Help Me with a School Math Project About Rubiks Cubes!

[Pablo17]

Hi everyone! Im in highschool and im going to be taking IB math this year, and we have to do a project at some point. So im planning on doing one about the rubiks cube. Ive already okayed this with my teacher but id like to get some of your ideas. Id like to talk about the degree of an algorithm ( how many times you have to do an alg. to return it to its original state I believe, correct?). I also want to talk about gods number and calculating that. I also want to explain how to calculate the possible permutations of a 3x3x3, a 7x7x7, and a 17x17x17 because its the largest cube that has been made to my knowledge. Now some of this stuff is completely over my head right now, but ive been learning. Any other ideas on what to talk about? And links to sites to help explain this to me in a relatively basic, high school level? If it helps in any way, my pr is 24 seconds for 3x3x3 and 4.84 for a 2x2x2, and I use 4LLL with F2L currently and Ortega, I practice 3x3x3 and 2x2x2 the most so I just posted those. Any help is appreciated, id really like to understand this.

 

[Akiro]

For the number of permutations on a cube :
https://en.wikipedia.org/wiki/Rubik%27s_Cube#Permutations
And apply a similar idea for bigger cubes, adding the other center pieces in the product.

 

[Ollie]

I've always liked this video by Dan Sarnelli. He explains how the total permutations of a 3x3x3 are calculated in a way I could understand and goes on to talk about fewest moves (which might be another topic of discussion.)

Perhaps the ultimate example -the Devil's algorithm aka Hamiltonian circuit.

Don't be a ****** either - cite these people in your work. The mental effort that goes into actually working these things out is incredible, and completely beyond most people.

 

[sneaklyfox]

If it helps in any way, my pr is 24 seconds for 3x3x3 and 4.84 for a 2x2x2, and I use 4LLL with F2L currently and Ortega, I practice 3x3x3 and 2x2x2 the most so I just posted those. Any help is appreciated, id really like to understand this.

lol... knowing how to solve a Rubik's cube and the math behind it are very separate things. It's like non-cubers thinking that cubers are math whizzes.

But anyway, cool idea. I saw a youtube video about similar things. You could check out a few of them by searching "numberphile rubik's cube".

 

[Sa967St]

Are you talking about the 4000-word extended essay for IB? If so, mine was a comparison of different 3x3x3 methods based on case and skip probabilities. If you decide to do something based on math, I strongly suggest you do your own calculations instead of searching around for it.

 

[Pablo17]

I was actually debating if I should do it as a video project for IB Math or if I would do it for the essay. And don't worry, I will definitely sight all my sources!