Message #3391

From: Sid Brown <synjanbrown@gmail.com>
Subject: Re: [MC4D] Cube puzzles and math
Date: Sun, 26 Jun 2016 15:56:52 +0100

i mean as a list of moves not a set (a set is unordered and for that to be
correct it must be commutative)
furthermore:
S set of all moves then R = S* (* in this case is the kleene star not the
operation) under the operation +
(changed it to + so not to be confused with kleene star)

kleene star of a set is all possible compositions of elements of the set.
for example if S = {a,b} then S* = {0,a,b,aa,ab,ba,bb,aaa …. to infinity
}

Sid

On 26 June 2016 at 15:48, Sid Brown <synjanbrown@gmail.com> wrote:

> Hi,
>
> It is possible to define a rubik’s cube configuration as a non-commutative

> ring (see https://en.wikipedia.org/wiki/Noncommutative_ring).
> ring R. a,b are elements of the ring R. a,b are possible moves. a*b is the
> move a followed by the move b. => a*b != b*a therefore non-commutative. 0
> is the ID for the operation * and is therefore a solved cube. a fully
> scrambled cube is the product of many moves and may not be in the simplest
> form. a*a*a*a=a^4=0.
> Storing it as a set of moves is an alternative to the type of group Joel
> mentions which is storing the position of each piece and constraining the
> movements. In the construct I describe the constraints are applied in the
> definition of the possible elements of the ring R.
>
> parity is formed as a move earlier in the algorithm has a side effect of
> rotating 2 pieces when performed and later on the move that places these
> pieces can only rotate 3. 3 modulo 2 != 0.
>
> I hope this is easy enough to understand. It is probably worth researching
> group theory to be able to fully understand this.
>
> Regards
> Sid
>
> On 26 June 2016 at 14:22, e.kennedy.a@gmail.com [4D_Cubing] <
> 4D_Cubing@yahoogroups.com> wrote:
>
>>
>>
>> Hello everyone!
>>
>> There has been a question on my mind for some time and after solving the
>> 3x3x3x3 recently I getting to know that this group existed I thought that I
>> could manage to find the answer here.
>>
>> I would like to know what’s the connection between maths and puzzles like
>> the rubik’s cube. What specific areas of mathematics explain how rubik’s
>> cube dinamics work?
>>
>> What do you think?
>>
>>
>> P.S.: I was also wondering why does parity also exist in a 4x4x4 which
>> orientable center pieces like the 4x4x4 axis cube.
>>
>>
>> Thank you and best wishes!
>>
>>
>>
>
>