# Is it true?



## TrollingHard (May 22, 2010)

Solving a 6x6x6 is the minimum for solving all cubes big and small...?

6x6x6 uses center-switching alg, edge parities, LL parities, 3x3 solving, etc.

Figured that would be the minimum.


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## PatrickJameson (May 22, 2010)

With just a bit of intuition, 4x4 is the 'minimum', in my opinion.


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## TheCubeMaster5000 (May 22, 2010)

What exactly do you mean by minimum?


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## ianini (May 22, 2010)

I'd say 5x5 for the edge parities and centers.


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## cincyaviation (May 22, 2010)

ianini said:


> I'd say 5x5 for the edge parities and centers.


i agree with this


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## PatrickJameson (May 22, 2010)

ianini said:


> I'd say 5x5 for the edge parities and centers.



Edge parity is the same. Actually it depends which 4x4 parity you use. I first learned the r2 B2 U2 etc one, which allowed for extremely easy transfer to the 5x5.

Centers are pretty easy to figure out if you try a bit.


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## DavidWoner (May 22, 2010)

I'd agree that it's 4x4. Just use comms and do r if you get parity.


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## TemurAmir (May 22, 2010)

I think its 4x4, I can solve 5x5 edge parity with some 4x4 edge algs. Also, for centers, I can do the same thing on a 5x5 except applying it to a bigger puzzle.


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## TMOY (May 24, 2010)

I would say 2^3. Once you understant how commutators work on corners you can apply them to all other type of pieces as well.


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## jms_gears1 (May 24, 2010)

lol id say 3^3 i had n ever solved a 4x4 before, i got one solved it w/o a method, then solved my 5x5, and solved someones 7x7, all w/o learning a real method.


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## MiloD (May 24, 2010)

i don't understand why people even post in these threads. this trolling effort isn't even funny, its just stupid. 

trollinghard, try harder next time please or just give up. you made me laugh in the past but i think you may have lost your magic.


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## Kirjava (May 24, 2010)

MiloD said:


> i don't understand why people even post in these threads. this trolling effort isn't even funny, its just stupid.
> 
> trollinghard, try harder next time please or just give up. you made me laugh in the past but i think you may have lost your magic.




Uh, wow. Are you sure you understand what trolling is?


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## MiloD (May 24, 2010)

do you? 

this is truly ****ty trolling. 0/10 forever you all lose and suck why has /b/ come to speedsolving. i thought that place was out of my life forever. i hate all of you.


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## EnterPseudonym (May 24, 2010)

MiloD said:


> do you?



I do, and it seems to me that you don't.
Edit:Never mind, you're trolling now. lol trolls trolling trolls


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## Kirjava (May 24, 2010)

Because I'd totally question your use of the word 'troll' if I didn't understand it myself. >_>


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## rachmaninovian (May 24, 2010)

4x4 is minimum I guess.

you can lerntosulve 4x4 without learning 3x3. my friend learned to solve the 4x4 first before he learned how to solve the 3x3 a few months later. pretty lame but that's how it is.


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## Kirjava (May 24, 2010)

I'd say that there isn't a minimum, it depends on the person.


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## MiloD (May 24, 2010)

hmm. maybe i didn't understand the point of this thread after all. it had not occurred to me that all those participating actually find this kind of thread amusing(.../b/tards). my first post clearly indicates i know what trolling is, but pardon me for not assuming the rest of you ***holes(seriously meant in the nicest way possible) were trolling too.


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## Kirjava (May 24, 2010)

This is the part where everyone ignores you.


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## MiloD (May 24, 2010)

PM


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## mrCage (May 24, 2010)

Any nxnx cube larger than size 3 can be solved entirely without 3x3x3 algs. I would say the 15-puzzle or pyraminx is the 'mother' of all puzzle solving

Per


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## Christopher Mowla (May 27, 2010)

Certainly, anyone who has learned the 4X4X4 or 5X5X5 and then applied that knowledge to solve larger size cubes is certain that the 4X4X4 is technically the minimum in introducing methods to solve an entire new category of puzzles (although knowing how to solve the 5X5X5 is probably a better representation of larger cube sizes since it has a central slice): ones with inner-layer orbits. This obviously applies to higher order minxs as well. The reason this is true (although obvious to those who solve large puzzles) is due to the fact that the same algorithms used on the puzzles with one inner-layer orbit can be *directly *translated to puzzles with multiple inner-layer orbits.

Obviously, r2 U2 r2 (Uu)2 r2 u2 cannot be successfully translated to the 5X5X5 (or any other odd cube for that matter) without discoloring the front and back centers a little, but having an X permutation of wing edges between two composite edges of odd cubes can be ignored using select edge pairing techniques.

This is the obvious/common knowledge. I will now present the non-obvious.

There are algorithms which cannot be directly translated to larger cube sizes than, say the 4X4X4 and 5X5X5, or even not applicable to larger cube sizes at all. Though not ideal for speedsolving purposes, these algorithms do exist.

Since we are discussing the minimum representation for NXNXN cubes, the first step is to realize that in this new "universe", even and odd size cubes must be treated differently because the central slice on odd cubes DOES matter now. The 6X6X6 is the minimal representation for even cubes and the 7X7X7 is the minimal representation for odd cubes. The reason is simple: those two cube sizes are the smallest cube sizes which contain more than one inner-layer orbit, namely two.

Since the 6X6X6 and 7X7X7 cubes have two inner-layer orbits, there are three possible cases an algorithm must pass to be officially transferable to them. Although obvious, I am going to mention these three cases anyway, so that I can assign them case numbers for future reference.

Using the 7X7X7 as a model,
Let 0's represent the wing edges in the orbits for which the algorithm is translated to and let X's represent the slices which the algorithms are not be translated to.

Case 1:
X00X00X
Case 2:
X0XXX0X
Case 3:
XX0X0XX

Unlike any big cube algorithms you have ever seen before, there are algorithms that only work for case 1 (treating a 6X6X6 as a 4X4X4 and a 7X7X7 as a 5X5X5, or more generally, turning half of the inner-layer slices on a big cube as if they were one).

There is another category of algorithms which work for all three cases, but only on even cube sizes (4X4X4 and greater). This category contains some algorithms which are rather complicated.

And there is a third category of algorithms which only work on the 4X4X4: they cannot be translated to larger cube sizes (besides matching case 1 on even cube sizes) without scrambling them.

Despite these different cases, it turns out that if an algorithm survives all three cases (for both the 6X6X6 and 7X7X7 cubes), it can be applied to all big cube sizes.

In summary, for a person who has strong determination and patience, the 4X4X4 and the center commutator is sufficient to eventually learn how to solve NXNXN cubes. At the same time, there exists algorithms which do not support the idea of direct tranlation. So truly technically speaking, the 6X6X6 and the 7X7X7 are the minimal sizes to represent all big even and odd cubes, respectively.

So, TrollingHard, you're instinct for the 6X6X6 as the minimum cube size representation was correct (for even cubes, that is), although you didn't know exactly in what way it was.


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