# My Rubik's Cube Science Fair Project



## AlGoreRhythm (Jan 19, 2015)

Hello everybody! I have been competing in science fairs for my entire educational career, even when optional. I am in 7th grade, and have come in first at school and gone on to the County Science Fair 4 years in a row. Last year I was one place away from making it to theState Science Fair. Anyway, this year's science fair project is called "Rubik's Revenge" named for the the original 4x4. It is testing weather the number of combinations to any nxnxn rubik's cube type twisty puzzle significantly increases difficulty. I compared concepts to algorithms to permutations, even did a poll here on speedsolving a couple months back. My conclusion was that after 4x4, where most necessary cubing concepts are learned (for the rest of the nxnxn puzzle series) nxnxn puzzles do not get much more difficult to learn. I used Chris Hardwick's Formula to find the number of permutations, and my data was more or less accurate. 

The School Science Fair is in 2 days, and I really want to make a good impression on the judges so I can go on to County, then maybe State this year. *However, I am a bit stumped as to how I will explain the wold of cubing to a non-cubing science fair judge in 10 minutes or less.* Should I explain the reduction method? Or just say that I have a passion for puzzles, and that as I learned them, I realized it wasn't getting harder as each puzzle got larger.

If anybody on here has any advice, I would be open to it. Thanks!


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## AlGoreRhythm (Jan 21, 2015)

My Question was, "*Does the number of permutations of any NxNxN Rubik's Cube Type Twisty Puzzle Significantly increase difficulty to learn?"*, where I measured difficulty by new algorithms and concepts learned as on travels up the ladder of NxNxN Twisty Puzzles, then compared it to permutations. My results told me that as these puzzles get larger, they do not get significantly harder to learn. Basically, about half of the necessary NxNxN algorithms necessary for 5x5+ are learned in 4x4,* making the transition between 3x3 and 4x4 most difficult.*

I would like to see if others would agree with this statement, as it was the Hypothsized and Final Result to my Science Fair Project. I would hate to be representing Rubik's Cubes with results that the rest of you disagree with. Thanks!


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## Christopher Mowla (Jan 21, 2015)

AlGoreRhythm said:


> *making the transition between 3x3 and 4x4 most difficult.*


That is correct.

I just don't quite understand the significance (or depth) of this topic that you would consider making it your science fair project.

The number of permutations of the nxnxn cube increases exactly by the rate of:





(where \( f\left( n \right) \) is the number of permutations formula) for any given cube size \( n \), but this has _nothing_ to do with the number of required algorithms to iteratively solve the nxnxn cube.

Assuming that the reduction method is used to solve the 4x4x4, only one additional algorithm is required to solve the nxnxn: an 8 move center commutator. Only beginners might argue that more than a center commutator is required to solve the nxnxn. In fact, I'm sure there are some on this forum who could debate that even a center commutator is not necessary to learn to solve the last two centers of the nxnxn.

Your project is analogous to someone asking "Does the size of a positive integer _n_ affect how many different positive integers you *need* to add together to get that integer"? Clearly the answer is NO, because we can just simply choose to sum _n_ 1's to get any integer_ n_. If this is not clear to anyone, then you would simply need to explain how to add two numbers (and define the term "integer"), but you wouldn't have to explain this result itself, as it follows. Similarly, if the result of answering your science fair question is unclear to anyone, it's simply because they don't know how to solve the cube. Therefore, once you explain how the nxnxn cube is solved with reduction (which I can only assume is your entire presentation), this result naturally follows.

That is, I call a result which only requires prerequisite information to be made clear as trivial/not significant. No research, experimentation or investigation (science) is required.

As far as you doing a presentation in 10 minutes, I believe everything that needs to be said can be said in four or fewer minutes, given that you have prepared a speech ahead of time and you are organized.

A better topic would have been to answer a question like: "Does an increase in the number of permutations decrease the rate (pieces per minute) humans solve the nxnxn in?". Clearly the answer is yes (because it's simply harder to recognize pieces when there are more of them), but there are several ways to set up an interesting experiment and/or gather data from the WCA records to test this hypothesis.

Lastly, I recall several people making threads like this, but in all of the threads I remember, at least, the members who started them started them 5 or more days ahead of time, not a single day. The forums are unpredictable in terms of which day will have more activity, and thus it's risky to want a topic to be seen in this sub-forum, especially, just in one day's time.


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## AlGoreRhythm (Jan 21, 2015)

> Originally Posted by *Cmowla*
> I just don't quite understand the significance (or depth) of this topic that you would consider making it your science fair project.



Well I am in in middle school. I thought it would be interesting to do a science fair project on cubes, and it was. I like seeing numbers back up a statement I made, and I can see that you do, too. I think telling a non-cuber that an 11x11 is not much harder than a 4x4 or 5x5 would blow their mind, and that's kinda the best part of the science fair, too. A couple years ago, some kid made that Marshmallow Air Cannon that made it to the white house. People have been doing that for years, but that didn't take away from the awesomeness. Marshmallow Cannons don't really contribute to the scientific community that much, yet some kid won the National Science Fair with one. I had fun doing this project, and I wouldn't change it now if I could.




> Originally Posted by *Cmowla*
> That is, I call a result which only requires prerequisite information to be made clear as trivial/not significant. No research, experimentation or investigation (science) is required.
> As far as you doing a presentation in 10 minutes, I believe everything that needs to be said can be said in four or fewer minutes, given that you have prepared a speech ahead of time and you are organized.



Technically, since some of the kids in my class are doing the old "Ball rolling down a grassy hill" and "Teeth dissolving in soda" experiments, and they already knew what the results would be. They could just google it of they really want to know, without putting that much time and effort into it. But they do it anyway, *to show that they are capable of using the Scientific Method.* That's a useful tool for High School or College, or life, if you want to become a scientist. 'As far as me doing a ten minute presentation', I was factoring in questions. And kinda exxagerating. 

Anyway, thanks for replying! I honestly didn't expect anyone to respond, and your input was enlightening. I really just kinda wanted to get the whole thing out here, and I am glad that you agree with the result, however non-trivial it may seem to you. I will make sure that I tell the judges how obvious it is. By the way, this-- 



> Originally Posted By *Cmowla*
> 
> 
> > Originally Posted by *AlGoreRhythm*
> ...



--was awesome to see, coming from you. Again, thank you for your input, and I am glad to have cleared up any misconceptions you may have had about the Middle School Science Fair.


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