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 Post subject: Re: Patterns
PostPosted: Sat Apr 05, 2014 6:47 am 
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perfredlund wrote:
Yet another quite small improvement:

4X: Fat Anaconda (Order 6) (-4) (37 btm).

Done like so:

1. CU2 CF- M2U2 R- B2 D R- M2U- R M2F D- M2R- B2 L M2F2 NR2 T3U2 NR2 TU2 NR2 TD2 CU CR-
2. D2 L2 NU- NR NU NR- L2 D2 B2
3. NB2 NU- NL- NU R NU- NL NU R- NB2

It could still be improved i guess :wink:

Per :solved:

Yes, it can be done! :wink:

4x: Fat Anaconda (Order 6)
WF2 U' L2 B U' WF' U WR B' SD' B2 D WF2 MU2 R2 MD2 TR2 MU2 TR2
(TF2 U' MB2 U MF2 U' MB2 MD' U' MB MD MB' U2 F2) R2 (34 btm) -3 moves


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 Post subject: Re: Patterns
PostPosted: Sat Apr 05, 2014 6:57 am 
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Waran wrote:
These are two different approaches with the same length:

4x: Weird Fat Linked Anaconda
WF2 U' L2 B U' WF' U WR B' SD' B2 D WF2 MU2 R2 MD2 TR2 MU2 TR2
U2 F2 (MD' MB MD MB') F2 U2 TR2
MD' MF' MD B MD' MF MD B' MR2
SD L' U WR' U' L U WR D'
SF' MD MR MD MR' MD2 SF (53 btm) -3 moves

4x: Weird Fat Linked Anaconda
WR2 D' F2 R D' WR D WF' R' SD R2 U WR2 MD2 B2 MU2 TB2 MD2 TB2
D2 L2 (MU' MR MU MR') L2 D2 TB2
MU' ML' MU R MU' ML MU R' MB2
TU ML TF2 MR' ML' TF2 MR TU'
TR MF TR2 MF' MB' TR2 MB TR' (53 btm) -3 moves

The previously posted solution enables to improve this one too:

4x: Weird Fat Linked Anaconda
WR2 D' F2 R D' WR D WF' R' SD R2 U WR2 MD2 B2 MU2 TB2 MD2 TB2
(TL2 D' MR2 D ML2 D' MR2 MU' D' MR MU MR' D2 L2) B2
TU ML TF2 MR' ML' TF2 MR TU'
TR MF TR2 MF' MB' TR2 MB TR' (50 btm) -3 moves


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 Post subject: Re: Patterns
PostPosted: Sat Apr 05, 2014 9:51 am 
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These are two different approaches for the same pattern:

4x: Twisted Anacondas (Order 3)
F' (MD' TR U2 TL' MF TL U2 TR') F
L' (MU' TB D2 TF' ML TF D2 TB') L
D (ML TU' L' TU ML' TU' L TU) SD'
(MF TD' F' TD MF' TD' F TD) U' (39 btm)

4x: Twisted Anacondas (Order 3)
F L B U WF2 L WF2 L' SD
ML2 SD' L SD ML2 SD' L' U' B' L'
(MU' R2 MU WR' MU' R2 MU WR) F'
D (MB' L2 MB WR MB' L2 MB WR') D' (38 btm)

Well, it certainly can be improved. :wink:


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 Post subject: Re: Patterns
PostPosted: Sat Apr 05, 2014 11:04 am 
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Another pattern where I found different solutions with the same length:

4x: 2 Tetrahedrons in a Cube
F L2 F D F' R U2 B R D' F' L2 D' B R' B' U2
F (WD' MR' MU' MR ML MD ML') F' B'
TR TU' TB TD TF2 TR2 TU' TF' TR TF' (37 btm)

4x: 2 Tetrahedrons in a Cube
F L2 F D F' R U2 B R D' F' L2 D' B R' B' U2 B'
WR' MD MF' MD' MU' MB MU WF WR
TR TU' TB TD TF2 TR2 TU' TF' TR TF' (37 btm)

4x: 2 Tetrahedrons in a Cube
F L2 F D F' R U2 B R D' F' L2 D' B R' B' U2 B'
SR (MF MU' MF' (MB' MD MB) WD') L
MR TU' TB TD TF2 TR2 TU' TF' TR TF' (37 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Apr 08, 2014 5:29 am 
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Waran wrote:
These are two different approaches for the same pattern:

4x: Twisted Anacondas (Order 3)
F' (MD' TR U2 TL' MF TL U2 TR') F
L' (MU' TB D2 TF' ML TF D2 TB') L
D (ML TU' L' TU ML' TU' L TU) SD'
(MF TD' F' TD MF' TD' F TD) U' (39 btm)

4x: Twisted Anacondas (Order 3)
F L B U WF2 L WF2 L' SD
ML2 SD' L SD ML2 SD' L' U' B' L'
(MU' R2 MU WR' MU' R2 MU WR) F'
D (MB' L2 MB WR MB' L2 MB WR') D' (38 btm)

Well, it certainly can be improved. :wink:


Yes indeed, and it was not very hard to do:

4X: Twisted Anacondas (-9) (29 btm).

Done like so:

1. U F ND- F2 ND F- NR- F2 NR U-

2. D L NU- L2 NU L- NB- L2 NB D-

3. D NR- U- L- U NR NL U- L U NL- D-

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Tue Apr 08, 2014 4:46 pm 
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@ Per
Nice solution! That's indeed a much more obvious approach. :mrgreen:


I recently did a few 'Chessboard Cube' patterns on different cube models:

4x: 2 Chessboard Cubes (3x3x3)
F2 U' T3L' U F' U SF' L WD' L' B' L U L2
SR D2 L2 (SD' F' MU2 F SD F' MU2 F) L2 D2
MF MU' MF' MB' MD MB WD' SR' (35 btm)

5x: 2 Chessboard Cubes (3x3x3)
TU TR2 TU TL2 TF2 TL2 TF' TR2 TU' TL' TB' TR TD TF TU TL TB' TL2
SF L2 B2 (SR U' NR2 U SR' U' VR2 U SR U' MR2 U SR') B2 L2 SF' CR CD' (37 btm)

6x: 2 Chessboard Cubes (3x3x3)
T3F T3R' T3F T3U T3R2 T3F2 T3D' T3B' T3U T3R'
SR D2 L2 (SU F' NU2 F SU' F' NU2 F) L2 D2 R2
D2 B2 (MF' NU MF' NU' NF' MU NF' MU' VF2) B2 D2 R L (39 btm)

6x: 2 Chessboard Cubes (5x5x5)
F2 U' T5L' U F' U SF' L WD' L' B' L U L2
SR' (WF MU' ND MF' NB WD' NU2 MD2 NF' MB NU MD') SR2
D2 L2 (SU F' NU2 N3D2 F SU' F' NU2 N3D2 F) L2 D2 SR' (43 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Apr 10, 2014 3:56 am 
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Slight improvement:

6X: 2 Chessboard Cubes (3x3x3) (-2) (37 btm).

And a new version:

6X: 2 Chessboard Cubes (4x4x4) (44 btm).

This latter i'm sure could be improved, but today i'm lazy to try optimize it :wink:

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Fri Apr 11, 2014 2:12 pm 
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Nice Mixup Plus pattern.


Attachments:
0411141449b.jpg
0411141449b.jpg [ 792.82 KiB | Viewed 2707 times ]

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 Post subject: Re: Patterns
PostPosted: Sat Apr 12, 2014 8:53 am 
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Another slight improvement: :mrgreen:

5x: 2 Chessboard Cubes (3x3x3)
TL' MD' TF' TL T3F2 TD' TB2 TU' TR' TB2 S2D2 TR MF' TU TR2 TU TF'
SF L2 B2 (SR U' NR2 U SR' U' VR2 U SR U' MR2 U SR') B2 L2 SF' (36 btm) -1 move


… and something similar on a 7x7x7:

7x: 2 Chessboard Cubes (3x3x3)
SR D2 L2 (SD' F' NU2 F SD F' NU2 F) L2 D2 R2
F2 D2 NF N3D NF' N3F ND N3F' VD' D2 F2 L
VR' T3D2 T3R T3B' T3U2 T3B T3R' T3D2 T3R T3B' T3U2 T3B (38 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Apr 13, 2014 8:25 am 
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A pattern inspired by Australian boomerangs: :wink:

4x: Boomerangs (u,b,r,d,f,l)
MR2 WD2 MR2 WR' WD' WR WD'
MD2 MB MF MD' B' MD MF' MB' MD' B MD2
L2 MD' MR' MD L2 MD' MR MD2 (26 btm)


This pattern looks easier then it is to achieve:

5x: 2 Rings (4x4x4)
TU' TB2 TU' NF S2D' NF TD TB2 TD' NF' S2D NF' TU2
S2R2 TB2 ND' TB2 ND TB2 NU' TB2 NU TR2 ND' NL2
F2 VF' NR' VF WR' VD' NR VD WR F2 L2
TU' R' NU' MR NU2 MR' NU' R TU2
NR2 TU' VL2 TU NR2 TU' VL2 (52 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Apr 14, 2014 4:37 pm 
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Slight improvement:

5x: 2 Rings (4x4x4)
F2 R2 U' F' U R' U2 R U' F'
NF2 R2 NF2 TR2 NF2 NR2
TF2 TR2 TU' TF' TU TR' TU2 TR TU' TF'
MF2 R2 MF2 R2
NU2 TL2 U MF NU2 MF' U' NU2 TL2 NU2
U' MF2 U R2 U' MF2 U MF2 R2 MF2 (50 btm) -2 moves


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 Post subject: Re: Patterns
PostPosted: Tue Apr 15, 2014 2:11 pm 
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Further improvement:

5X: 2 Rings (4x4x4) (-5) (45 btm).

I guess you (Walter) can work out how i did it :P

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Tue Apr 15, 2014 3:43 pm 
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@ Per
Sure! Part 2 is a shifted version of part 1, but in reverse order.
The rest of the algorithm is repairing the side effects of part 1 and 2. :wink:

I originally had the same idea, but my solution for the clean up turned out to be longer.

I tried again and found an algorithm that gains another 3 moves: :mrgreen:

5x: 2 Rings (4x4x4)
F2 R2 U' F' U R' U2 R U' NF
TU TR' TU2 TR TU' TF TU TR2 TF2
NB' U' NR' MU NR U NR' MU' NR NB
D2 NL2 D B' R B D' NL2 D B' R' B D (42 btm) -3 moves


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 Post subject: Re: Patterns
PostPosted: Thu Apr 17, 2014 2:11 pm 
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Same pattern on V6 cube:

6X: 2 Rings (5x5x5) (32 btm).

Much easier to obtain :wink:

Per :roll:

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 Post subject: Re: Patterns
PostPosted: Fri Apr 18, 2014 12:19 pm 
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This is an Anaconda variation that looks different on its backside:

5x: Viper
R (NF' U2 NF WD NF' U2 NF WD') (ND' MR U' MR' ND MR U MR') (NU L' U' L NU' L' U L) R'
TR' TU TB2 TU' NF' TU TB2 TU' NF TR (36 btm or 35 btm actually)


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 Post subject: Re: Patterns
PostPosted: Sat Apr 19, 2014 2:11 pm 
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Waran wrote:
This is an Anaconda variation that looks different on its backside:

5x: Viper
R (NF' U2 NF WD NF' U2 NF WD') (ND' MR U' MR' ND MR U MR') (NU L' U' L NU' L' U L) R'
TR' TU TB2 TU' NF' TU TB2 TU' NF TR (36 btm or 35 btm actually)

Small improvement:

5X: Viper (-2) (33 btm).

Nice pattern!

Per :)

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 Post subject: Re: Patterns
PostPosted: Sat Apr 19, 2014 5:14 pm 
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I think this pattern looks even more interesting on a 6x6:

6x: Asymmetric Viper
R (MF' U2 MF M3U' MF' U2 MF M3U) (NU TL' U' TL NU' TL' U TL) ND' M2R U' M2R' ND M2R U V3R' R2
(TU TB2 TU' NF' TU TB2 TU' NF) TR (35 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Apr 20, 2014 2:22 pm 
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Waran wrote:
I think this pattern looks even more interesting on a 6x6:

6x: Asymmetric Viper
R (MF' U2 MF M3U' MF' U2 MF M3U) (NU TL' U' TL NU' TL' U TL) ND' M2R U' M2R' ND M2R U V3R' R2
(TU TB2 TU' NF' TU TB2 TU' NF) TR (35 btm)

This could also quite easily be improved:

6X: Asymmetriv Viper (-2) (33 btm).

Per :oops:

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 Post subject: Re: Patterns
PostPosted: Sun Apr 27, 2014 12:11 pm 
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I am sure these patterns can be much further optimized, especially the second one. :wink:

4x: Tetrahedron Cube
WF D MR2 U' SR D' MR2 U SR MD' ML' MD MR ML MU MR' TU' WR2 U SR' U' ML2 U D WR2 U' SR' U ML2 D' WF' (31 btm)

6x: Tetrahedron Cube
D B D2 L B2 D L2 D2 B2 U B' WR' B' WR U'
WF (U' MR2 U D MR2 D' SR' D MR2 U' D' VR2 NL2 U D NR2 NL2 D' SR D NR2 NL2 U' D' NR2 NL2 U) WF'
VB' L2 VF VB L2 VF'
WD VB' L2 VF VB L2 VF' WD'
SD2 SR
(NR NL' NF' NB NR' NL NF NB')
(MF MU' MF' MB' MU MD MB MD')
(MD NF NB' MD' NF' NB) (NU' ND MF NU ND' MF')
SR' SD2 (90 btm or 84 btm actually)


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 Post subject: Re: Patterns
PostPosted: Sat May 03, 2014 8:38 am 
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Tiny improvement:

6x: Tetrahedron Cube
D B D2 L B2 D L2 D2 B2 U B' WR' B' WR U'
WF (U' MR2 U D MR2 D' SR' D MR2 U' D' VR2 NL2 U D NR2 NL2 D' SR D NR2 NL2 U' D' NR2 NL2 U) VF'
L2 VF VB L2 VF'
SD' VR' B2 VL VR B2 VL' SD'
SR (MF MU' MF' MB' MU MD NF MB NB' NU' MD' ND MF NU ND' MF' NU' ND NF' NB NU ND') SR' SD2 (82 btm) -2 moves


This is a very similar looking variation:

6x: Tetrahedron Cube 2
SD' F2 D F' D2 R' B' U F' B D F2 L D SF U2 L
NU MD' R D R' NU' MD R D' SR'
SF' D' F NU' MD F' D F NU MD'
F U2 (R' D SR ND2 MU2 SR' D' SR ND2 MU2 L) U2 F' B'
SD2 SR (V3F V3D V3F' V3D') (NU' MD WF ND MU' NF' MB WD' NB MF') (V3U' V3B' V3U V3B) SR' SD2 (75 btm)


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 Post subject: Re: Patterns
PostPosted: Sun May 04, 2014 12:23 pm 
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This S pattern wraps around four sides of the cube.
On the 3x3 version there is only one continuous string, but on the 4x4 we got two double strings and on the 5x5 we have three: :mrgreen:

3x: 4 S
CD2 U R2 F MR2 B2 MR2 F' R2 U' (9 btm)

4x: 4 Double S
MD2 SF' MR' SF MD2 SF' MR' B'
WD' WR' B' U2 B WR WD F'
R2 WD MR2 WD' TR2 F2 (22 btm)

5x: 4 Triple S
U L2 F' L2 SD2 R2 B' R2 U'
MD2 SR MF SR' MD2 SR MF SR'
NR2 NL2 MD' NR2 NL2 VD F2 R2 NU' ND NR2 NU ND' TR2 F2 ND' (33 btm)


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 Post subject: Re: Patterns
PostPosted: Wed May 07, 2014 2:56 am 
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Can someone explain the notation in this thread? I really don't understand any of it. I get the standard F, R, B, L, U, D, S, E, and M notations, but things like NR, WR, WD, etc are completely lost on me. Searching Google has yielded no results either. Help?

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 Post subject: Re: Patterns
PostPosted: Wed May 07, 2014 4:41 am 
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I think this is the notation used here:
http://www.randelshofer.ch/rubik/profes ... G_5x5.html

This notation has certainly benefits for big nxnxn cubes.
I have never written down anything beyond the 5x5x5, so I stuck to the former WCA notation.
(That could be called an improved Singmaster notation, lower case letters for slice moves on the 5x5x5, e.g. r the next layer below R)
Superset ENG is more general, but something new to learn. :wink:

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 Post subject: Re: Patterns
PostPosted: Wed May 07, 2014 3:58 pm 
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And here comes the enhanced S pattern for the 6x6 cube: :mrgreen:

6x: 4 Quadruple S
ND2 SF' NR' SF ND2 SF' NR' SF
F' WD' WR' B' U2 B WR WD F
F2 L2 M2U ML2 M2U' ML2 SR2 NU' ND NR2 ND' NU TR2 F2
F2 M2R2 F2 ND' F2 M2R2 F2 ND
SR MB M2R MB2 M2R' MB SR'
MU2 (47 btm or 42 btm actually)


@ Fred Berfel
It is indeed a very powerful notation for NxNxN cubes and has many other advantages too.

Maybe someone could post an algorithm in the former WCA notation?
I then translate it into the SSE notation, so that the two can be compared.
This might also be interesting for others who like to know more about the notation in this thread. :D


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 Post subject: Re: Patterns
PostPosted: Wed May 07, 2014 4:17 pm 
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Ferd Berfel wrote:
Can someone explain the notation in this thread? I really don't understand any of it. I get the standard F, R, B, L, U, D, S, E, and M notations, but things like NR, WR, WD, etc are completely lost on me. Searching Google has yielded no results either. Help?

Did you ever try out one of the links? The interactive applets are self explanatory with regards to the notation. Just step through any pattern with a given link :wink: The only small drawback is that the applets are java-based. I would recommend java 8 ...

Per 8-)

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 Post subject: Re: Patterns
PostPosted: Wed May 07, 2014 4:51 pm 
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Found a small improvement for the Triple-S pattern:

5x: 4 Triple S
U L2 F' L2 SD2 R2 B' R2 TU'
B2 TR2 NU ND' NR2 NU' ND R2 B2 NU
NR2 NB2 MD2 NB2 NR2
SR MF SR' MD2 SR MF SR' (31 btm) -2 moves


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 Post subject: Re: Patterns
PostPosted: Thu May 08, 2014 2:12 pm 
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Waran wrote:
Found a small improvement for the Triple-S pattern:

5x: 4 Triple S
U L2 F' L2 SD2 R2 B' R2 TU'
B2 TR2 NU ND' NR2 NU' ND R2 B2 NU
NR2 NB2 MD2 NB2 NR2
SR MF SR' MD2 SR MF SR' (31 btm) -2 moves


And why not simply:

5X: Triple-S pattern (-9) (22 btm). :!: :?:

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Fri May 09, 2014 1:28 am 
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perfredlund wrote:
Ferd Berfel wrote:
Can someone explain the notation in this thread? I really don't understand any of it. I get the standard F, R, B, L, U, D, S, E, and M notations, but things like NR, WR, WD, etc are completely lost on me. Searching Google has yielded no results either. Help?

Did you ever try out one of the links? The interactive applets are self explanatory with regards to the notation. Just step through any pattern with a given link :wink: The only small drawback is that the applets are java-based. I would recommend java 8 ...

Per 8-)


I have seen the applets on the links, and following them was rather helpful. I would just like to understand the notation without having to see an animation to make sense of it; it seems like a very useful notation for big cubes.

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 Post subject: Re: Patterns
PostPosted: Fri May 09, 2014 2:42 am 
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Ferd Berfel wrote:
...I would just like to understand the notation without having to see an animation to make sense of it; it seems like a very useful notation for big cubes.
Have you seen my post from May 7th? That link should explain it very well (e.g. for the 5x5x5).

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 Post subject: Re: Patterns
PostPosted: Sat May 10, 2014 1:20 am 
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Konrad wrote:
Have you seen my post from May 7th? That link should explain it very well (e.g. for the 5x5x5).


I did see it, yes. Thank you for the link; it was very helpful. I wasn't even aware that this notation existed, but it makes a lot of sense. Now it's time to try some patterns...

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 Post subject: Re: Patterns
PostPosted: Sun May 11, 2014 5:00 am 
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Waran wrote:
And here comes the enhanced S pattern for the 6x6 cube: :mrgreen:

6x: 4 Quadruple S
ND2 SF' NR' SF ND2 SF' NR' SF
F' WD' WR' B' U2 B WR WD F
F2 L2 M2U ML2 M2U' ML2 SR2 NU' ND NR2 ND' NU TR2 F2
F2 M2R2 F2 ND' F2 M2R2 F2 ND
SR MB M2R MB2 M2R' MB SR'
MU2 (47 btm or 42 btm actually)


@ Fred Berfel
It is indeed a very powerful notation for NxNxN cubes and has many other advantages too.

Maybe someone could post an algorithm in the former WCA notation?
I then translate it into the SSE notation, so that the two can be compared.
This might also be interesting for others who like to know more about the notation in this thread. :D


And here is the pattern done more efficiently:

6X: 4 Quadruple S (-17) (25 btm).

Per :roll:

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 Post subject: Re: Patterns
PostPosted: Sun May 11, 2014 9:06 am 
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Well, it can be done even more efficiently: :wink:

6x: 4 Quadruple S
T3U L2 TF2 ND NU' VF2 M2D MF2 WD' F2 L2 VU'
R2 F2 SR2 F WR2 B2 WR2 F L2 U MU2 ND2 (24 btm) -1 move


I also improved its 4x4 version: :mrgreen:

4x: 4 Double S
MU' R2 (TB2 WD MB2 WD' B2) R2 TU
R2 F2 SR2 F WR2 B2 WR2 F L2 U MD2 (20 btm) -2 moves


… and here an unoptimized solution for the 7x7:

7x: 4 Quintuple S
D L2 B L2 SD2 R2 F R2 U2 T3D
R2 TF2 NU ND' V3F2 (MD MF2 M3D') N3F2 VU' VD F2 R2 VD'
NU2 MD2 ND2 (27 btm)

Edit: A first improvement:

7x: 4 Quintuple S
T3D (SR B2 SR TL2 NU ND' V3L2 MD MR2 M3D' N3L2 VU' VD F' L' R' B2 L R F R2) T3D'
NU2 MD2 ND2 (26 btm) -1 move


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 Post subject: Re: Patterns
PostPosted: Sun May 11, 2014 4:03 pm 
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perfredlund wrote:
And why not simply:

5X: Triple-S pattern (-9) (22 btm). :!: :?:

Per :wink:


… or just: :wink:

5x: 4 Triple S
D B2 L' B2 SD2 F2 R' F2 TD' R2 F2 WD' MF2 MD VF2 NU' ND TF2 R2 ND MD2 (21 btm) -1 move


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 Post subject: Re: Patterns
PostPosted: Thu May 15, 2014 4:52 am 
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Okay, so I could not resist:

8X: 4 "Hexuple" S (28 btm).

Per :mrgreen:

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 Post subject: Re: Patterns
PostPosted: Wed May 21, 2014 3:22 am 
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I found another major improvement: :wink:

4x: 4 Double S
TU' TL2 F2 TD2 TF2 D2 TR2 TD2 MR2 TB2 TU'
MU2 D2 (13 btm) -7 moves


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 Post subject: Re: Patterns
PostPosted: Wed May 21, 2014 7:12 am 
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This is the shortest solution I found so far for this pattern:

4x: Color Edge Hexagon (Order 3)
SD' F' D WF D' F D WF' U'
SR MU MB MU MB' MU2 SR'
TD MF TL2 MB' MF' TL2 MB TD'
TB ML TB2 ML' MR' TB2 MR TB' (32 btm)


Edit: ... I just found a better algorithm: :mrgreen:

4x: Color Edge Hexagon (Order 3)
U D R2 B WD2 R' WD2 R B' R2 D
L' F2 B WR MB WR' TB' F2 L D
(MF ML MF ML' MF2) SD (27 btm) -5 moves


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 Post subject: Re: Patterns
PostPosted: Wed May 21, 2014 9:17 am 
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... and here a few color versions of the pattern above:

4x: Color Edge Hexagon (Version 2)
L' D2 B WD F L2 B' WD' SR' D' B2 U2 SR
U' B F2 (MF MR2 MU2 WF' MR2 MU2 MB') F2 B' U L
MF MR' ML' F WR MB2 WR' F' MR MB2 ML MF' (39 btm)

4x: Color Edge Hexagon (Version 3)
WR2 D' F2 R D' WR D WF' R' SD R2 U WR2 MD2 B2 MU2 TB2 MD2 TB2
(TL2 D' MR2 D ML2 D' MR2 MU' D' MR MU MR' D2 L2) B2
TU ML TF2 MR' ML' TF2 MR TU'
TR MF TR2 MF' MB' TR2 MB TR' (50 btm)

4x: Color Edge Hexagon (Version 4)
L2 D2 MR2 F2 ML2 D2 TF2 MR2 MF2 D2 F2 L2 WD2
TD' R U2 MD MB U2 MR2 U2 MB' U2 MD' R' MD MR2 D
TU ML TF2 MR' ML' TF2 MR TU'
TR MF TR2 MF' MB' TR2 MB TR' (44 btm)


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 Post subject: Re: Patterns
PostPosted: Sun May 25, 2014 7:45 am 
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A Latin Square is an n x n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.

Imagine you would like to build such a Latin Square on all faces of a 6x6x6, using colors instead of symbols.
This means we have to arrange all six colors on each face in a very special way.
… is it possible on a 6x6x6, what do you think?


Well, in fact it is! Check this out!: :D

6x: Latin Square
U SF SR SD' F2 SR2 B U SF2 D2 WR2 U WR2
TU S2F S2R S2D' TF2 S2R2 TB TU S2F2 TD2 M2R2 TU M2R2
T3U2 T3B T3L2 T3U' T3L2 T3U T3B2 T3L' (34 btm)


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 Post subject: Re: Patterns
PostPosted: Mon May 26, 2014 2:14 pm 
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@Walter: Nice Latin Square :wink:

Here is an alternative version of a previous pattern:

6X: 4 Quadruple S (24 btm).

Same btm, but better ltm, ftm and qtm :)

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Mon May 26, 2014 2:49 pm 
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This can be improved quite easily: :wink:

6x: 4 Quadruple S
T3U SF L2 F' B' R F B L2 F' B' R WD' MR2 M2U' VR2 NU' ND TR2 B2 T3U NU2 ND2 (23 btm) -1 move


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 Post subject: Re: Patterns
PostPosted: Tue May 27, 2014 6:32 am 
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Waran wrote:
This can be improved quite easily: :wink:

6x: 4 Quadruple S
T3U SF L2 F' B' R F B L2 F' B' R WD' MR2 M2U' VR2 NU' ND TR2 B2 T3U NU2 ND2 (23 btm) -1 move


Haha. It was late last night. How could i miss that tiny improvement :?: :lol:

Per :roll:

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 Post subject: Re: Patterns
PostPosted: Tue May 27, 2014 2:41 pm 
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Waran wrote:
I found another major improvement: :wink:

4x: 4 Double S
TU' TL2 F2 TD2 TF2 D2 TR2 TD2 MR2 TB2 TU'
MU2 D2 (13 btm) -7 moves


Hi Walter! You also missed out a slightly shorter finish:

4X: 4 Double S (-1) (12 btm).

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Tue May 27, 2014 3:11 pm 
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And another tiny improvement:

6X: 4 Quadruple S (-1) (22 btm).

Done like so:

1. U- R2 B R2 SU2 L2 F L2 (prepare corners)
2. VU B2 TR2 NU ND- VR2 M2U N3R2 WU- R2 B2 (diagonals)
3. T3U NU2 TD2 (completion)

EDIT:

Slight optimization:

1. U- R2 B R2 SU2 L2 F L2 (prepare corners)
2. VU- B2 TR2 NU ND- VR2 M2U N3R2 WU- R2 B2 (diagonals)
3. T3U- M2U2 (completion)

6X: 4 Quadruple S (-1) (21 btm).

I am now quite convinced this is fully optimal :D

Per

Per :D

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 Post subject: Re: Patterns
PostPosted: Fri May 30, 2014 4:04 am 
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And finally a new contribution:

6X: 4 Long Slashes (order 2) (34 btm).

I'm sure this could be optimized quite a bit :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Fri May 30, 2014 5:10 am 
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Ok. So here is the similar 7X optimization:

7X: 4 Quintuple S (-1) (25 btm).

and 8X optimization:

8X: 4 "Hexuple" S (-3) (25 btm).

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Fri May 30, 2014 10:45 am 
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@ Per
Nice optimization work! 8-)

perfredlund wrote:
And finally a new contribution:

6X: 4 Long Slashes (order 2) (34 btm).

I'm sure this could be optimized quite a bit :wink:

Per

Of course it can be optimized! :wink:

6x: 4 Long Slashes (Order 2)
B2 U SF2 SR2 D' R2 B2 D2 L2 F2 U2 R
B' (VU F2 VU2 TF2 NU ND' VF2 M2U N3F2 WD F2 VU2 F2 VU') B R (29 btm) -5 moves


The same pattern on a 4x4 would look like this:

4x: 4 Long Slashes (Order 2)
B2 U SF2 SR2 D' R2 B2 D2 L2 F2 U2 R'
B MD' ML2 MD' MU' ML2 WD' MD' B' R' (22 btm)


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 Post subject: Re: Patterns
PostPosted: Fri May 30, 2014 11:14 am 
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I further optimized it: :mrgreen:

6x: 4 Long Slashes (Order 2)
B2 U SF2 SR2 D' R2 B2 D2 L2 F2 U2 R
B' (ND NB2 NU ND NB2 NU' VD2
MU MB2 MD' MU' MB2 MD') B R (28 btm) -1 move


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 Post subject: Re: Patterns
PostPosted: Sun Jun 01, 2014 4:02 pm 
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A few more, very similar patterns for the 4x4 and 6x6:

4x: 4 Long Slashes v2 (Order 2)
WF2 WR2 U2 WF2 WR2 TD2
R2 WF WR WF' R2 MD2 WF WR' WF' (15 btm)

6x: 4 Long Slashes v2 (Order 2)
WF2 WR2 U2 WF2 WR2 D2
SR' (VD R2 TF2 NU ND' VF2 M2U MF2 WD F2 R2 VD') SR (20 btm)



4x: 4 Long Slashes (Order 4)
WF2 U2 WR2 D WF2 D2 WR2 U'
B (TR MD MB WR' MU' ML' MB' WD' R') B' (19 btm)

6x: 4 Long Slashes (Order 4)
WF2 U2 WR2 D WF2 D2 WR2 U'
B ML L MD2 ML' MF' ML MD MF MD NL ML' ND2 NL' NF' NL ND NF ND TL' B' (29 btm)


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 Post subject: Re: Patterns
PostPosted: Wed Jun 04, 2014 6:49 am 
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Hi Walter!

You missed out on this rather obvious slight optimization:

6X: 4 Long Slashes v2 (order 2) (-1) (19 btm).

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Thu Jun 05, 2014 4:36 am 
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With one delayed turn the 6X: 4 Long Slashes (Order 4) can be slightly optimized:

6X: 4 Long Slashes (Order 4) (-1) (28 btm).

EDIT:

Further optimization:

6X: 4 Long Slashes (Order 4) (-1) (27 btm).

Good luck improving this :roll:

Per :wink:

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy


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