Help with mathematics of Cubing?

[Reex]

Ah alright here it goes,

I’m currently still attending high school in Australia and would love to relate cubing somewhat in a current mathematics assignment.

My school is weird and I have to relate this mathematics assignment to a "Fertile question" of, “Life - Harmonious? - Predictable? - What’s Possible?"

I know there is heaps of mathematics involved but some extra help would be appreciated..

I was thinking of just relating my whole assignment to Rubik’s cubes and the fact that if you swap around some stickers, or try and get ahead strategically by cheating, you will never be able to complete it.

Any ideas?

 

[Jason]

I thought it would be more on the topic of fractal structures in nature, emergence phenomena, and models and predictions with regard to chaos theory

 

[LNZ]

I will try to answer this question but I won't be very good at it.

It is possible to solve a 3x3x3 or any other cube by pure luck by randomly turning sides. But when we work out methods to do it a bit better and with high certainty of actually solving it, skill replaces luck and the impossible turns to a simple set of algorithms.

And I did take apart and resticker the 3x3x3 cube alot when trying to solve the last layer back in 1981.

 

[daniel0731ex]

group theory, group theory, group theory.....

although i have no idea of what that is

 

[MW1990]

I would say look into fractals and stochastic processes, those are fun Do some harmonic analysis or complex analysis But... for rubiks cube related mathematics, the number of combinations and permutations or group theory seem to be the most popular.

 

[qqwref]

I think you should prove that P does not equal NP, and then show that solving the NxNxN Rubik's Cube can be done in polynomial time even though the number of positions increases exponentially.

 

[Reex]

Thanks for your help and ideas.

 

[AndyRoo789]

Don't know if this has to do with maths, but you need a bit of logic to solve the Rubik's Cube.

You need to know the centers don't change in position to each other, you need to understand that its made up of pieces that go in particular places - not just stickers that have to match and etc etc.

You're from Australia? What part?

 

[Reex]

I'm from South Australia, and i've just pretty much finished the assignment I was working on.

wonder if anyone would be interested in having a look at it?

 

[LewisJ]

I think you should prove that P does not equal NP, and then show that solving the NxNxN Rubik's Cube can be done in polynomial time even though the number of positions increases exponentially.

This would be amusing. Although I'm not sure that number of possible positions would be a good measure of the computational complexity of some NxNxN cube....