# Message #3388

From: Joel Karlsson <joelkarlsson97@gmail.com>

Subject: Re: [MC4D] Cube puzzles and math

Date: Sun, 26 Jun 2016 16:41:22 +0200

Hi!

A bit of a quick (and short) answer. I believe that the two areas of

mathematics that are most closely related to Rubik’s Cube and similar

puzzles (aka twisty puzzles) are group theory and combinatorics.

Combinatorics, obviously, for calculating the number of configurations of

the puzzles (although some group theory might be required as well).

Group theory is the branch of mathematics that really describe the dynamics

of twisty puzzles. In general, group theory is a branch of mathematics that

studies groups (which are a kind of abstract algebraic structure). Twisty

puzzles can be seen as a special kind of group, namely a permutation group,

where each sticker is a member of the group. It’s through group theory that

twisty puzzles are analyzed and we can prove what restrictions a twisty

puzzle has by using group theory. Moreover, the concept of commutators and

conjugates comes from group theory so it also helpful when trying to solve

twisty puzzles. If you would like to get an introduction to group theory

and how it can be applied on Rubik’s Cube I highly recommend that you

read *Group

Theory via Rubik’s Cube *by Tom Davis (

http://www.geometer.org/rubik/group.pdf)

Best regards,

Joel

2016-06-26 15:22 GMT+02:00 e.kennedy.a@gmail.com [4D_Cubing] <

4D_Cubing@yahoogroups.com>:

>

>

> 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!

>

>

>