The Cube, Do You Hate it or Love it? (Article for distribution)
How the Cube is held together?
What is the real spelling for this puzzle?
What happens if I don't put the cube together properly?
How many possible positions are there?
More
information about Mathematics
The Cube, Do You Hate it or Love it?
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If you can complete the Rubik's cube then you love it, but if you can't then you hate that piece of plastic with 20 parts and one frame.
For 18 years I fiddled and got frustrated by the cube. When you are young there is lots of time to spend on this sort of thing.
At the age of 21 someone showed me the moves required to solve the cube. I was very pleased but also highly annoyed that it took 18 years for me to find the solution.
I am now 26 and I have done some research on that rigid time waster some people call a puzzle. It is way more than a puzzle!
Many people have studied the math of the cube, hence the algorithms available on some sites that will solve any cube so long as you enter the colors in correctly.
The math used in the cube is of a higher form that is studied at school, it is called group theory. Enough of that though!
There are two ways to do the cube. The short way, and the long way.
The long way involves completing one side first and then completing the rest of the cube, using sequences of moves that move certain blocks around. There are a few different methods and they all require you to remember sequences of moves for different situations. The number of sequences is usually less than 10, quite manageable.
Each person is different and one person might prefer one method over another, but for me the main criteria for a solution is the ease with which the solution can be remembered, so that a couple of months down the line you will still be able to do the cube without having practiced.
The short way involves hours of dedication and a good memory. Sequences of turns are memorized along with what the sequence achieves. The difference here is there are over 40 different sets of moves, and even more depending how determined you are.
To complete the cube in the world record time of 16.5 seconds (averaged over 3 attempts, in front of an audience) requires you to know just the right turns to get the mixed up cube to the completed state. I would imagine that a person would have to almost become “one with the cube” to be able to achieve this consistently.
One of the main issues is the number of turns. Each turn takes time, albeit a very short time because these guys do there turns at a rate faster than 4 turns per second.
Imagine this (sounds like something from The Matrix), you get given a mixed up cube, you look at the cube for 30 seconds, you then pick the correct set of turns from your memorized list of over 40 sets and use that to complete the cube. Being blindfolded makes no difference because you are “one with the cube”. Reality is being altered.
Ok, come back to reality for a while and say to yourself, what do I want to achieve. Do you want to be able to complete the cube in 3 minutes, or in 30 seconds.
To be able to solve the cube in 3 minutes will probably take you about 4 hours to learn the moves from a book or a web site, it will then take you a further 4 hours to complete the cube a number of times, before you can remember it and do it without looking at the book or the website.
That is if you use a good book or a good web site; don’t waste your time trying to follow the solution that comes with the cube that you bought, that is maybe for Einstein, although I am sure even he would find it a challenge!
If someone can sit with you and show you the moves, then it will take you about 1 hour to complete the cube the 1st time, and then about 4 hours to get all the moves into your head.
However, to be able to solve the cube in 30 seconds will probably require in excess of 1000 hours of practice, and you will have to remain “fit” by practicing for at least 4 hours a day, to keep your speed up.
So the short way is actually the long way and the long way is actually the short way. Decide for yourself!
About the Author:
Chris Loans is the author of a Layman’s Rubik’s Cube solution. Visit his site or email him to find out how you can complete the ultimate puzzle.
http://www.chrisloanshome.8m.com/Rubics_Cube/cube_complete.htm; solution@chrisloanshome.8m.com
How the Cube is held together?
It is a very clever design and the pieces fit well together. The middle blocks are secured with screws into the main structure and are able to swivel. The corner and edge pieces simply fit into the cube and once all the pieces are in then they all hold each other in.
What is the
real spelling for this puzzle?
The real spelling for the cube is Rubik's Cube. Named after the person who designed it, Erno Rubik, in 1974.
The safest way, that will not break your cube, is to turn one side 45 degrees, then use a knife to gently ease out the middle block. Some other people might take the corner block out first, but this puts a lot more strain on your cube.
When putting back your cube, the last piece to go in is an edge piece, not a corner piece. This will ensure that your cube lasts, and lasts. The piece will fit in quite easily, so long as the face is rotated 45 degrees to open the hole as much as possible.
It is quite fun to put it back together, but you must make sure that the cube is put back completed otherwise it might not be able to be completed no matter how much you turn the cube.
What happens if I don't put the cube together properly?
If you take your cube apart and then put it back together, you have 1 in 12 chances of the cube being able to be completed. With such low odds it is always advisable to put the cube back in the completed state so as to prevent frustration.
How many possible positions are there?
One of the first questions we ask is, How many processes are there in the group of the cube? In other words, what is the order of the group of the cube. We can solve this question by counting the permissible permutations of edges and the permissible permutations of corners.
There are 8 corner cubelets and 12 edge cubelets. Each corner cubelet can have three possible orientations ("twists") and each edge cubelet can have two possible orientations ("flips"). Thus the possible states of the cube can be no more than
Upper Bound on Order of Cube Group = (8!)(12!)(38)(212)
However, as we have seen in the previous chapter not all of these configurations are reachable from the initial (solved) state. There we learned that only 1/12 of all conceivable states are actually reachable so to get the order of the cube we must divide the upper bound given above by 12
Order of the Cube Group = (8!)(12!)(38)(212) ÷ 12
This is a rather large number: 43,252,003,274,489,856,000 (or a little over 43 quintillion). At the rate of 1,000,000 configurations per second it would take well over a million years to run through them all. From this we can safely conclude that coupling random twiddling with patience is a poor strategy for solving the cube.
Speed cubing is exactly as the term describes. The cube is completed in outrageous times like 32 seconds, 40 seconds and 50 seconds if you are a bit slow!
To achieve these sort of times, over 40 different sequences of moves have to be memorized, along with what each of the sequences achieves. Along with remembering all these sequences of moves, you also have to be able to choose the right sequence immediately; there is no time to think about it.
If you are considering this challenge then prepare yourself for many hours of practice. In the long-term it is well worth it though because you will be among the elite few who can do this.
For further information on how to learn speed cubing, including the various records related to the cube see the speed-cubing link below.
Some records involving cubes and speed cubing, great reading. For detailed speed cubing information follow the links at the top of the record page.