# Is cubing mathmatical?



## Mudkip (Oct 18, 2011)

Many cubers say cubing is non mathmatical. Most non-cubers say it is.
Form both perspectives:

Cubers: We're not actually doing math in the solve.
Non- Cubers: They use patterns, based on math.

So who's right?


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## Kirjava (Oct 18, 2011)

It is, but you aren't exactly doing calculations when solving.


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## 5BLD (Oct 18, 2011)

It depends on how you look at it.


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## Cubenovice (Oct 18, 2011)

Cubes are sometimes used in math lessons, therefore cubing = mathematical


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## Stefan (Oct 18, 2011)

Cubenovice said:


> cubing = mathematical


 
Since when is let's say calculus cubing?
And how mathematical is let's say Lubix?


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## bwronski (Oct 18, 2011)

Cubenovice said:


> Cubes are sometimes used in math lessons, therefore cubing = mathematical


 
i dont know it that logic transfers over. i have used chocolate bars in math lessons before that doesn't make chocolate = mathematical

i think that math can be applied to solve it in very loose terms, but overall i think it is more logic and spacial thinking than math


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## Ickenicke (Oct 18, 2011)

Mudkip said:


> Many cubers say cubing is non mathmatical. Most non-cubers say it is.
> Form both perspectives:
> 
> *Cubers: We're not actually doing math in the solve.*
> ...



The right answer


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## Kirjava (Oct 18, 2011)

bwronski said:


> i think that math can be applied to solve it in very loose terms


 
Aren't commutators a strictly mathematical approach to solving the cube?


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## Stefan (Oct 18, 2011)

bwronski said:


> more logic [...] than math



Now I'm curious: What do you think is math?


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## Godmil (Oct 18, 2011)

Are commutators mathematical, or can they just be expressed mathematically?

The cube is no more mathematical than a ball is. It's fantastic for demonstrating many mathematical concepts, but it was created as it was, the mathematics were studied afterwards.


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## aronpm (Oct 18, 2011)

Godmil said:


> Are commutators mathematical, or can they just be expressed mathematically?


 
Math? In my commutators? I think not!

(They have a mathematical basis but it's not necessary to understand it to make commutators)


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## Kirjava (Oct 18, 2011)

afaik they're a mathematical concept.


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## Cubenovice (Oct 18, 2011)

LOL at Stefan and bwronski 

Hint: It's like goldy and bronzy, only it's made of iron.


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## bwronski (Oct 18, 2011)

uh oh, i will try an explain my self.

yes commutators are a strictly mathematical approach to solving the cube, from the mathematical stand point, but while actually solving i get a different idea, how I think when I do comms is basically this "A gets to B with proper orientation and C goes to A with proper orientation", that is more logic to me than math, the idea and system is mathematical but not math when doing moves on the cube.

Im not a math guy so I don't know how commutator are really used in mathematics, but form what I know that is how I look at it.

And I think math is a way for us to quantify our surroundings based on measurements, observations and patterns we find in numbers.


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## Kirjava (Oct 18, 2011)

bwronski said:


> how I think when I do comms


 
You can think of it in a more mathematical sense if you want it to fulfill that requirement.


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## bwronski (Oct 18, 2011)

so to some people cubing is mathematical and others its not?


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## Kirjava (Oct 18, 2011)

No.

Maths can be an aspect of different parts of cubing. It usually isn't.


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## bwronski (Oct 18, 2011)

different parts meaning what? because i can see how we get the ideas from math or use mathematical ideas so describe what we do in a solve, but is solving mathematical?


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## Kirjava (Oct 18, 2011)

Maths is often used to discover the number of different permutations for a step. While not using during a solve, it's an aid in developing a solving method.

BLD solvers may do x + 1 mod 2 after solving each edge or corner during M2/Pochmann to store a boolean value for parity.

Of course there will be better examples, but I'm not majorly into cube theory.


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## Stefan (Oct 18, 2011)

bwronski said:


> And I think math is a way for us to quantify our surroundings based on measurements, observations and patterns we find in numbers.


 
Sounds like a very very narrow definition. How do let's say set theory, game theory or predicate logic fit in this?


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## Cubenovice (Oct 18, 2011)

bwronski said:


> how I think when I do comms is basically this "A gets to B with proper orientation and C goes to A with proper orientation"



What is this "A" "B" "C" and "orientation" stuff you talk about? almost sounds like math to me...

With commutators I think in terms like "this solves this piece" , "this swaps these two" and twice "this undoes this"


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## bwronski (Oct 18, 2011)

@kirjava
i agree with that post

especially the first example


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## bwronski (Oct 18, 2011)

Cubenovice said:


> *What is this "A" "B" "C" and "orientation" stuff you talk about? almost sounds like math to me...*
> 
> With commutators I think in terms like "this solves this piece" , "this swaps these two" and twice "this undoes this"


 
it sound like math because thats where the idea come from

Edit:to avoid triple post

@stefan, it probably sound narrow because i have pretty basic math knowledge


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## qqwref (Oct 18, 2011)

I would say that typical speedsolving requires essentially no math, but as you start to try to understand the cube better and move into more complicated theory (including getting better at FMC or BLD), the amount of math increases. A good cube theorist will typically have a very strong intuitive grasp of the group theory that applies to twisty puzzles.


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## chrissyD (Oct 18, 2011)

cubing can involve math 

but you don't actually need any math to solve a cube


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## Hyrtsi (Oct 18, 2011)

Yes. Cubing is mathematical because it involves thinking logically and solving problems. You don't actually calculate anything but it's not about that. Everyone thinks mathematically every day - whether they knew any math or not. For example choosing the fastest way to work or school is mathematics. Please read this and see for yourselves: http://en.wikipedia.org/wiki/Algorithm


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## Cubenovice (Oct 18, 2011)

qqwref said:


> I would say that typical speedsolving requires essentially no math, *but as you start to try to understand the cube better* and move into more complicated theory *(including getting better at FMC or BLD), the amount of math increases. *



I don't really agree with the bolded parts: you can have good understanding about the cube, FMC and BLD solving without knowing / relying on any math whatsoever.




qqwref said:


> A good cube theorist will typically have a very strong intuitive grasp of the group theory that applies to twisty puzzles.


If with 'cube theorist' you mean people like yourself, Lucas, Chris, Per, Cmwolla etc then I agree


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## macky (Oct 19, 2011)

Cubenovice said:


> If with 'cube theorist' you mean people like yourself, Lucas, Chris, Per, Cmwolla etc then I agree



They're all certainly theorists in the wider sense that they pose puzzle-theoretic questions and attempt to answer them, but not all of them use much that's actually theoretical, and I'm sure some don't know much group theory. To pick on Cmowla, he's much more of an experimentalist. Not that I have any problem with that in itself; doing often produces more useful things, and he's definitely done some cool stuff. But ad-hoc constructions and computations barely qualify as theory. More theory could help him become a more productive experimentalist, if only by pointing out provably fruitless paths of exploration....

[edit]
To clarify, almost any interesting exploration on the cube has to be more experimental than theoretical. I mean, the cube group is abstractly just a finite group whose structure can easily be written down explicitly; aside from its size, it's a relatively simple object. So it's to be expected that most mathematically natural questions about the abstract cube group are easy (e.g. order, commutator subgroup). The long-standing "theoretical" question of God's number was the explicit computation of some quantity related to this one Cayley graph, and relative to a set of generators that's pretty unnatural from a mathematical point of view (why include half turns?); the reason it was hard was because the thing is huge by the standard of today's computers, which meant that you had to be clever to make the computation feasible.

Most of the difficulty in cube theory comes from the fact that many questions we consider are only natural for the specific realization of the abstract cube group as a Rubik's Cube, and more specifically as a Rubik's Cube solved by a speedcuber. This means that many questions that are interesting for us are very unnatural mathematically. For example, one natural question for a speedcuber is whether it's possible to execute every PLL once and get back to the solved state. On the cube group, the subgroup P of elements that permute the last layer while preserving orientation is still a mathematically decent object (though you're already fixing a particular realization of the cube group rather than looking at it abstractly). But identifying different permutations as a single PLL by factoring out rotations and AUFs means (as you can convince yourself) looking not at P but at R\P/R, where R is subgroup of U turns. If you treat the cube as an abstract group, there's no good mathematical reason to look at these double cosets; P/R already fails to be a group, and there's no reason to expect much structure in R\P/R under the induced operation. Theoretical considerations may still somehow lead to a nice solution (more likely negative, if anything), but precisely because this question is mathematically unnatural, it's hard to solve it theoretically...which means we'll probably have to just compute. On the other hand, theoretical considerations may help simplify computation and make it feasible.

To summarize, many interesting problems for speedcubers are hard and more computational than theoretical because they're mathematically unnatural. There isn't much theory to know for cubing, say some group theory (say enough to fully understand the above) and some standard counting tools, and otherwise large computations will often be necessary. But knowing this much theory will help you organize and effectively carry out these computations. In other words, cube theorists are by nature be more experimentalist than theorist, but the best experimentalists are those well-versed in theory.

[edit]
In response to the thread, I think the key point is the difference between an abstract mathematical concept/object and its various realizations. Cubing (for 3x3) deals with one particular realization of one group that, abstractly, is mathematically relatively uninteresting. Rather, it is this realization and all its consequences (including consequences for cube theory described above) that make cubing interesting.


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## stoic (Oct 19, 2011)

Hyrtsi said:


> http://en.wikipedia.org/wiki/Algorithm


 
Not sure about the relevance of this link, as it explicitly defines an algorithm "In mathematics and computer science"


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## Florian (Oct 19, 2011)

Why should cubing be math?
Are there numbers on each sticker which build an equation system?

And i don't know why commutators should be math, for me commutators are just a logical way to solve the cube.
And logic≉math.


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## Kirjava (Oct 19, 2011)

can be and should be are different things


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## Stefan (Oct 19, 2011)

Florian said:


> Why should cubing be math?
> Are there numbers on each sticker which build an equation system?


 
Wait, are you suggesting that math is just about numbers and equation systems?


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## macky (Oct 19, 2011)

Florian said:


> Why should cubing be math?
> Are there numbers on each sticker which build an equation system?
> 
> And i don't know why commutators should be math, for me commutators are just a logical way to solve the cube.
> And logic≉math.


 


Stefan said:


> Wait, are you suggesting that math is just about numbers and equation systems?


 


Kirjava said:


> can be and should be are different things



Kirjava and Stefan, as fun as it is to watch you two shoot down logical fallacies in superficial non-arguments, I'm actually hoping to get some input from prominent puzzle theorists. Private forum?


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## Cheese11 (Oct 19, 2011)

Cubenovice said:


> What is this "A" "B" "C" and "orientation" stuff you talk about? almost sounds like math to me...
> 
> With commutators I think in terms like "this solves this piece" , "this swaps these two" and twice "this undoes this"


 
To me it kind of sounds like the stuff I'm learning in Science...


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## Kirjava (Oct 19, 2011)

macky said:


> I'm actually hoping to get some input from prominent puzzle theorists.


 
Honestly, I don't consider myself that much of a puzzle theorist.

My knowledge of group theory specifically is severely lacking. I've never really needed it on my adventures and therefore never bothered to educate myself on the subject. Any maths that I'm required to do for cubing activities is almost always trivial.

Out of interest, what do you class as 'exploration'?


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## macky (Oct 19, 2011)

Kirjava said:


> macky said:
> 
> 
> > I'm actually hoping to get some input from prominent puzzle theorists.
> ...


Yes, I was talking about the likes of Kociemba and Rokicki. =)



Kirjava said:


> Out of interest, what do you class as 'exploration'?


Anything you might call cube/speedcubing theory/development, including things as non-mathematical as finding algorithms using ACube and computing case counts for method variants.


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## Kirjava (Oct 19, 2011)

lols, embarrassing misinterpretation >_<


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## kirtpro (Oct 19, 2011)

sheldon cooper: 'first of all we must ask ourselves "what is physics"'

ok, not sure if anyone else watches that show lol.

so, to me in a way cubing is like math
im sure we've all stumbled upon (or get taught) a way of solving pieces in a more optimized solution, after learning we understand how some steps are not needed, or "hey, it's the same thing".

in math, if you're given the fraction 2x/8x, you know it's equal to 1x/4x.

thats if you say math is about problem solving (in the easiest way)
..then cubing can be thought of as also learning to solve in the easiest way

secondly, math has a bunch of formulas, we remember as text (e.g. a2+ b2 = c2)
us in cubing also have to remember things; algorithms, which we remember in muscle memory

third, there's terms (jargon)
in math, perpendicular, quadratic, exterior angles lol
in cubing, cfop, f2l, ollcp, petrus, zeroing (jokes)
these things, no one would know unless they've studied the subject

but.. if you're like me and basically cube all the time then..
math is not like cubing because it's boring lol


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## StachuK1992 (Oct 19, 2011)

kirtpro said:


> secondly, math has a bunch of formulas, we remember as text (e.g. a2+ b2 = c2)
> us in cubing also have to remember things, algorithms, which we remember in muscle memory


People memorize formulas in text?
I've always done so with auditory signals "asq basq is casq" but maybe that's just me.

Either way, I hope people seldom memorize algorithms in text, even at the very start.


I guess you could show some comparison of how you use 'muscle memory' both in cubing and performing mathematical operations, but you do the same with walking. Is math walking? Is walking cubing? No, that's stretching it at this point. We need to be more specific.


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## Cubetastic (Oct 19, 2011)

Well, in my opinion, everything in life has a certain degree of mathematics involved even to the slightest degree(not sure if i spelt slightest right D

As an example, When you go to eat a pie and you are watching your weight, 2000 calories a day on average you must subtract the amount of calories from each portion, if the pie is 500 calories in total, you aren't going to eat the whole pie, you'are going to eat a portion, normally using a fraction to deduct everything and to calculate the amount of calories.

Another example would be the rubiks cube, there are 43,252,003,274,489,856,000 possible combinations, but as they say only one of them is the correct solution, but you must go through multiple multiple stages of the cube, eliminating more and more possible combinations on your way to that single possibility. Wich is why the further you get into solving it, the less moves it takes.

But that is just my opinion and i have enjoyed overseeing this topic.


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## kirtpro (Oct 19, 2011)

just saying they have similarities,

i remember pythagoras in the sentence, "a squared plus b squared equals c squared."


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## Cubenovice (Oct 19, 2011)

macky said:


> Cubenovice said:
> 
> 
> > If with 'cube theorist' you mean people like yourself, Lucas, Chris, Per, Cmwolla etc then I agree
> ...


 
Good stuff!

Note however that my post was a response to qqwref's "A good cube theorist will typically have a very strong* intuitive grasp of the group theory *that applies to twisty puzzles. "
Neither of us claimed that they use much that's actually theoretical and / or know much group theory. 

Seriously, I think your post can be considered a thread closer. Very well put


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## The Bloody Talon (Oct 21, 2011)

IMO, speedsolving doesn't involves math, 
but discovering algorithms involves math.

Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, space, structure, and *change*. 
-wikipedia


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## Gabo (Oct 21, 2011)

The Bloody Talon said:


> IMO, speedsolving doesn't involves math,
> but discovering algorithms involves math.
> 
> Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, space, structure, and *change*.
> -wikipedia


 
Agree... if you do math you MUST understand what you are doing, and most cubers don't understand it at all. Thats why when you learn math you start with the basic stuff and don't learn the whole bunch of formulas at once, while you can go and learn the whole friedich method and solve the cube with no to much problem (it will be realy slow, but you can ). You could use the math formulas, but if you don't know what those mean, it's barely useless.


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## dada222 (Oct 22, 2011)

Hyrtsi said:


> Yes. Cubing is mathematical because it involves thinking logically and solving problems. You don't actually calculate anything but it's not about that. Everyone thinks mathematically every day - whether they knew any math or not. For example choosing the fastest way to work or school is mathematics. Please read this and see for yourselves: http://en.wikipedia.org/wiki/Algorithm


 
Oh come on, maths is a humanly defined branch of science - saying that everything we think involves maths is beyond overt. So is suggesting that everything that involves change is based on maths (to the posts above me).



> but discovering algorithms involves math.



Wrong. I've "discovered" several algs in my two year "career" and even if I didn't know how to count I'd still have done it. For example, solve F2L and orient the last layer, make some random turns, then fix it so the first two layers are solved again. There, there you have an OLL. It's not rocket science.

Sort answer: no.
Long answer: nooooooooo
It just sounds cool to non-cubers.



> My knowledge of group theory specifically is severely lacking. I've never really needed it on my adventures and therefore never bothered to educate myself on the subject. Any maths that I'm required to do for cubing activities is almost always trivial.



Just curious and you don't have to answer lol: "adventures"?


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## The Bloody Talon (Oct 25, 2011)

dada222 said:


> Wrong. I've "discovered" several algs in my two year "career" and even if I didn't know how to count I'd still have done it. For example, solve F2L and orient the last layer, make some random turns, then fix it so the first two layers are solved again. There, there you have an OLL. It's not rocket science.
> 
> Sort answer: no.
> Long answer: nooooooooo
> It just sounds cool to non-cubers.


 
lol
well, nooooooooooo to you. 
how come you discovered an algorithm and you don't know what *change* it does to the cube? do you know when to use that algo?

if you discovered an algo, you should know what certain change it do.

math is not all about counting.


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## Christopher Mowla (Oct 25, 2011)

The Bloody Talon said:


> how come you discovered an algorithm and you don't know what *change* it does to the cube?


He made it very clear how: "random turns." When one does random turning, he or she does not care about the details (the cycles) he or she is actually doing to the cube.

Also, with all of the algorithms I have discovered, I never used math to find anyone of them. One who does not know mathematics well can very well interpret every move in every algorithm I have made strictly in terms of moving pieces. I don't consider the definition of math from Wikipedia you posted earlier to have any grounds whatsoever in an argument that says we use math to create algorithms because, whenever anyone says they use math to solve any type of problem, they are using equations, inequalities, relations, functions, arithmetic, and some branch of mathematics (e.g. Discreet Math, Calculus, Linear Algebra, etc.).

The only "math" one has to really know to make algorithms is to know the difference between an odd number and an even number, which is so simple, it's redundant to use it as an example of how one uses math to create algorithms.

Like dada222 said, we can even use less effort than even considering an odd number of turns or an even number of turns by simply doing random moves.

Don't get me wrong, it's always better if we have at least an educated guess to build on so that we are more productive in creating algorithms, and we definitely have to be knowledegable to find algorithms efficiently and systematically. However, even at that level, no math is really required.

As some have probably already said, math can be used for calculating case counts, creating formulas describing a puzzle, etc.


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## cubecraze1 (Oct 25, 2011)

more memorisation but is memory linked to maths


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## The Bloody Talon (Oct 25, 2011)

cmowla said:


> He made it very clear how: "random turns." When one does random turning, he or she does not care about the details (the cycles) he or she is actually doing to the cube.


 

"trial and error". very important in mathematics
but if you discovered algorithm X by trial and error, you should study what it do.
If you don't, you couldn't use it again.

for example.
I discovered R U R' U R U2 R' by trial and error. 
and by studying that I learned that it rotates three edge pieces clockwise. 
and by that, with proper orientation, I discovered that you could properly orient all the edge pieces of the last layer by performing at most two R U R' U R U2 R' algorithm.

expanding my knowledge by starting with trial and error, clearly, It is math.
or are we discussing different things? 

what is your definition of mathematics?
you don't believe wikipedia?

Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with *logical reasoning *and quantitative calculation.
- Britannia Concise Encyclopedia

mathematics, deductive study of numbers, geometry, and various abstract constructs, or structures; the latter often "abstract" the features common to several models derived from the empirical, or applied, sciences, although many emerge from purely mathematical or *logical considerations*. Mathematics is very broadly divided into foundations, algebra, *analysis*, geometry, and applied mathematics, which includes theoretical computer science.
-Columbia Encyclopedia


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## Christopher Mowla (Oct 25, 2011)

"Trial and error" is nothing more than a "science experiment," not mathematics. What you described is nothing more than the scientific method. As for my definition of mathematics, I'll stick to defining only applied mathematics because you are claiming to apply skills of mathematics to solve a real world problem. 

Mathematics is the *tool* by which one can model a real life phenomena. Once the phenomena is modeled with mathematics (see the different branches of applied mathematics if you need a specific example), it is "translated" into mathematical language. Once we have translated a problem properly to the language of mathematics, we do not need to refer back to the object we modeled to help us solve the problem we wish to solve about that object. Rather, we refer back to the object after we have made calculations with the math, and we want to see how the mathematical solutions can be interpreted back in the real world. That is, we "translate" the math solutions back to reality. 

We know we are using a branch of applied mathematics to solve a real world problem when, after we have successfully modeled _ with mathematics, we are able to use that branch of mathematics we modeled _ with (which does not involve experimentation, rather, a clear list of axioms, theorems, algorithms, and arithmetic) to find any solution we wish. Since _ is now in mathematical language, we can even consider how the other branches of mathematics are related to the initial branch of mathematics we chose to model _ with, and possibly discover something new about _ which we didn't know from experimentation already.

If we have properly modeled _ with some branch of mathematics, then we can calculate everything possible there is to calculate with that branch of mathematics. Once all calculations have been made, we can then look back at _ and try to interpret what the math is telling us about _.

As a simple example, I can model what my grade will be in a class by modeling the restrictions and conditions the teacher enforces in his/her syllabus with an equation. From this equation, I can calculate my grade with zero experimentation. With this equation, I can calculate every grade that a student can possibly get if I want to. I can exchange what is a variable and what is a given.

On the other hand, relating to "trial and error," if I didn't know how to express my teacher's grading system with an equation and I have a C average before the final exam, I would have to experiment to see exactly what I would have to make on the final to make an A, B, or keep the C.

In summary, using mathematics to solve a problem _ , relieves one from having to experiment to find solutions. In effect, mathematicians dream of being able to model a real life situation with an equation because it not only relieves them from having to experiment, but it gives them assurance (assuming that they properly modeled the situation with math) that any conclusions which can be drawn from the results of the math are correct (that is, if the solutions the math yielded can be translated back to reality).

See the difference?


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## The Bloody Talon (Oct 25, 2011)

this will end this topic.

http://en.wikipedia.org/wiki/Group_theory


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## Christopher Mowla (Oct 25, 2011)

The Bloody Talon said:


> this will end this topic.
> 
> http://en.wikipedia.org/wiki/Group_theory


No. You in particular are NOT using group theory to find algorithms. Group theory is based on very abstract concepts and theory, quite contrary to raw experimentation.



The Bloody Talon said:


> Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with *logical reasoning *and quantitative calculation.
> - Britannia Concise Encyclopedia


What is meant by "logic" is a systematic approach using truth tables to determine whether a statement is true or false (or compositions of statements are true or false). When you experiment with moves on the cube, you are unsure of whether something is true or false: you have to experiment first to see if it is true. I don't think you used truth tables to find out what you did about the <U,R> algorithm, did you? Here's a better question, did you even know that "you could properly orient all the edge pieces of the last layer by performing at most two R U R' U R U2 R' algorithm" before you _experimented_ with R U R' U R U2 R'? No, you used conclusions of your experimentation. You're not even using "if this is true, then that is true" from mathematical logic in your observations of the <U,R> algorithm. Why?

If A, then B. Okay, well, if A = R U R' U R U2 R', then what is B? Do you know what B is before you experiment with A? No, you didn't. Math is used to figure out a clearly defined problem.



The Bloody Talon said:


> Mathematics is very broadly divided into foundations, algebra, *analysis*, geometry, and applied mathematics, which includes theoretical computer science.
> -Columbia Encyclopedia


Analysis is referring to Advanced Calculus, not simply "analyzing what you have from experimentation."


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## The Bloody Talon (Oct 25, 2011)

what's with your self interpretation of every fact I post?



cmowla said:


> I don't think you used truth tables to find out what you did about the <U,R> algorithm, did you?



duh! do I really need to make truth tables? lol 


Let me know what you think of this sentence:
If Rubik's cube is not mathematical, no robot could ever solve it.


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## ric d (Oct 25, 2011)

In a month or two I am talking with a college math professor about how it is mathimatical. I'm not sure how it's mathimatical yet, but i'll come back to this thread after I talk to him.


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## xabu1 (Oct 25, 2011)

The Bloody Talon said:


> Let me know what you think of this sentence:
> If Rubik's cube is not mathematical, no robot could ever solve it.


 
so, if I make a robot to open a cupboard, and nothing else
opening cupboards is mathematical?


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## The Bloody Talon (Oct 25, 2011)

xabu1 said:


> so, if I make a robot to open a cupboard, and nothing else
> opening cupboards is mathematical?


 
hahahaha! 
bwahahaha!

cool cupboards!
what is that? a puzzle cupboard? 
does it involve much thinking to open it?!
LOL


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## Christopher Mowla (Oct 25, 2011)

The Bloody Talon said:


> what's with your self interpretation of every fact I post?


I'm surprised no one who actually knows math hasn't told you that I am not "self interpreting" anything about what I mentioned.



The Bloody Talon said:


> duh! do I really need to make truth tables? lol


Of course you don't. That was a rhetorical question illustrating how little (none in fact) math YOU, me, and most others use to solve a puzzle.



The Bloody Talon said:


> Let me know what you think of this sentence:
> If Rubik's cube is not mathematical, no robot could ever solve it.


1) I never argued that the cube isn't mathematical, and anyone (well, others besides you, obviously, since you have gotten the idea that I have somehow) can see that since I didn't edit my posts like you did. You first were absolutely determined that a human must know how moves change a cube before he or she could make an algorithm, even when dada222 mentioned (not that he even was debating whether or not a person needs to understand moves before he or she makes an algorithm) that he did random moves once for an OLL, which in turn definitely did not require any mathematical skill (not that he doesn't have mathematical skills, rather he did not need to use any that he has to do what he did). (I'm sure he has used more constructive trial and error on other occasions, however). I happened to also mention in that post that *humans do not need to use math to make any algorithms* (post47). The only time that a human could possibly need to use math is when he or she is trying to find an optimal solution and creates an optimal solving algorithm (e.g., like the 2-phase algorithm like Herbert Kociemba made).

2) I defined what applied mathematics was in the following post and explained that when humans use trial and error in the manner you did with your <U,R> discovery, they are not using any form of mathematics whatsoever.

3) A robot does not need to know a bit of group theory to solve a cube, as it can be programmed to select a pre-made algorithm from a table of thousands (probably more) algorithms based on the cube position it senses with its sensors. Its actions are governed by programming and nothing more. That being said, yes programming directly corresponds to mathematical logic, but, as I've said, that's just to get the robot to move and to match the scrambled cube case with what was put in its database: it does not necessarily need to be an optimal solver itself or know any math behind the cube.

I have programmed my Ti-83 plus calculator to solve an orbit of wing edges in the last layer of a big cube (K4 style) doing just this. Did I or the calculator have to know any math that may be associated with the cube to do this? Well my calculator sure didn't, and the little math that I needed to know had nothing to do with the algorithms I typed into it for it to select for specific cases.

4) Yes, Herbert Kociemba and others who made optimal solvers did use math to some degree (predominately programming I presume), and there are ways to interpret each move on a cube in terms of group theory for sure. But again, this wasn't my argument at all.


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## The Bloody Talon (Oct 25, 2011)

*"humans do not need to use math to make any algorithms"*
-speak for yourself.

learning an algorithm (which can be get by experimentation) and modifying it (it can be "set up" move or performing it twice or thrice) to come up with a new algorithm is already a mathematics. 
N perm + a certain set up move = J perm.
doing a certain OLL algo *2 = another OLL algo
G perm *4 = 0
tell me, is it math? or still not?

and please don't expect me to show you numbers and tables. 

about the "robot" thingy, it is just an exaggeration of my point. It proves that an algorithms for solving a whole cube can be achieved through mathematics.
so a certain application of mathematics can solve the last layer, or orienting edge pieces.or swapping 3 edges. And yes, human can't compute it by just facing a cube.


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## Gaétan Guimond (Oct 25, 2011)

Have an aptitude and the knowledge of math is two worlds. We can draw comparisons with the cuber and chess gamer. World champion Carlsen does'nt have much interest and knowledge in math

I love this page ....

The effect of math and chess
The Chess Academy, Chicago, USA
Research studies have shown that chess can be used as an effective game-based teaching method. However, all the past studies used chess as a separate instructional tool. There were no math contents in chess instruction provided and there was no math and chess integrated workbook used. This study examined the effect on pupils’ math scores when a truly integrated math and chess workbook was used as an instructional practice workbook. The results show that the integrated math and chess workbook significantly increased pupils’ math scores between pre-tests and post-tests among grade 1 to grade 8 pupils. 

Introduction
Research papers have demonstrated that chess instruction improves analytical reasoning, problem solving skills, and academic achievement (Chrisiaen & Verholfstadt (1978); Frank & D’Hondt (1979); Smith & Cage (2000)). Research conducted by Gaudreau (1992) shows no significant differences among the groups on basic calculations. These research studies point to the direction that chess has strong effect on improving children’s cognitive ability than their arithmetic computation ability. By teaching math and chess as two separate subjects, children do not have opportunities to work on basic arithmetic operations using acquired chess knowledge, this may explain why by playing chess, it may not statistically significant improve children’s basic arithmetic computation ability. 

How to maximize the benefits of chess instruction in such a way that not only chess benefits children’s cognitive development, but also their computation ability? All the past chess instruction research studies have used chess instruction as an independent teaching tool and it is not truly integrated with math instruction. The author Frank Ho created a math and chess integrated workbook. The theoretical basis of how math and chess are integrated has been published by Ho (2006). We believe that with the creation of truly integrated math and chess workbooks, pupils will be able to increase their computation ability by working on these math and chess integrated workbooks. This is particularly important for those children who have no interest in playing chess, but they could still get benefit of chess instruction by working on math and chess integrated workbooks. 

No research has been done before on the effects of using math and chess integrated workbook, this study will compare the effect of pupils’ math computation ability before using the math and chess integrated workbook and after using it to see if there is a significant difference.


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## Christopher Mowla (Oct 25, 2011)

The Bloody Talon said:


> *"humans do not need to use math to make any algorithms"*
> -speak for yourself.


No comment.



The Bloody Talon said:


> learning an algorithm (which can be get by experimentation) and modifying it (it can be "set up" move or performing it twice or thrice) to come up with a new algorithm is already a mathematics.
> N perm + a certain set up move = J perm.


People can use math symbols to abbreviate words used to describe many things. For example, I can use this same argument to "prove" that everyone who speaks a language is using mathematics because "one phrase" + "another" = a sentence. Not to mention that many languages use verb conjugations. We have conjugation (set up moves) in cubing too, so language is definitely mathematics, right?

Take cooking as another example. "One ingredient" + "another ingredient" + ...+ "a final ingredient" constitutes a particular food type. Is cooking mathematics? 

My (current) point is, *by your definition, everything is mathematics*, seriously.



The Bloody Talon said:


> doing a certain OLL algo *2 = another OLL algo
> G perm *4 = 0
> tell me, is it math? or still not?


Yes, those two examples, as well as the ones above can be interpreted mathematically (which I have already said in point #4 in my previous post), but what good, for example, does repeating an algorithm until the identity is reached help you make algorithms? Repeating that OLL alg twice to get another OLL alg is experimentation yet again.



The Bloody Talon said:


> about the "robot" thingy, it is just an exaggeration of my point. It proves that an algorithms for solving a whole cube can be achieved through mathematics.


You are right, but no this is not what I was debating with you, as I HAVE JUST SAID in point #4 of my previous post.


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## The Bloody Talon (Oct 25, 2011)

cmowla said:


> Yes, those two examples, as well as the ones above can be interpreted mathematically (which I have already said in point #4 in my previous post), but what good, for example, does repeating an algorithm until the identity is reached help you make algorithms? Repeating that OLL alg twice to get another OLL alg is experimentation yet again.



you are *assuming* that I discovered by experimentation.

how come it become experimentation?
I studied the algorithm and discovered that if i set it up first or do it twice will make another new algorithm. 

i studied an algorithm and *its effect* and found out that it do this and do that.
and by doing this. I could do that. or mirroring or using its anti will do this. 

true example is my N perm. 
i know which edge and corner pieces switch with J perm. So I think of a set up move to make it an N perm. And it is not experimentation. I think first before I tried it.
it is math.

i think things to you needs a ballpen and a paper or something where you can put your data to be considered as math, seriously.


btw, peace bro. we're cool right? 

edit: 
everything is math: http://cemela.math.arizona.edu/english/content/workingpapers/ELEMTMSJ_AERA_2007.pdf
lol. just kidding.


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## tozies24 (Oct 25, 2011)

Your argument is so ridiculous The Bloody Talon. There are so many different things that I could say about how your argument is lacking but I think that the other people on this thread have already taken care of that. But I will say that your trial and error statement is not mathematical at all. 

Trial and Error is not strictly mathematical and I would not consider it to be a good base argument for why cubing is or isn't mathematical. Of course, there are situations in mathematics that have required trial and trying to figure out what to do with a certain expression. But trial and error is part of everyone's daily life; something as simple as choosing the correct path to take when driving somewhere, or considering what words and sentences to put into a essay. 

Let's say that we were to argue that putting an essay together is mathematical, for an example of how ridiculous your argument is. Say that the essay is an argumentative essay and you have taken a side on side A (There are two sides to the problem). Now, by the use of logic and careful reasoning, you put together a solid discussion on why your point of view on the problem is right. But wait, isn't logic and careful reasoning used in mathematics? So writing an essay must be mathematics, too. 

Moral of the story: Please don't try and think into things more than you have to especially if they are going to make people upset. Also, don't post quotes that you don't back up or understand completely. 

Last example: 



> IMO, speedsolving doesn't involves math,
> but discovering algorithms involves math.
> 
> Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, space, structure, and change.
> -wikipedia



Change, in a mathematical sense, is about the rate of change of things. Calculus is all about change. Derivatives and Integrals give us the tools to take a look at situations that would be hard to figure out without those concepts. Of course you could say that turning sides on the cube is change, but so is your hair growing and so is a law coming into effect from the government. 

Have a nice day.

EDIT:There are going to be holes in someone's argument on the forums because we are just writing this from nowhere so I am sorry if I jumped around.


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## dada222 (Oct 25, 2011)

> "trial and error". very important in mathematics
> but if you discovered algorithm X by trial and error, you should study what it do.
> If you don't, you couldn't use it again.



Simple, take a solved cube, apply the alg some number of times, then it will be solved again, the last state it was before it was solved is the one the alg was made for. Of course, it's pretty random but I assumed the people that first made algs on the Internet and before it did it that way, but I could be wrong.


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## chris410 (Oct 25, 2011)

Non-cubers think the cube is mathematical because of the apparent complexity to those who have no knowledge of the cube. To date, I have never used addition or division (two fundamental operations in mathematics) to solve a cube. Can mathematics be used to solve a cube yes, based off of group theory (and I will admit that I have not studied group theory but I have read over papers that talk about solving the cube using group theory).

Good link: http://www.ryanheise.com/cube/group_theory.html However, I would venture to say that most of us do not use this method to solve the cube. 

To answer the question, in my opinion, the cube "can" be mathematical if you consider group theory. Do we use mathematics while solving...NO but we do use spacial intelligence.


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## tozies24 (Oct 25, 2011)

I think that considering cubing to be mathematical is just looking into something too much when it is just a puzzle. Obviously anything with some observable properties can be modeled by math, but those things are not needed to be modeled by math for us to understand them. We understand the cube and that's why we can solve it. We don't need to understand vector spaces, topology, and other higher mathematics to solve it. We don't even need addition and multiplication (which was stated earlier).


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## xabu1 (Oct 25, 2011)

The Bloody Talon said:


> hahahaha!
> bwahahaha!
> 
> cool cupboards!
> ...


 you said that because a robot can solve a cube, it must be mathematical
by your logic there
if a robot can open a cupboard, cupboards are mathematical


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## insane569 (Oct 25, 2011)

the cube is mathematical if you think about its design and pieces and all the posibillities
when you solve you go from permutation # whatever and you get closer to the final solved state 
if you use CFOP then eventually you get to the last 21(22 if you count it solved) permutations which can be found mathematically since there is only 21 last layer permutations if you keep orientation
there is only 57(58 if you count it solved)OLLs for the last layer. no more and no less. these can also be found mathematically since you cant get a parity.
on bigger cubes you can get parities which have a mathematical reason they exist 
but if you think about just solving i wouldnt consider solving mathematical but there is a bit of thought process.
just my mind.


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## The Bloody Talon (Oct 26, 2011)

tozies24 said:


> Your argument is so ridiculous The Bloody Talon. There are so many different things that I could say about how your argument is lacking but I think that the other people on this thread have already taken care of that. But I will say that your trial and error statement is not mathematical at all.
> 
> Trial and Error is not strictly mathematical and I would not consider it to be a good base argument for why cubing is or isn't mathematical. Of course, there are situations in mathematics that have required trial and trying to figure out what to do with a certain expression. But trial and error is part of everyone's daily life; something as simple as choosing the correct path to take when driving somewhere, or considering what words and sentences to put into a essay.
> 
> ...



Your argument is so ridiculous Tozies24. 
I never said trial and error is strictly mathematical. 
But trial and error is important in gathering data. In my previous examples, I collect data by trial and errors. I modify some moves to come up with another new data (the product form the data which i get from trial and errors). 

tell me if this is math:
using a raw data to come up with a new product by modifying it is already a math. 

Have a nice day to you too. 
peace.



xabu1 said:


> you said that because a robot can solve a cube, it must be mathematical
> by your logic there
> if a robot can open a cupboard, cupboards are mathematical



:fp
what data do you need to input to a robot to open a cupboard?
what data do you need to input to a robot to solve a rubik's cube?
is it logical to compare these two?

anyway, my example in robot is not an issue here anymore.


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## Edward (Oct 26, 2011)

Cubing isn't math
We put math into cubing though 

Is checkers mathematical? What about Go? Chess? 
(hopefully those were proper examples. I don't really play checkers or chess often)


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## insane569 (Oct 26, 2011)

Edward said:


> Cubing isn't math
> We put math into cubing though
> 
> Is checkers mathematical? What about Go? Chess?
> (hopefully those were proper examples. I don't really play checkers or chess often)


chess is somewhat mathematical
you gotta predict the oponents next move and every single way to counter it and every move he will make to counter that one along with the chances that he will make that move
you gotta think about the chances that he makes this move or that move and in chess there is alot of moves possible and counter moves


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## Escher (Oct 26, 2011)

Edward said:


> Cubing isn't math
> We put math into cubing though
> 
> Is checkers mathematical? What about Go? Chess?
> (hopefully those were proper examples. I don't really play checkers or chess often)


 
Game theory.

So is cubing a game?


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## xabu1 (Oct 26, 2011)

The Bloody Talon said:


> what data do you need to input to a robot to open a cupboard?
> what data do you need to input to a robot to solve a rubik's cube?
> is it logical to compare these two?


 
for a rubik's cube to be solved by a robot, it needs to find locations of colours, then it just applies algorithms that are coded in
for a cupboard to be opened by a robot, it needs to find locations of a handle, then it just applies stuff that is coded in

hmm... I think they are similar


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## The Bloody Talon (Oct 26, 2011)

xabu1 said:


> for a rubik's cube to be solved by a robot, it needs to find locations of colours, then it just applies algorithms that are coded in
> for a cupboard to be opened by a robot, it needs to find locations of a handle, then it just applies stuff that is coded in
> 
> hmm... I think they are similar


 
so now, it is not simply opening a cupboard. but finding the handle of the cupboard and opening it?
do you have an idea with programming?

and why are you still making this an issue, all of us (except you) are convinced that a robot can solve a rubik's cube because of mathematics.
*this is not an issue here anymore.*

peace.


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## AvGalen (Oct 26, 2011)

have a solved cube... 
take out an edge..... 
close your eyes...... 
rotate the edge until you have no idea about it's orientation anymore..... 
put the edge back in the cube...... 
scramble the cube...... 
open your eyes......
determine if the cube is solvable without doing any turns
^^MATH

J-Perm = L' U R U' L U2 R' U R U2 R'
^^"no math"
J-Perm = Niklas + Sune = L' U R U' L *U R' + R U* R' U R U2 R' = L' U R U' L *U R' R U* R' U R U2 R' = L' U R U' L *U2* R' U R U2 R'
^^MATH

A girl at worlds solved the cube while she was only 4 years old and had never even heard about math
A girl in India (Chennai) solved a cube blindfolded while she was only 7 years old and had never even heard about math (she actually solved all 3 of her attempts)
They solved with a system that has a lot of mathematical background, but didn't need that math to actually solve it


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## The Bloody Talon (Oct 26, 2011)

AvGalen said:


> have a solved cube...
> take out an edge.....
> close your eyes......
> rotate the edge until you have no idea about it's orientation anymore.....
> ...


 
very nice explanation
this is what I am trying to say.
and I can't explain it very well because I'm not good with english.



tozies24 said:


> Your argument is so ridiculous The Bloody Talon. There are so many different things that I could say about how your argument is lacking but I think that the other people on this thread have already taken care of that.


Hahaha


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## ZincK_NOVA (Oct 30, 2011)

AvGalen said:


> have a solved cube...
> take out an edge.....
> close your eyes......
> rotate the edge until you have no idea about it's orientation anymore.....
> ...


um, math in the sense that one can tell the difference between odd and even numbers; I was under the impression that this discussion was more inclined to discussing how mathematics can be applied to a puzzle in order to reduce it's state to a specific single permutation, rather than "can you count?".
If we decide that because we're simply counting edge orientation, the cube involves maths, then surely every solver uses maths when describing the puzzle? (IE: 3x3x3).
I'm not arguing that this is why cubing _involves_ maths, rather that this approach seems to misinterpet by what is meant when people suggest that you need mathematics to solve the puzzle.


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## YrMyKnight (Nov 22, 2011)

*Does cubing have anything to do with Maths and Science?*

I was playing with my friends cube in class when maybe I impress my friends a little so the teacher came and ask me what was I doing.

I had no choice but to show here the cube which was scrambled that time. She said I couldnt solve it and even if i could it would be to slow.
I was kind of mad so i solve it for her and her jaws drop!

She didnt believe it at first but after a few solves she said I was a genius!
LMAO!

She asked me what I got for my maths which was A
And science which was B+
She asked me to keep up my good word and kept on praising me to other teachers :O
I became famous in my school :fp


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## Andreaillest (Nov 22, 2011)

Nope.


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## LeighzerCuber (Nov 22, 2011)

I would say it is mathematical to an extent due to the fact that in the back of your head you are keeping track of how many more edges you need to pair, f2l slots to fill, pieces to orient etc. However, when solving a particular puzzle you don't go," hmmmm, so if this piece is here 4-3=1 so I do these moves aaaand solved." which is what non-cubers are probably thinking (because they don't have a single clue) that you are thinking when you solve it. ( but not with that 1st grade math though obviously. ) 
So techinically both sides are a little right, but I think for the most part that you aren't doing "true" math during a solve.


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