# 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!

>>

>>

>>

>

>