# Need Help Deciding a Research Project

#### Sion

##### Member
Hello Speedsolving forums.

I am currently in an undecided situation. What happened is that I was accepted into a STEM research program, and I want to do something regarding the rubik's cube. However, I'm largely undecided on what I want to research, and I need some suggestions.

I want to do something that is possible, researchable (I can find some research on already), and something that could be potentially helpful to the speedsolving community. I would greatly appreciate any help and suggestion.

Thanks,

Sion

magnetic clock

#### Sion

##### Member
magnetic clock

I mean mathematically, though I may do side research on making a clock for the sake of design.

U

#### Underwatercuber

##### Guest
I mean mathematically, though I may do side research on making a clock for the sake of design.
Research why Moyu sucks at understanding how clocks work lol

#### WombatWarrior17

##### Member
How many combinations and permutations there are in a 33x33 would be interesting.
The probability of solving a cube by only using random moves is also interesting.
You could also try to predict how much faster WRs can get, and if we have almost reached the limits.

#### TipsterTrickster

##### Member
The gods number for other cubes like super cube, 4x4+ etc...

#### cuber314159

##### Member
How many combinations and permutations there are in a 33x33 would be interesting.
The probability of solving a cube by only using random moves is also interesting.
You could also try to predict how much faster WRs can get, and if we have almost reached the limits.
I already have that in the 33x33x33 thread and the chances of turning a 3x3x3 and randomly solving it are almost non existent, a non Cuber probably wouldn't turn all the layers before giving up on a 33x33x33.

Please just get on with your cube (or a 4x4x4 that's better than the wuque would be very nice?)

##### Member
Hm. Off the top of my head:

Cube solving program employing some sort of heuristic to speed up the solve.
Group theory and how it applies to the cube and parity etc
Prediction of future world records based on differential equations/models of growth
Hardware of cubes and a study into materials used/ progression of designs
Creating a new cube by slowly and smoothly transforming existing cubes (similar to aerodynamics modelling)
Chemistry of cube plastics, lube, spring coefficients etc
Alg explorer type thing like what @Teoidus experimented with for a while
Learning algorithm to solve the cube
Altered states of consciousness for cube solvers when solving (like putting one into an MR machine or something lol)
Progression in speed as a function of time spent practising/number of solves (needs a group of people willing to learn and report back though)

Well, run out of things to say for now will edit if I think of anything more. Hope this helps!

E: Oh there was a thread a while back about how cubing relates to some types of particles but that went over my head at the time though it seemed really cool. You could also try decomposing algorithms into comms and conjugates (which sort of relates to group theory too).

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#### Oatch

##### Member
The question is, what sort of results are expected of you to produce by the end of your research? That factor alone may already eliminate some of the more ambitious ideas due to time/resources constraint. If you're cluely with programming, then as @shadowslice e mentioned, writing up an alg generator could be pretty nice and would be really useful in terms of direct applications to speedcubing.

I'm also a big fan of group theory (my current research is on classifications of groups and symmetries + I'm a maths buff despite my degree not actually being in maths!) and while it is a little more abstract, is still quite useful in developing interesting methods. For instance, the ZZ method is based on the concept of initially reducing the cube to a subgroup generated by <L, R, U, D, F2, B2> which allows for 3-gen F2L. Thistlewaite and Kociemba methods relies on even further reduction to more restricted subgroups to reduce case number. Something you may be interested in exploring is reduction to a cube state generated by <R, U> (i.e. a 2-generator) by virtue of corner permutation, something long sought after and still currently being developed to this day.

Although of course, if you just want to go more practical and hands-on, hardware seems to be a popular demand.

#### xyzzy

##### Member
How many combinations and permutations there are in a 33x33 would be interesting.
The probability of solving a cube by only using random moves is also interesting.
Both solved problems; the first one is just a matter of multiplying a bunch of factorials and powers of 2 and 3 together, and the second one is a standard exercise in Markov chains (the answer is 1 if you can use as many random moves as you want). (That said, it becomes an interesting question if you look at how many random moves are needed on average. Obviously this number is going to be large, but I don't think anyone's looked into exactly how large this number is. My intuition says that it should be within two orders of magnitude of the number of possible scrambles.)

For instance, the ZZ method is based on the concept of initially reducing the cube to a subgroup generated by <L, R, U, D, F2, B2> which allows for 3-gen F2L. Thistlewaite and Kociemba methods relies on even further reduction to more restricted subgroups to reduce case number.
Also worth mentioning that reduction to subgroups also forms the framework of some other speedsolving methods (e.g. Roux) and has been the main approach for bounding God's number not just on 3×3×3, but on big cubes as well (e.g. this or this).

Oh there was a thread a while back about how cubing relates to some types of particles but that went over my head at the time though it seemed really cool.

#### cuber314159

##### Member
A nice project would actually be to find the smallest number of moves required to solve a 4x4x4.
This hasn't really been done before, but last time Google lent out computing power to the mathematicians, maybe they would allow you to do the same for 4x4x4 now.

#### TipsterTrickster

##### Member
The gods number for other cubes like super cube, 4x4+ etc...
Megaminx would be cool to.