^4 - ZZ-type method for 3^4"

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Congratulations for your achievement! I find 3D-ZZ beautiful, it's great yo=
u managed to adapt it. For some time I thought there would be orientation i=
ssues which would prevent it; thank you for proving me wrong :)

=C2=A0

As for the methods, the most used are CFOP-like methods (possibly with Petr=
us-like blockbuilding at the beginning), which are move-efficient but requi=
re more thinking, and methods using commutators, which are simpler but long=
er. There has been some tries to develop other methods; here are two of min=
e:

- One was inspired by Thistlethwaite's method (http://www.ryanheise.com/cub=
e/human_thistlethwaite_algorithm.html). The goal is to fix more and more in=
variants without actually placing pieces until the very end of the solve; i=
t relies on the fact that the only configuration with all invariants fixed =
is the solved state.

I used it once, and beat the previous record on 3^4 by 22 moves (although I=
cheated at the end by using an optimal solver for 3^3); I found it extreme=
ly tedious. You can find a laconic explanation on my userpage on the wiki: =
http://wiki.superliminal.com/wiki/User:Thomas_Leh%C3%A9ricy#Sketch_of_my_me=
thod

- I've been working on a Roux adaptation, which I think is now functional. =
It might prove a bit simpler than CFOP, but I'm not quite sure about the mo=
ve count. I'll post a solve that uses it someday.

=C2=A0

Thomas

=C2=A0

=C2=A0

> I finally cracked a ZZ variant for the 3^4, which orients the two-colour =
centre pieces relative to the front, back, top and kata cells. It also make=
s full F2L in one step, rather than as the F2L then S2L of the existing CFO=
P-type method documented on the wiki. I have attached a log file of a full,=
albeit inefficient solve using this method. (note - I used green as the bo=
ttom cell, brown as the top cell, red as the left cell, teal as the right c=
ell, and purple, yellow, cyan and blue cells as the centre four which are o=
riented to, so when viewing the log use that orientation to perhaps get an =
understanding of the method.)




>
I will be posting a more concrete analysis and explanation of the method so=
on, but as of yet I only have the basic steps, which are EOSquare, F2L bloc=
ks, OLC (orient last cell) and PLC (permute last cell) (note 2 - I used RKT=
CFOP for the last cell, but in hindsight I should have used RKT ZZ to lowe=
r the move count.) I do not yet have an understandable way to teach the met=
hod through text, although I could show it to anyone who has a good underst=
anding of ZZ and would be willing to talk to me for a few hours for a walkt=
hrough solve. (if that's you, email me at scarecrowfish@gmail.com and we ca=
n sort something out)

>
I'm very excited to progress and develop this method, and I hope that other=
s can help and that we can finally find an efficient and quick method, whic=
h would bring together move count and speed, and which could also possibly =
bring in more cubers to higher dimensional puzzles as a gateway method. (I =
like to dream)

>
Share your thoughts with me.

>
~ Luna=3D._,___




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Congratulations for your achievement! I find 3D-ZZ beautiful, it's great=
you managed to adapt it. For some time I thought there would be orientatio=
n issues which would prevent it; thank you for proving me wrong :)

=C2=A0

As for the methods, the most used are CFOP-like methods (possibly with P=
etrus-like blockbuilding at the beginning), which are move-efficient but re=
quire more thinking, and methods using commutators, which are simpler but l=
onger. There has been some tries to develop other methods; here are two of =
mine:

- One was inspired by Thistlethwaite's method (http://www.ryanheise.com/=
cube/human_thistlethwaite_algorithm.html). The goal is to fix more and more=
invariants without actually placing pieces until the very end of the solve=
; it relies on the fact that the only configuration with all invariants fix=
ed is the solved state.

I used it once, and beat the previous record on 3^4 by 22 moves (althoug=
h I cheated at the end by using an optimal solver for 3^3); I found it extr=
emely tedious. You can find a laconic explanation on my userpage on the wik=
i: http://wiki.superliminal.com/wiki/User:Thomas_Leh%C3%A9ricy#Sketch_of_my=
_method

- I've been working on a Roux adaptation, which I think is now functiona=
l. It might prove a bit simpler than CFOP, but I'm not quite sure about the=
move count. I'll post a solve that uses it someday.

=C2=A0

Thomas

=C2=A0

=C2=A0

000 2px solid;">> I finally cracked a ZZ variant for the 3^4, which orie=
nts the two-colour centre pieces relative to the front, back, top and kata =
cells. It also makes full F2L in one step, rather than as the F2L then S2L =
of the existing CFOP-type method documented on the wiki. I have attached a =
log file of a full, albeit inefficient solve using this method. (note - I u=
sed green as the bottom cell, brown as the top cell, red as the left cell, =
teal as the right cell, and purple, yellow, cyan and blue cells as the cent=
re four which are oriented to, so when viewing the log use that orientation=
to perhaps get an understanding of the method.)

>

I will be posting a more concrete analysis and explanation of the meth=
od soon, but as of yet I only have the basic steps, which are EOSquare, F2L=
blocks, OLC (orient last cell) and PLC (permute last cell) (note 2 - I use=
d RKT CFOP for the last cell, but in hindsight I should have used RKT ZZ to=
lower the move count.) I do not yet have an understandable way to teach th=
e method through text, although I could show it to anyone who has a good un=
derstanding of ZZ and would be willing to talk to me for a few hours for a =
walkthrough solve. (if that's you, email me at scarecrowfish@gmail.com and =
we can sort something out)

>

I'm very excited to progress and develop this method, and I hope that =
others can help and that we can finally find an efficient and quick method,=
which would bring together move count and speed, and which could also poss=
ibly bring in more cubers to higher dimensional puzzles as a gateway method=
. (I like to dream)

>

Share your thoughts with me.

>

~ Luna=3D._,___

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After the extension of the number of Magic Tile problems from 600 to 1000:

Chasing Michael I have solved the following Magic Tiles

2243 eb_MT_eucl_torus=
_{4,4}_9_f010_ev100.xml

9865 eb_MT_eucl_torus=
_{3,6}_14_f0-0-1,2.xml

4526 eb_MT_hyp_{8,3}_=
10_f0,4-0-1_f0,8-0-1.xml

4631 eb_MT_hyp_{10,3}=
_12_f0,4-0-1_f0,8-0-1.xml

4703 eb_MT_eucl_klein=
_{6,3}_9_f0,4-0-1_f0,8-0-1.xml

537 eb_MT_hyp_{5,4}=
_32_R5-3_f001.xml

366 eb_MT_hyp_{5,4}=
_32_R5-3_e100.xml

492 eb_MT_hyp_{5,4}=
_32_R5-3_v1,33-0-0.xml

282 eb_MT_hyp_{4,5}=
_40_R5-3_e0,75-0-0.xml

505 eb_MT_hyp_{4,5}=
_40_R5-3_v001.xml

1 eb_MT_hyp_{6,=
6}_2_f0-1,2-0.xml

2 eb_MT_hyp_{6,=
6}_2_e0,75-0-0.xml

2 eb_MT_hyp_{6,=
6}_2_e100.xml

6 eb_MT_hyp_{6,=
6}_2_e0,61-0-0_e100.xml

2 eb_MT_hyp_{6,=
6}_2_v010.xml

1 eb_MT_hyp_{6,=
6}_2_v1,2-0-0.xml

38 eb_MT_hyp_{6,6=
}_2_f010_v100.xml

2 eb_MT_hyp_{6,=
6}_2_eh00_v100.xml

74 eb_MT_hyp_{6,6=
}_2_f0,7-0-0_f100_eh00.xml

44 eb_MT_hyp_{6,6=
}_4_f0-1,2-0.xml

39 eb_MT_hyp_{6,6=
}_4_e0,7-0-0.xml

4 eb_MT_hyp_{6,=
6}_4_v010.xml

41 eb_MT_hyp_{6,6=
}_4_v1,2-0-0.xml

122 eb_MT_hyp_{6,6}=
_4_v001.xml

28 eb_MT_hyp_{6,6=
}_4_f010_v100.xml

158 eb_MT_hyp_{6,6}=
_4_eh00_v100.xml

96 eb_MT_hyp_{6,6=
}_4_f0,7-0-0_f100_eh00.xml

18 eb_MT_hyp_{6,6=
}_4o_e0,7-0-0.xml

4 eb_MT_hyp_{6,=
6}_4o_v010.xml

4 eb_MT_hyp_{6,=
6}_4o_v1,2-0-0.xml

20 eb_MT_hyp_{6,6=
}_4o_f010_v100.xml

46 eb_MT_hyp_{6,6=
}_4o_eh00_v100.xml

46 eb_MT_hyp_{6,6=
}_4o_f0,7-0-0_f100_eh00.xml

6 eb_MT_hyp_{6,=
6}_6_R4,7_f0-1,2-0.xml

16 eb_MT_hyp_{6,6=
}_6_R4,7_f001.xml

100 eb_MT_hyp_{6,6}=
_6_R4,7_e0,7-0-0.xml

6 eb_MT_hyp_{6,=
6}_6_R4,7_v010.xml

115 eb_MT_hyp_{6,6}=
_6_R4,7_f010_v100.xml

158 eb_MT_hyp_{6,6}=
_6_R4,7_eh00_v100.xml


Nowbody else is solving MT? :-(

Kind regards
Ed
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