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 Post subject: I need help with the 2x2x4
PostPosted: Wed Jul 27, 2011 10:47 pm 
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It arrived in the mail today and it's a snazzy puzzle, but I'm stuck with it. I can solve every regular cube from 2x2x2 to 5x5x5, so I'm pretty sure I just need to know the steps and apply knowledge accordingly. I can already complete the two ends of the puzzle, but this leaves the middle, and when I try using standard 2x2x2 sequences to solve that part it messes up the caps, so am I just doing it wrong?

Again, I don't need a really detailed guide, just some basic steps. Help would be appreciated :)

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Thu Jul 28, 2011 2:21 am 
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What I do is match up the extensions with their base first. (what's that word :? You know making a 7x7x7 a 3x3x3?). After that it can be solved like a normal 2x2x2.

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Thu Jul 28, 2011 2:43 am 
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Reducing.

If outside in doesn't work.. try inside out :wink: .

PS Are you aware that it shape shifts? (just checking).

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Thu Jul 28, 2011 3:12 am 
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Burgo wrote:
Reducing.

If outside in doesn't work.. try inside out :wink: .

PS Are you aware that it shape shifts? (just checking).

Thanks :oops:

Apart from the actual pieces, solving inside out and outside in are identical. Both are solving a 2x2x2 and then solving a second 2x2x2 without mixing up the first one. I would "try" solving it that way but I figured out by reducing it to a 2x2x2 it is a lot faster and super simple.

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Thu Jul 28, 2011 11:39 am 
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Burgo wrote:
Reducing.

If outside in doesn't work.. try inside out :wink: .

PS Are you aware that it shape shifts? (just checking).

Yes. Would using the edge-pairing algorithms from the 4x4x4 help? I know a really good edge-pairing alg that should work on any size cube (as long as you adjust the deepness of the first and last turns). It swaps two pieces like so (danger: bad ASCII art ahead):
OOOO
XOOO
OOOX
OOOO
On the 4x4x4, it swaps the two Xs. Yeah, I was too lazy to make a proper image :P

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3x3x3 PB: 38.9 seconds
Well, I accumulated puzzles without even trying this Christmas. Whoops.
(Bermuda 8 planets, Rex Cube, Master Skewb, London Natural History Museum keychain 2x2x2, Impossiball)


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Thu Jul 28, 2011 9:30 pm 
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actually, the 2x2x4 is not equivalent to solving a 2x2 then another 2x2, but solving a 2x2 then domino corners, or the top and bottom layer on a 2x2x3.
Yes, you can use the algorithms that you use to flip an edge pair or to swap 2 edges (edge parities) on a 4x4x4 or 5x5x5 cube to flip a corner pair or swap 2 corners on a 2x2x3, 2x2x4, or a domino.

Hope that helps. :D

Elijah

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Fri Jul 29, 2011 12:03 pm 
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I managed to solve it using the Japanese directions (possibly the first time Japanese directions have helped?) and I also thank you guys in this thread for helping me.

So it turns out there's an algorithm to swap two of the cap-pieces without shape-shifting the puzzle, so I solved the middle like a 2x2x2 and used that algorithm to finish the caps (after I made one cap blue and the other white, of course.)

I'll make a shoddy picture and write the algorithm here for those people trawling Google and seeking solutions:
Image

_________________
3x3x3 PB: 38.9 seconds
Well, I accumulated puzzles without even trying this Christmas. Whoops.
(Bermuda 8 planets, Rex Cube, Master Skewb, London Natural History Museum keychain 2x2x2, Impossiball)


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sat Jul 30, 2011 1:40 am 
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Gooday GoombaGeek,

That algo just scrabled my cube.. you might like to check it?
I would use (R2 U R2 U' R2) U' D (R2 U' R2 U R2) D' to achieve that (it swaps the RHS top).

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sat Jul 30, 2011 12:01 pm 
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Burgo wrote:
Gooday GoombaGeek,

That algo just scrabled my cube.. you might like to check it?
I would use (R2 U R2 U' R2) U' D (R2 U' R2 U R2) D' to achieve that (it swaps the RHS top).

Cheers,
Burgo.

I may have messed it up by simplifying a turn (you were told to turn the top 3 layers, I translated that to "turn the bottom layer the other way", I may have screwed up the direction of that turn. If you kept your instructions, then check the last step: that's the algorithm I used.

_________________
3x3x3 PB: 38.9 seconds
Well, I accumulated puzzles without even trying this Christmas. Whoops.
(Bermuda 8 planets, Rex Cube, Master Skewb, London Natural History Museum keychain 2x2x2, Impossiball)


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sun Jul 31, 2011 5:42 am 
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Joined: Thu Jan 20, 2011 6:05 pm
Location: Netherlands
I have one too, but not yet scrambled it.
If you start shapeshifting the puzzle and then restore it to a tower (but not how it was before shapeshifting), can you then always still solve it with the 2x2 and domino algorithms, or are some extra algorithms needed?


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sun Jul 31, 2011 3:44 pm 
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Location: Littleton CO
Scrambling it by shapeshifting is just like scrambling a normal 2x2. You can do all the same moves and everything like normal.


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sun Jul 31, 2011 5:28 pm 
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GoombaGeek wrote:
Burgo wrote:
Gooday GoombaGeek,

That algo just scrabled my cube.. you might like to check it?
I would use (R2 U R2 U' R2) U' D (R2 U' R2 U R2) D' to achieve that (it swaps the RHS top).

Cheers,
Burgo.

I may have messed it up by simplifying a turn (you were told to turn the top 3 layers, I translated that to "turn the bottom layer the other way", I may have screwed up the direction of that turn. If you kept your instructions, then check the last step: that's the algorithm I used.


I correct for the odd-parity first by turning U and then I just do a three-cycle of the three broken corners with a [3,1] commutator (needs a setup).

U, [F'2, [[U', L'2, U], R'2, [U', L'2, U], R'2], F'2]

This is [1] [1:[[1:1],1]] for 11 moves total. I haven't proven it but I'm pretty sure this is the shortest possible sequence. If there is no [3,1] commutator sequence that cycles 3 corners in the same face (which I don't think there is) then it is the shortest sequence.

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sun Jul 31, 2011 9:02 pm 
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Joined: Wed Jun 22, 2011 4:57 pm
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I've never figured out what the square brackets in algorithms refer to :oops:

Do I just do all the moves in normal order, or do I have to repeat them in some way?

Anyway, I'm pretty sure that solving by shapeshifting will let you do the center pieces, but the caps need special treatment - either you use an algorithm or keep doing non-shapeshifting turns (R2, move the caps how you want, R2 again).

_________________
3x3x3 PB: 38.9 seconds
Well, I accumulated puzzles without even trying this Christmas. Whoops.
(Bermuda 8 planets, Rex Cube, Master Skewb, London Natural History Museum keychain 2x2x2, Impossiball)


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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sun Jul 31, 2011 10:17 pm 
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I wonder which method is better, my reduction way or solving the 2x2x2 then outside. I take about 25 twists then a 2x2x2 solve to solve it with my method. How long does it take using yours? (just solve it like normal and count the rotations)

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 Post subject: Re: I need help with the 2x2x4
PostPosted: Sun Jul 31, 2011 11:11 pm 
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GoombaGeek wrote:
I've never figured out what the square brackets in algorithms refer to :oops:

Do I just do all the moves in normal order, or do I have to repeat them in some way?


Yeah it's notation overloading. When I write:
U, [F'2, [[U', L'2, U], R'2, [U', L'2, U], R'2], F'2]

The [] are just grouping and don't actually have any meaning.

When I write [1,1] I mean there is an X part of length 1 and a Y part of length 1 and they are put together like X Y X' Y'. So [1,1] is a 4 move commutator.

[1:1] is a conjugate so it is X Y X'.

Nesting works too:
[[1:1],1] -> [[A:B],C] -> A B A' C A B' A' C'

To me the most important thing about sharing "algorithms" is not the full sequence of moves laid out in order but rather the parts of the sequence and how they are put together to make the whole routine. I'm not a big fan of posting a 11-move sequence without saying how it was made.

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