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Re: [OT] Re: Rubik Cube

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  Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-06 23:04 +0800
    Re: [OT] Re: Rubik Cube "K Wills (Shill #3)" <compuelf@gmail.com> - 2016-12-07 03:47 -0600
      Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-07 20:32 +0800
        Re: [OT] Re: Rubik Cube "K Wills (Shill #3)" <compuelf@gmail.com> - 2016-12-07 18:24 -0600
          Re: [OT] Re: Rubik Cube Kaz Kylheku <221-501-9011@kylheku.com> - 2016-12-08 01:36 +0000
            Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 10:36 +0800
              Re: [OT] Re: Rubik Cube Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-08 02:56 +0000
                Re: [OT] Posting algorithm "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 12:31 +0800
            Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 10:37 +0800
      Re: [OT] Re: Rubik Cube marston shores <kp@of.fire> - 2016-12-07 09:47 -0700
    Re: [OT] Re: Rubik Cube fir <profesor.fir@gmail.com> - 2016-12-07 07:01 -0800
      Re: [OT] A: Rubik Cube equation? "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 10:45 +0800
    Re: [OT] Re: Rubik Cube David Brown <david.brown@hesbynett.no> - 2016-12-08 10:58 +0100
      Re: [OT] Re: Understanding mathematics through learning "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 21:30 +0800

#7075 — Re: [OT] Re: Rubik Cube

On 6/12/2016 10:24 PM, edrhodes@hotmail.com wrote:
>>>
>>> Rubik Cube <https://s16.postimg.org/5r2hg8z4l/Rubik_Cube.png>
>>> Rubik Cube <http://i.imgur.com/aLzn76G.png>
>>
>> Only evils and daemons know how to play with and solve it? :)
>
> Got stumped, huh?
>

Is there really continuous mathematics in solving Rubik Cube? Matrix?

But is matrix mathematics at all? Or just some sine-cosine-tangent 
tables that needs to be memorized?

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#7076

On Tue, 6 Dec 2016 23:04:57 +0800, "Mr. Man-wai Chang"
<toylet.toylet@gmail.com> wrote:

>On 6/12/2016 10:24 PM, edrhodes@hotmail.com wrote:
>>>>
>>>> Rubik Cube <https://s16.postimg.org/5r2hg8z4l/Rubik_Cube.png>
>>>> Rubik Cube <http://i.imgur.com/aLzn76G.png>
>>>
>>> Only evils and daemons know how to play with and solve it? :)
>>
>> Got stumped, huh?
>>
>
>Is there really continuous mathematics in solving Rubik Cube? Matrix?
>

     Math can be used. And it would likely make it even easier than
the way I do it.

>But is matrix mathematics at all? Or just some sine-cosine-tangent 
>tables that needs to be memorized?

     Try it and find out.
     The way I always did it was to keep randomly moving sides until I
saw a pattern. Then I would solve for the pattern. I would never have
won a speed contest, but I was always able to solve one.

-- 
Shill #3. 
Strategic Writer, Psychotronic World Dominator and FEMA camp
counselor.
https://c2.staticflickr.com/4/3618/5747904676_1e202191d3_b.jpg
All hail the taco! http://www.taconati.org/

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#7077

On 7/12/2016 5:47 PM, K Wills (Shill #3) wrote:
>      Math can be used. And it would likely make it even easier than
> the way I do it.
 > > ....
>      Try it and find out.
>      The way I always did it was to keep randomly moving sides until I
> saw a pattern. Then I would solve for the pattern. I would never have
> won a speed contest, but I was always able to solve one.

I do NOT have a good mathematics brain. My maths. skill is limited to 
Form 5 in Hong Kong (pre-1997 HKCEE).  :)

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#7082

On Wed, 7 Dec 2016 20:32:05 +0800, "Mr. Man-wai Chang"
<toylet.toylet@gmail.com> wrote:

>On 7/12/2016 5:47 PM, K Wills (Shill #3) wrote:
>>      Math can be used. And it would likely make it even easier than
>> the way I do it.
> > > ....
>>      Try it and find out.
>>      The way I always did it was to keep randomly moving sides until I
>> saw a pattern. Then I would solve for the pattern. I would never have
>> won a speed contest, but I was always able to solve one.
>
>I do NOT have a good mathematics brain. My maths. skill is limited to 
>Form 5 in Hong Kong (pre-1997 HKCEE).  :)

     I am better than average in math, but there are MANY who can, and
do, surpass me. This is why I would look for a pattern in the cube and
use it to solve it.

-- 
Shill #3. 
Strategic Writer, Psychotronic World Dominator and FEMA camp
counselor.
https://c2.staticflickr.com/4/3618/5747904676_1e202191d3_b.jpg
All hail the taco! http://www.taconati.org/

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#7083

On 2016-12-08, K Wills (Shill #3) <compuelf@gmail.com> wrote:
> On Wed, 7 Dec 2016 20:32:05 +0800, "Mr. Man-wai Chang"
><toylet.toylet@gmail.com> wrote:
>
>>On 7/12/2016 5:47 PM, K Wills (Shill #3) wrote:
>>>      Math can be used. And it would likely make it even easier than
>>> the way I do it.
>> > > ....
>>>      Try it and find out.
>>>      The way I always did it was to keep randomly moving sides until I
>>> saw a pattern. Then I would solve for the pattern. I would never have
>>> won a speed contest, but I was always able to solve one.
>>
>>I do NOT have a good mathematics brain. My maths. skill is limited to 
>>Form 5 in Hong Kong (pre-1997 HKCEE).  :)
>
>      I am better than average in math, but there are MANY who can, and
> do, surpass me. This is why I would look for a pattern in the cube and
> use it to solve it.

It is easy to solve the cube in a mechanical way, "layer by layer",
according to a memorized algorithm that has to deal with a relatively
small number of cases; not overwhelming the average intellect in any
way.

Under this approach, it can be tedious to begin completely from the
beginning, assembling a face. It is smarter to look for the most
complete face, and possibly work the cube randomly to obtain a better
one by chance.

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#7084

Could one use a single, unified mathematics equation to describe this 
algorithm?

On 8/12/2016 9:36 AM, Kaz Kylheku wrote:
> It is easy to solve the cube in a mechanical way, "layer by layer",
> according to a memorized algorithm that has to deal with a relatively
> small number of cases; not overwhelming the average intellect in any
> way.
>
> Under this approach, it can be tedious to begin completely from the
> beginning, assembling a face. It is smarter to look for the most
> complete face, and possibly work the cube randomly to obtain a better
> one by chance.
>

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#7087

"Mr. Man-wai Chang" <toylet.toylet@gmail.com> writes:

> Could one use a single, unified mathematics equation to describe this
> algorithm?

Yes.  There is a theorem in computability theory (the MRDP theorem) that
equates Turing machines and Diophantine equations.  But this is a formal
equivalence between computing something and solving a specific kind of
equation and may not be what you were asking about.

<snip>
(BTW, interleaved and bottom posting is usually preferred to top posting.)

-- 
Ben.

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#7088 — Re: [OT] Posting algorithm

On 8/12/2016 10:56 AM, Ben Bacarisse wrote:
> <snip>
> (BTW, interleaved and bottom posting is usually preferred to top posting.)

I knew and know. But sometimes I need to jump/GOTO to conclusion, aka, 
cut the crap.

It saves everyone's time! :)

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#7085

Could one use a single, unified mathematics equation to describe this 
algorithm?

On 8/12/2016 9:36 AM, Kaz Kylheku wrote:
> It is easy to solve the cube in a mechanical way, "layer by layer",
> according to a memorized algorithm that has to deal with a relatively
> small number of cases; not overwhelming the average intellect in any
> way.
>
> Under this approach, it can be tedious to begin completely from the
> beginning, assembling a face. It is smarter to look for the most
> complete face, and possibly work the cube randomly to obtain a better
> one by chance.
>

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#7079

On 12/7/2016 2:47 AM, K Wills (Shill #3) wrote:
> Try it and find out.
http://caselaw.findlaw.com/ia-supreme-court/1360099.html

Weiben's garage is haunting you, Kent!
Sean Bilyeu's parents think really very highly of you too.

Will those things distract you from the screen
capture of your Mom's facebook wall where
Tiffany and you chit-chatted, Kent?

http://2.bp.blogspot.com/-rfAl19rbEbk/TiImA61TYoI/AAAAAAAAAAk/2TCqaQv0ED0/s640/ma.jpg 

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#7078

W dniu wtorek, 6 grudnia 2016 16:05:00 UTC+1 użytkownik Mr. Man-wai Chang napisał:
> On 6/12/2016 10:24 PM, edrhodes@hotmail.com wrote:
> >>>
> >>> Rubik Cube <https://s16.postimg.org/5r2hg8z4l/Rubik_Cube.png>
> >>> Rubik Cube <http://i.imgur.com/aLzn76G.png>
> >>
> >> Only evils and daemons know how to play with and solve it? :)
> >
> > Got stumped, huh?
> >
> 
> Is there really continuous mathematics in solving Rubik Cube? Matrix?
> 
> But is matrix mathematics at all? Or just some sine-cosine-tangent 
> tables that needs to be memorized?

the question is quite good (unlike your typical questions) if i would have a moment of spare time i will look up in google and may answer to this (recently i was thinking on it but forgot to look up)

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#7086 — Re: [OT] A: Rubik Cube equation?

On 7/12/2016 11:01 PM, fir wrote:
>
> the question is quite good (unlike your typical questions)...

You should not ALWAYS expect some strangers in the streets to always ask 
good questions. Not even judges, lawyers, police officers and presidents 
could do that. It would demand a absolutely fast, sharp, smart, 
intelligent, clever, ... brain to do it.

Could there be such a mortal? :)

 > ...if i would have a moment of spare time i will look up
 > in google and may answer to this (recently i was thinking
 > on it but forgot to look up)

*I would bet* that the algorithm and solution is very much like a 
computer program rather than just a simple sometimes naive mathematics 
equation!

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#7089

On 06/12/16 16:04, Mr. Man-wai Chang wrote:
> On 6/12/2016 10:24 PM, edrhodes@hotmail.com wrote:
>>>>
>>>> Rubik Cube <https://s16.postimg.org/5r2hg8z4l/Rubik_Cube.png>
>>>> Rubik Cube <http://i.imgur.com/aLzn76G.png>
>>>
>>> Only evils and daemons know how to play with and solve it? :)
>>
>> Got stumped, huh?
>>
> 
> Is there really continuous mathematics in solving Rubik Cube?

In mathematics, "continuous" has a particular meaning - it means there
are no individual steps (or the steps can be made as small as you like).
 If you balance a Rubik's Cube on the end of your finger and spin it,
the movement is continuous.  But if you move the layers on the cube, the
movement is discrete.  You can turn a face once, twice, three times,
etc., but not half a turn (at least not if you want to get very far).

Thus the mathematics of the Rubik's Cube is discrete, not continuous.

> Matrix?

A matrix is a way of organising numbers or other mathematical entities
in a two-dimensional array.  I can't think off-hand how they would be
particularly useful in describing the maths of a Rubik's Cube.

> 
> But is matrix mathematics at all? 

Yes, matrices are extremely useful in many fields of mathematics.

> Or just some sine-cosine-tangent
> tables that needs to be memorized?

No, trigonometry is not useful for Rubik's Cubes (except when drawing 3D
images of them).


The key mathematics of Rubik's Cubes is group theory.  The positions on
the cube form a rather large and complicated group with a lot of
interesting cyclic patterns.  For mathematicians who like algebra and
group theory, it is a lovely real-world example of such groups.

But for most people, the group theory has no relevance to /solving/ the
cube.  It is only "mathematical" in that people usually solve it using
logical methods and a clear structured algorithm.  Typically this is
done by memorizing sequences with specific effects (like swapping two
cubes while leaving the others unchanged), and applying these sequences
in an appropriate order.

If you are interested in the maths, you can take a solved cube and pick
a short sequence of moves.  Repeat this sequence, and count how many
repetitions are needed to return the cube to solved.  It will /always/
get back to the starting point, no matter what sequence you use.  It can
be interesting to look at the prime factors of the sequence length, and
see how the same factors turn up regularly - they will all be factors of
the number of positions in the cube (43,252,003,274,489,856,000).

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#7090 — Re: [OT] Re: Understanding mathematics through learning

On 8/12/2016 5:58 PM, David Brown wrote:
> If you are interested in the maths, you can take a solved cube and pick
> a short sequence of moves.  Repeat this sequence, and count how many
> repetitions are needed to return the cube to solved.  It will /always/
> get back to the starting point, no matter what sequence you use.  It can
> be interesting to look at the prime factors of the sequence length, and
> see how the same factors turn up regularly - they will all be factors of
> the number of positions in the cube (43,252,003,274,489,856,000).

Some mathematics require a special brain if not DNA to understand. Some 
even requires you to force yourself to memorize certain equations and 
transformations.

It's my bet or guess. I don't have evidence nor proof.

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