Rubik’s cube has always intrigued me for many reasons. It was initially an intellectual challenge to solve a complex puzzle. But after I solved it, my fascination for it increased further.
Most methods, of solving Rubik’s cube focus on reducing the number of steps and are inherently based on group theory and other techniques from mathematics. See http://en.wikipedia.org/wiki/Rubik’s_Cube. In turn they make it more difficult to comprehend, but once the method is ‘learnt’, one can use it to put together the cube relatively quickly.
My method (Not entirely mine – see disclaimer below) does not focus on reducing number of moves or solving it fast. It, instead, focuses on complexity reduction, which in fact results in increasing the number of required moves. This is done by repeated application of a simple principle, I call ‘hint’, which I will describe shortly. The end result is that once the hint is understood, anyone with some dedication, can not only put together the entire cube but also get an understanding of why the moves one is making are in fact resulting in solving the cube.
Interestingly, I discovered this method around 1982 almost 31 years back, but even today although my quick internet search resulted in many methods of solving the cube, not only could I not find my method there, but I could not find any method that even had the goal of reducing complexity.
Main difficulty – exponentially growing complexity.
Anyone who has tried to solve the cube without help, would have realized that as you solve part of the cube, the complexity for remaining parts seems to increase dramatically. If fixing first surface is hard, the difficulty in fixing the 2nd is much more hard than twice and so on. Roughly on a scale of 1 to 1000, the degree of difficulty could be assigned as –
Surface. Complexity / Degree of Difficulty
(The difficulty does not increase any more from 5 to 6 – any idea why 🙂 )
One hint reduces complexity to around 10.
With one simple hint, the complexity can be reduced drastically. I would say, it roughly drops down from 1000 to 10, somewhere between the complexity of solving 2 and 3 surfaces.
The beauty is that the hint itself is so simple that it hardly looks likes a hint. Here it goes.
If you move the cube randomly any number of times and then reverse all those moves in opposite order, the cube will come back to the state from where you started.
See how simple it is. Probably an eight year old will be able to visualize that what I said above is in fact correct.
But trust me, the above hint alone, applied intelligently and repeatedly, is all you need to put together the entire cube.
Quiz for you.
I will share specifics of my method some other time. In the meantime, here is a quiz. Can you come up with an example where above hint has any potential whatsoever, in your progress towards solving the cube. (I mean apart from helping you getting back to where you were if you accidentally destroy even what you had :)).
Disclaimer: I did not discover the above hint entirely on my own. I over heard the words “Now just undo all the moves” when I casually passed by and paused where one of my colleagues was solving the cube in front of some of his friends. Those words remained stuck in my mind for next couple of days till I found meaning in them and eventually found the solution. As things stand I am not in touch with that colleague or remember his name, but have a desire to find him and then put his name here as the real inventor.