Rubik’sCube MEJaneWorley Introduction:Doyou ever think about all of the games that you played as a kid? Or puzzles thattricked you and you could never figure out? The first thing that comes to mymind when I think of troubling puzzles that were always difficult for me is a Rubik’scube. These are troubling puzzles for most people when they first pick them up,after a little bit of practice some people can end up solving them, but otherscannot. The goal of the puzzle is to move all the edge cubies and corner cubiesinto their correct positions with their correct orientation. This is a bigchallenge for a lot of people because there is not a manual to the puzzle or aYouTube tutorial video that tells you how to solve it. This mind boggling puzzle wascreated by a man named Erno Rubik who was a young professor of architecture inBudapest in 1974. The object was supposed to not be possible to solve. Hiscreation was had a new type of thinking linked to it with its ability to twistand turn and still not break and its colorful stickers on each side of thecube. The cube took its own creator over a month to solve his invention, littledid he know at the time that his new invention and past time would turn intoone the world’s best-selling toys ever made.
Erno was a teacher and was alwayslooking for new and innovative ways to teach his students by using techniquesthat would help them better understand the material. He used the Cube’s firstmodel to explain to his students the concept of special relationships. Ernothought of the Cube as an object of art, it was simple, but also complex. Inorder for his brand new toy to become a best-seller, he had to put time andeffort into his work. It took showing his students his prototype for him torealize the potential that was behind his creation. He got the Cubemanufactured, this took place in Hungary where it was made anddistributed. These first early cubeswere marketed as “Magic Cubes” and weighed about twice the weight as the onesthat are seen in stores today. During this time all Hungary was part of theCommunist regime and all imports and exports were closely watched andrestricted.
So Erno had to figure out a way to get his product past Hungary andinto the hands of people all over the world. This was accomplished bymathematicians and young entrepreneurs, they took them conferences and fairsaround their areas. At one of the events that it was taken to is where it wasdiscovered by a toy specialist, Tom Kremer, he agreed to sell it to sell it tothe rest of the world. Many names were thrown around that they thought wouldwork best to properly advertise this new and upcoming toy. It started out asbeing called the “Magic Cube”, but investors thought that it related towitchcraft so they changed it to “Rubik’s Cube”. And the infamous toy wasbranded from there. Since the product was internationally launched in 1980there have been an estimate of 350 million Rubik’s Cubes that have been soldaround the world. This cube that started out just as a tool for teachingstudents soon became an iconic toy original to that decade.
It started artmovements such as pop videos, Hollywood movies and even had its own TV show.But it also came to represent both genius and confusion. The cube was widelyused all over the world and became such an iconic toy to those of all ages. Rubik’s cube contains six centerpieces which do not move relative to each other, twelve edge “cubies” that eachhave two stickers on them, and eight corner “cubies” that each have threestickers on them. There is a typical cube solving procedure, first you need tosolve the two lower layers of the cube. Then orient the cubies in the toplayer, making sure that the top face of the cube is the correct color.
Andfinally you interchange the cubies in the top layer so that they are in theircorrect positions. In order to properly solve the Rubik’s cube in a fastmanner, there are several shortcuts that you can memorize for dealing withvarious cases and issues when it comes to the cube. The moves that one canperform on Rubik’s cube form a mathematical structure called a group. And youcan solve the cube by using two basic ideas from group theory, they arecommutators and conjugation. Investigation: About 30 years after the Rubik’scube first appeared and became a well-known puzzle, an international team ofresearchers proved that no matter how scrambled the cube got, it would alwaysbe solvable.
And to add to that statement, it could be solved in no more than20 moves. But there was no way that these researchers could evaluate all of thepossible moves and cases that could appear when attempting to solve a Rubik’scube. Several of these researchers and professors came together and showed thatthe maximum number moves required to solve a Rubik’s cube with N squares perrow is proportional to N^2/log N. The standard way to solve a Rubik’s cube isto find a square that’s out of position and move it to the right place whileleaving the rest of the cube as little changed as possible. The team of highly qualifiedindividuals recognized that under some events that a single sequence of twistscould move multiple squares into their proper places, this would potentiallycut down the total number of moves that it would take to solve the cube.
Thereis something called “God’s Number”, which is the 20. This is minimum amount ofmoves that it would take to solve a Rubik’s Cube. It is called “God’s Number”because it is very difficult to solve a Rubik’s Cube in general, but to solveit in only 20 moves is pretty difficult and this means that any configurationof a Rubik’s Cube can be solved in 20 moves or less.
“There are about 43,252,003,274,489,856,000 possibleconfigurations when it comes to a Rubik’s Cube.”1 Each ofthese configurations are classified by the minimum amount of moves that ittakes to solve the troublesome puzzle, this is called ‘distance’ of theconfiguration. Ifyou look at the table above, it shows that “more than two-thirds of the 43quintillion possible configurations are at distance-18.”2And then also a majority of the configurations fall into the categories ofdistance-15 and 20. So if you pick up a random Rubik’s Cube that is completelymixed up already, there is a higher chance of you getting a distance-18configuration. So what are the odds that you will be able to solve the Rubik’sCube in 18 moves? In order to figure that question out you need to know howmany possible moves there are to solve the Rubik’s Cube.
There are six sides to the Rubik’sCube, each of these can be turned 1, 2, or 3 times. If they are turned four times,then it just goes back to the original state it was in. So 6×3=18 which backsup the fact of solving the Rubik’s Cube in 18 moves. So if there are 18 movesmade randomly, then the odds of solving the Rubik’s Cube is 1 in 18^18. This issuch a low percentage that someone cannot really solve a Rubik’s Cube onaccident. They would need to know patterns and formulas that would help them. In something called statisticalphysics there is a hypothesis that is called the ‘ergodic hypothesis’. “Thishypothesis says that any given configuration that is in statistical physics isequally likely, and if you wait long enough then the system will eventuallypass through every possible state.
“3Now this hypothesis “would not be relevant to a Rubik’s cube where you use analgorithm, but a Rubik’s cube making random moves is exactly the sort of’random walk’ that the ergodic hypothesis applies to.”4 1 “Whatare the odds of solving a Rubik’s cube by making random moves?” Quarks &Coffee, 13 Dec. 2015,quarksandcoffee.com/index.php/2015/12/13/what-are-the-odds-of-solving-a-rubiks-cube-by-making-random-moves/.2 “What are the oddsof solving a Rubik’s cube by making random moves?” Quarks & Coffee,13 Dec.
2015,quarksandcoffee.com/index.php/2015/12/13/what-are-the-odds-of-solving-a-rubiks-cube-by-making-random-moves/.3 “What are the oddsof solving a Rubik’s cube by making random moves?” Quarks & Coffee,13 Dec.
4 “What are the oddsof solving a Rubik’s cube by making random moves?” Quarks & Coffee,13 Dec. 2015,quarksandcoffee.com/index.php/2015/12/13/what-are-the-odds-of-solving-a-rubiks-cube-by-making-random-moves/.