Underrated mathematical properties of twisty puzzles?

[Anti-Sune]

I’m creating short educational videos about the mathematics of twisty puzzles — some tutorials, but mostly theory and structure.
This could include:
Impossible states and parity
Probability distributions of cases
Move-count limits
Structural/group properties
Mechanical or reaction-time limits
What mathematical concept about any WCA puzzle do you think deserves more attention or clearer explanation?

 

[Caleb Valenzuela]

I’m creating short educational videos about the mathematics of twisty puzzles — some tutorials, but mostly theory and structure.
This could include:
Impossible states and parity
Probability distributions of cases
Move-count limits
Structural/group properties
Mechanical or reaction-time limits
What mathematical concept about any WCA puzzle do you think deserves more attention or clearer explanation?

the mathematical concept of how algs are genned

 

[qwr]

I've taken only an introductory group theory course. So showing how the group structure of the Rubik's group, center, conjugates, etc would be very interesting.

 

[abunickabhi]

I feel the underrated concept is nested commutators

 

[cmhardw]

Like qwr I also think the center of the cube group is fascinating.

The following are also interesting:

• The number of unsolved positions on a 3x3x3 is a prime number
• The number of unsolved positions on an 8x8x8 is a prime number
• The number of unsolved positions on an 11x11x11 is a prime number
• The 4x4x4 supercube is the only larger supercube (4+ layers) where you can swap two wings in the same wing piece orbit and have no affect on the permutation parity of any center piece orbit. I’ve always found that fact fascinating.
• All even permutation parity positions can be solved using one commutator sequence
• Although there are six sides, the cube group is actually a five generator puzzle (see my signature)

 

[acrystal]

Maybe how many permutations the WCA puzzles could have

 

[Yann1qua12DagOat]

I’m creating short educational videos about the mathematics of twisty puzzles — some tutorials, but mostly theory and structure.
This could include:
Impossible states and parity
Probability distributions of cases
Move-count limits
Structural/group properties
Mechanical or reaction-time limits
What mathematical concept about any WCA puzzle do you think deserves more attention or clearer explanation?

The link to your YouTube is broken. Could you enter your channel so that we can watch these videos? I'm super interested to watch these kinds of video formats.

 

[Martyt7777]

The link to your YouTube is broken. Could you enter your channel so that we can watch these videos? I'm super interested to watch these kinds of video formats.

AntiSune

thought it was cubing. ended up engineering things instead...

www.youtube.com

Also, your supposed to put your channel handle (like @Anti-Sune) in, not an entire link

Edit: I didn’t mean to tag you but that’s what you’re supposed to put in

 

[Yann1qua12DagOat]

@Martyt7777 are you his 1 subscriber

 

[Martyt7777]

@Martyt7777 are you his 1 subscriber

no