day 43 quintillion, 252 quadrillion, 3 trillion, 274 billion, 489 million, 856 thousand minus 43,252,003,274,489,855,666.
43,252,003,274,489,856,000.
It’s a big number. It’s the number of unique patterns there can be on a normal 3x3 Rubik’s cube. It sounds impossible. But the maths holds true. What’s more, it is beyond improbable that there have been every possible combination done in history. It’s literally impossible.
A Hungarian sculptor and Professor of Architecture, Ernő Rubik invented the cube in 1974. Six years later, it was widely marketed and became, what is considered to be, the world’s best selling toy.
Over that time, the world’s population has nearly doubled from a little over 4 billion people to almost 7.8 billion people today. Even if the population was consistently 7.8 billion for the past 46 years since the cubes inception, every single person would have to make 330,258 turns every day, to completely unique patterns to get through all 43 quintillion permutations . That’s 3.82 turns, per second, per person, without duplication, for 46 years. If a single cube turned once per second from the Big Bang to now, it still wouldn’t be finished. In fact, it’s impossible for it to come even close before our sun becomes a white dwarf.
”That’s great James… we already know you’re a massive nerd! What’s the point of all of this?”
Well… it depends. If I’m honest, there is none. It’s just an example of one of the ways I occupy my brain; a way to stop the self-effacing voices that at times seem to want to destroy any sense of self-worth or esteem. But, traits of pareidolia aside, there’s an interesting twist.
Mathematicians have been seeking a ‘magic’ number - ‘God’s Number’. It’s the minimum number of moves required to return the cube to its solved state from any one of the 43 quintillion possible scrambles. It took a very long time, and a bunch of brilliant mathematicians and computer scientists to devise a program and borrow/hijack the latent computing power at Google to crunch the numbers. In the end, it’s surprisingly low. 20. That’s all. You can spend nearly an eternity scrambling and screwing the cube up, and you’re, at worst, only ever 20 moves away from it being solved.
As ridiculous as it is, there’s something comforting about that. Maybe, regardless of our situation, we’re closer to the solution that we realise, no matter how messed up it may seem.
Kilt of the day - Macleod Tartan
Soundtrack of the day - Unsquare Dance - Dave Brubeck Quartet
https://www.youtube.com/watch?v=lbdEzRfbeH4&ab_channel=DaveBrubeck-Topic
Mathcore Soundtrack of the day - In the Absence of Strong Evidence to the Contrary, One May Step Out of the Way of the Charging Bull - What Burns Never Returns - Don Caballero
https://www.youtube.com/watch?v=eB15DiAkb6w&ab&ab_channel=DonCaballero-Topic
Link of the day - 43,252,003,274,489,856,000 Rubik's Cube Combinations - Numberphile
https://www.youtube.com/watch?v=QV9k6dRQQe4&ab_channel=Numberphile
Using maths to solve the Cube - Associate Professor Burkard Polster - School of Mathematical Sciences - Monash University
https://www.youtube.com/watch?v=UqQaqbvDZUA&ab_channel=MonashUniversityFacultyofScience
Link of the day (lite) - Have we solved every scramble? - Cubeorithms
https://www.youtube.com/watch?v=Xt_RwIQaRFA&ab_channel=Cubeorithms
Also, may I give a massive shout-out to my brilliant friend, juggling and maths guru, Mark Douglass, who taught me about the cube many years ago.
