Thursday, February 4, 2021

Rubik's Facts

I am always fiddling with the Rubik’s Cube (I’m talking about the standard 3x3 cube) since I sort of rediscovered it about two years ago.  I used to solve it in my math class in 9th grade, keeping it below desk level and racing an Asian guy in front of me who was very adept at solving his quickly.  

We were always competing with each other to solve them, and somehow, not once did we ever get caught by the teacher since, clearly, we weren’t paying attention to the classroom math.  But I suppose that we were teaching ourselves about permutations and combinations in some peripheral way.  Back then, there were no speed cubes, so in order to make them feel fluid and fast, we would disassemble the cube, rub Vaseline on the insides of the cube, and then reassemble them.  This would allow for the cube to be moved much more efficiently without having the cube get caught on its insides.

Now of course, along with all other technologies, there are Rubik’s Cubes available that are called speed cubes.  These are not the stiff Rubik’s cubes that you can get at Walmart for a few bucks, but are ordered generally online via Amazon and such and are designed with interior mechanics that are completely smooth in their movement.  They are amazing.  I can usually solve my Rubik’s Cube in about a minute and a half.  I'm always playing with it while watching TV or waiting to pick up a food order at a restaurant.  It keeps my hands busy. 

There are a couple of fascinating things about the Rubik’s Cube that are math oriented.  One fact is that from any position that the cube might be in, it takes nineteen moves or fewer to solve it.  Now, normally, only a computer could do it, since humans use a series of algorithms to solve it, which take more than nineteen moves.  But I find that very interesting in combination with the next, really astounding fact.  

The other truth about Rubik’s Cubes is that there are a total of 43 quintillion possible arrangements of the cube.  That’s 43,252,003,274,489,856,000 to be exact. To give you an idea of how large a number that is, this means that you would have to cover the entire earth with Rubik’s Cubes, stacking them 275 high to get to that number.  Or, if you stacked them on on top of each other in a single pile, then they would reach up 261 light years high.  Yes, I said “light years.”  Just let that sink in for a few moments.

And, just in case you were wondering, as of this writing, the fastest official single solve for a Rubik’s Cube was done by Yusheng Du of China in 3.47 seconds in 2018.  I’m still not sure how these competitors solve them in just a few seconds.  There must be short cuts on top of short cuts that I am just not yet aware of.  But maybe I’ll get there someday.  

It’s crazy that in that little puzzle in my hand is a possible set of combinations that is so vast.