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 Post subject: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 12:37 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
[Moderator: Pete had suggested to split the following posts from this original thread]
Hi Pete (and hi Patrick),

This is a 444 reduction to 222 method:
http://twistypuzzles.com/forum/viewtopi ... =8&t=24349
(remember )

And I've had an interesting method for the 333 (non-speed) that I've had going for quite a while, I'll have to put it on the tube.

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: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 5:57 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Pete,

The technique of reducing a 4x4 to a 2x2 and solving that is an interesting one. For example it would completely remove the issue of parity which is a result of an incorrect reduction of the 'dedges'. However whilst removing the need for a parity algorithm or disassembling and reassembling the edges, it also has the problem of enormous difficulty recreating the last 2x2 block. Sometimes this is easy and sometimes tough.

The bandaged AI cube was the first to force us to use this technique and stumped a whole lot of us for a long time. SuperAntonioVivaldi produced a video tutorial to help but was not particularly clear on this last block. Only Rline was able to definitively help us with a "here's the solution" video series.

Interestingly the camouflage series also need to be solved in just this way (although 1 or 2 of them can be done in other ways) and I love this series. The 4x4x3 camouflage and 3x3x4 are particularly fun and I use just this reduction system and finish off solving a 2x2.

They are all very cheap puzzles and give a nice new solving experience - you probably don't need the whole set.

_________________
Kevin

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 Post subject: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 9:31 am

Joined: Sun Mar 02, 2008 11:33 am
Location: Hiram, Ohio
Pete,

The technique of reducing a 4x4 to a 2x2 and solving that is an interesting one.

I am very interested in this!
Does this technique have a name?

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 Post subject: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 10:28 am

Joined: Thu Dec 15, 2011 10:04 pm
Burgo, Puzzlemad - I tried this reduction of a 4x4 to 2x2 myself after I posted last night. Indeed it quickly started to look like the AI Bandaged Cube. The first pair of 2x2(x2) sections was quite easy and after that...

Hunter, I would go with Burgo's "444 reduction to 222 method". This is all very cool.

The CubeTwist AI Bandaged cube has been sold out at the HKNowStore for a while; can anyone comment on the quality of the WitEden version?

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 Post subject: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 11:14 am

Joined: Tue Sep 11, 2012 1:51 pm
Location: Bedford, England
I've got the witEden one. First of all it's tiny! It's based on the mini 4x4, which also happens to be the same mechanism that all the camouflage cubes are based on.

The quality of it isn't great, but it's not truly awful either. If you can cope with the camouflage cubes, you can cope with this, however it does tend to catch a little bit more because of all the tiny pieces

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Latest videos: Unboxing / Review of Curvy copter Plus, David Gear Cube, Octo-star Cube

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 Post subject: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 1:04 pm

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Pete the Geek wrote:
Burgo, Puzzlemad - I tried this reduction of a 4x4 to 2x2 myself after I posted last night. Indeed it quickly started to look like the AI Bandaged Cube. The first pair of 2x2(x2) sections was quite easy and after that...

Oh yes! As I said, it can be done this way and it IS fun but it's certainly not for the fainthearted! I find it very easy right up to the very last 2x2 block and you usually find that you need to break at least one, if not 2, of the previously made blocks to allow finally recreation of the last one.

Pete the Geek wrote:
Hunter, I would go with Burgo's "444 reduction to 222 method". This is all very cool.

It was Burgo's initial idea that got me right to the last block but his explanation of the final solve went over my head (I find that a lot of Burgo's techniques do that!! the man's a twisty genius!)
The best tutorial is on Rline's site here:
http://twistypuzzling.blogspot.co.uk/2012/11/4x4x4-ai-bandaged-cube.html

Pete the Geek wrote:
The CubeTwist AI Bandaged cube has been sold out at the HKNowStore for a while; can anyone comment on the quality of the WitEden version?

I have the Cubetwist version which is very nice if a little on the large side. The Witeden one is based on the mini 4x4 like all the camouflage cubes and is nice quality but probably a little catchy too. If you are careful then it will be a nice useable puzzle.

This is a really nice unusual way to solve an even order puzzle.

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Kevin

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 Post subject: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 1:16 pm

Joined: Tue Sep 11, 2012 1:51 pm
Location: Bedford, England

This is a really nice unusual way to solve an even order puzzle.

I'm tempted to bandage my new 6x6 into a 6x6 AI type puzzle and give that a shot

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Latest videos: Unboxing / Review of Curvy copter Plus, David Gear Cube, Octo-star Cube

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 Post subject: Re: 444 reduction to 222 methodPosted: Tue Mar 12, 2013 7:29 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Solving face-by-face on a 4x4 octahedron is a great way to practice this.

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 Post subject: Re: 444 reduction to 222 methodPosted: Wed Mar 13, 2013 6:46 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Jared wrote:
Solving face-by-face on a 4x4 octahedron is a great way to practice this.
I view this as the natural way solving a Trajber's 4x4x4 octahedron.
The octahedron is quite a bit easier, though: "Corners" have no orientation and the three edges / centres per 2x2 block are identical.

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 Post subject: Re: 444 reduction to 222 methodPosted: Wed Mar 13, 2013 10:31 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
I view this as the natural way solving a Trajber's 4x4x4 octahedron.
The octahedron is quite a bit easier, though: "Corners" have no orientation and the three edges / centres per 2x2 block are identical.

I don't actually own one of these - maybe I should get one soon - any recommendations for others like this?

_________________
Kevin

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 Post subject: Re: 444 reduction to 222 methodPosted: Wed Mar 13, 2013 1:00 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
I've done the 4x4x4 -> 2x2x2 reduction a few times. It's a fun way to solve. I've also done an analogous reduction from the Gigaminx to Megaminx by forming corner and edge blocks.

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Prior to using my real name I posted under the account named bmenrigh.

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 Post subject: Re: 444 reduction to 222 methodPosted: Wed Mar 13, 2013 3:40 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
I view this as the natural way solving a Trajber's 4x4x4 octahedron.
The octahedron is quite a bit easier, though: "Corners" have no orientation and the three edges / centres per 2x2 block are identical.

I don't actually own one of these - maybe I should get one soon - any recommendations for others like this?
Kevin, I can recommend the 4x4x4 Trajber's Octahedron without any hesitation. And you should do it by reduction: one face = 2x2x2 block on the 4x4x4. It is easier by far than the AI

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 Post subject: Re: 444 reduction to 222 methodPosted: Sat Mar 16, 2013 5:15 pm

Joined: Fri Dec 28, 2012 1:50 pm
Location: Near Las Vegas, NV
This actually gave me an idea for a challenge: can you use a solving technique in which you reduce a 5x5 cube into a deeper-cut 3x3x3? From this:
Attachment:

5x5.jpg [ 275.75 KiB | Viewed 2668 times ]

...to this?
Attachment:

5x5 2.jpg [ 270.51 KiB | Viewed 2668 times ]

...and then solve it from there?

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 Post subject: Re: 444 reduction to 222 methodPosted: Sat Mar 23, 2013 5:46 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hey guys,

I hope this is not ot.
Another reduction is to 2x2x3. This great solver shows it:

I love this technique. If you had forgotten the parity sequence, you can solve the 4x4x4 with this method. It combines 2x2x2, 3x3x3, 2x2x3 sequence.
In my opinion this is a very interesting idea.

Very genial is the step which makes the upper face yellow. With easy , sune like, sequences that exchange two centers (with same color) swap two edges together.
This is the genial part!

I tried to adapt this method to 5x5x5 and 7x7x7. To solve with this method is not faster , but makes more fun.

cheers,
Andrea

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 Post subject: Re: 444 reduction to 222 methodPosted: Sat Mar 23, 2013 7:41 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Hey Andrea,
Andrea wrote:
...
Another reduction is to 2x2x3. This great solver shows it:
...
This may be an interesting method, but I could not recognize a 4x4x4 reduced to a 2x2x3. Close to the end it looks like this screenshot:

The video is called "InterestingSolve4x4x4." The solver does not say anything.
In a 2x2x3 reduction method we should see a slightly scrambled 2x2x3 pattern close to the solution (corners = eight 2x2x1 blocks with correct orientation; middle layer = four 2x2x2 blocks - each consisting of 6 visible cubies).

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 Post subject: Re: 444 reduction to 222 methodPosted: Sat Mar 23, 2013 10:15 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany

I want not a conflict with you. But I want show this method show puzzle interested people. If this not is a reduction you can delete my posting.

He only reduces the last layer in four 2x2x1 blocks and swap this blocks with 2x2x3 sequence.
Interesting is the exchanging of single edges with exchanging equal colored centers.
[url]
http://tw.myblog.yahoo.com/jw!X7fY2vKfG ... &l=f&fid=9
[/url]

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 Post subject: Re: 444 reduction to 222 methodPosted: Sat Mar 23, 2013 12:41 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea wrote:

I want not a conflict with you. But I want show this method show puzzle interested people. If this not is a reduction you can delete my posting.

He only reduces the last layer in four 2x2x1 blocks and swap this blocks with 2x2x3 sequence.
Interesting is the exchanging of single edges with exchanging equal colored centers.
[url]
http://tw.myblog.yahoo.com/jw!X7fY2vKfG ... &l=f&fid=9
[/url]
No, I do not see a conflict. Maybe, we could change the title of the topic to cover more alternative methods solving the 4x4x4?
I just wouldn't call it 4x4x4 reduction to 2x2x3.
I have no doubt, that it is an interesting method solving a 4x4x4, if you say so. The Author says (translated by Google)
Quote:
4x4 interesting solution ~ ~ 2011.07.23

This method is actually a the 4x4 layer by layer method, but because in the middle of the layer 2 and layer 3, the recovery center side of the block and recovery block each other independently of each other, and sometimes must recover the central part of layer 3, and there is no way to write to LBL , this method is purely fun
I have not watched the video completely. Maybe you can point us to the part where we see a reduced 2x2x in the video? As I said, close to the end there is none.
In my view a 4x4x4 reduced to a 2x2x3 would look like this example.

I have marked the two piece types corner (URF) and middle layer block (BL) in purple.
From there we can just solve it using our favourite 2x2x3 method.

Other opinions?

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 Post subject: Re: 444 reduction to 222 methodPosted: Mon Apr 01, 2013 9:03 pm

Joined: Thu Mar 28, 2013 7:14 pm
bmenrigh wrote:
I've done the 4x4x4 -> 2x2x2 reduction a few times. It's a fun way to solve. I've also done an analogous reduction from the Gigaminx to Megaminx by forming corner and edge blocks.

How do you do this? I've been working on this for a few days and always end up running out of room to form the blocks. My basic method is to just do it intuitively with no real algorithms and form 15 of the 20 corner blocks, and 25 of the 30 edge blocks.

I get as far as forming all but the final 5 edge blocks and final 5 corner blocks (which I then place into the top surface, the top two slices) and can't seem to go any further without messing up one of the formed blocks.

Oh and hi this is my first post.

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 Post subject: Re: 444 reduction to 222 methodPosted: Tue Apr 02, 2013 6:09 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Rplass, welcome to the forum,

Have you tried reducing the LL edges first and then using the 444 method on the corners?

_________________
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: 444 reduction to 222 methodPosted: Tue Apr 02, 2013 7:39 pm

Joined: Thu Mar 28, 2013 7:14 pm
Burgo wrote:
Have you tried reducing the LL edges first and then using the 444 method on the corners?

Sorry, but I'm not sure what you're asking. Let me rephrase what I'm trying to do on the Gigaminx. I'm trying to create 7-pc corner blocks composed of the corner piece and the six surrounding pieces, which would be three edge wings and three center dots. Also trying to create 3-pc edge blocks composed of the edge center and the trapezoidal center dots on either side. I made a crude image of what I mean (and tried to attach it to this post). (After all blocks are created, solve the gigaminx like a megaminx with only turns of double slices)
Attachment:

gigareduce.jpg [ 44.59 KiB | Viewed 2166 times ]

Sorry for confusion as I'm new here. I do appreciate your patience.

I was able to create 15 of the 20 corner blocks and 25 of the 30 edge blocks, but ran out of room. I know how to reduce LL edges to tredges (which is how I solve the gigaminx normally) but this method of forming corner blocks and edge blocks compels one not to do that. So my question was how to create the remaining corner blocks and edge blocks? Thanks so much.

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 Post subject: Re: 444 reduction to 222 methodPosted: Wed Apr 03, 2013 1:18 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Rplass,

I understand what you mean by reducing the Gigaminx to a Megaminx. And here you say that you are making a LL:
rplass wrote:
I get as far as forming all but the final 5 edge blocks and final 5 corner blocks (which I then place into the top surface, the top two slices) and can't seem to go any further without messing up one of the formed blocks.

In the first post in this thread^^ I linked to the CT Bandaged 444 thread: viewtopic.php?f=8&t=24349 This demonstrates what is now a known way to reduce a 444 to a 222. I demonstrated my method and made an example video, Superantoniovivaldi made a tutorial and a link was given, and Rline identified all the cases and made some videos. My presumption is that you would have read this thread and been able to reduce a 444 to a 222.

My suggestion here^^ is simply to apply that to your Gigaminx method. The only difference is the edges (which would be like reducing a 555 to the less popularised version of a 333), when you do the LL you would just reduce the edges first. To follow your method, and not do the more popular (or normal) edge reduction, I would do a U twist and swap or reorient edge-blocks and then a U' twist, while maintaining the 5 unmade corners on Uu. The corners wouldn't differ from the 444 method.

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: 444 reduction to 222 methodPosted: Wed Apr 03, 2013 5:56 am

Joined: Thu Mar 28, 2013 7:14 pm
Thank you for your response and for pointing me in the right direction. Very much appreciated!

--rplass

EDIT: I figured out how to form the final blocks!

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 Post subject: Re: 444 reduction to 222 methodPosted: Sun Jun 02, 2013 6:32 pm

Joined: Thu Mar 28, 2013 7:14 pm
This method of solving the Gigaminx is now my standard method. No more edge pairings, which I hate. It's far more difficult to reduce it to a megaminx, especially at that last layer. Also it takes longer. So of course I like it the best.

For the last layer I can build 2 of the 5 corner blocks using intuitive moves and corner piece series... and for the last 3 corner blocks, I can build entirely except for 1 edge each... so I use a three-cycle for edges to place the final three edges: f R f' L' f R' f' L.

For the small center pieces, another three-cycle comes in handy: r U'2 l' U2 r' U'2 l U2

and the final 5 edge blocks I build by placing the trapezoidal center pieces using yet another three-cycle Rr' Ll u Rr Ll' F'2 Rr' Ll u' Rr Ll' F2

(apologies if I'm not using proper TP notation!! please suggest correction if I boofed)

The image I posted above is silly now to me; I now solve the blocks in order and then place them correctly so after I'm done I don't have to go back and solve the entire "megaminx."

I recently acquired a Master Kilominx and use this same method which is the same as just building the 20 corner blocks of the Gigaminx. Edge pairing takes 1/2 the time on the Master Kilominx but I still hate it. And then you still have to deal with 'parity' so I just use this reduction method instead. Have not experienced 'parity' yet using this method on the Master Kilominx.

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