Rubik's Cube and its Mathematical Background

DISCLAIMER : This blog post is not one of those articles in which you find a step by step procedure to actually solve a rubik's cube. On the contrary, this is for helping you to figure them out.

Nowadays we find a very few number of people with interest in Mathematics. The importance of mathematics is unknown to the larger part of the Engineering crowd. Does anyone know why any of you had mathematics in at least half of your engineering curriculum?

Mathematics is the essence of everything, when people say I am an expert in physics, they have to know at least a bit of mathematics to understand and implement physics.

Likewise in programming, mathematics is important. The better you are at mathematics, better you are as a programmer. You will find this book interesting if you are a hard-core programmer. “The Art of Computer Programming” By Donald Knuth

Now lets begin with the actual topic in hand. Rubik's Cube. People tend to ask question like “what are the physical application of mathematics?”. I am sure most of you know the answer. But many also tend to ask “What is a fun way of learning mathematics?”. Most of you don't know this answer. One such way is Rubik's Cube. Has anyone heard of Group Theory? I believe this is the very core concept behind rubik's cube.

Now think of your scrambled Rubik's Cube as Television or Bike that you want to fix on your own. Imagine how you feel when you fix one of your home appliances all by yourself. Happy obviously, isn't it? I have had this experience of people asking me “You are an engineer, right? Then why can't you fix a simple machine”. But in your heart you know that is not its all about.

Ok coming back to topic, this bike or TV you need to fix, needs a set of tools. Not only you need them, but you also need to know how to use them. That basic knowledge of tools here is Set Theory. The mathematics of the Rubik’s Cube involves understanding combinatorial
ideas, such as permutations and counting arguments, functions, Mathematical Induction etc... (Ring any bells?)

A simple concept called a Cycle notation (Circular notation) will change your perception of the world around you. It is actually a form of Permutation which you might already know. Understanding this deeply gives you a deep perspective of the Rubik’s Cube.

This is really a vast topic. I think immersing ourselves deep into this topic needs quiet bit of knowledge in mathematics. I can suggest some Ebooks for full mathematical involvement in solving a Rubik’s Cube. Please let me know if you need those by leaving a comment below. I can also point you people to some very good Rubik’s Cube solutions, but that is no fun.


Rubik’s Cube is the one that started it all, now there are tens and hundreds of varieties you can find in the internet. Some of them are Pyraminx, Holey-cube, Megaminx, 4x4x4 Rubik’s cube, Professor cube and what not.

The ultimate purpose of this blogpost is to explain the importance of mathematics and puzzles like Rubik's Cube which are present in all walks of life. One cannot imagine the world as it is without the achievements of great mathematicians. If you remember Permutations and Combinations you might find this link about Rubik's Cube interesting

http://en.wikipedia.org/wiki/Rubik%27s_Cube#Permutations.

The best reference for an in-depth knowledge of Mathematics and Rubik’s Cube is “Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys” by David Joyner

Homily on the Run

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      He who believes in god, is always blessed and is never left alone,helpless’,says Ram Sharan as he oars his boat along the gusts of ‘Narmada Maiyaa’. It was about a decade ago when my feet landed into this mystical place; I was in search of earning a livelihood for myself and my family. The almighty never left me alone. He offered me with a satisfactory occupation of serving the pilgrims who have come in search of him. I am as happy as the mother of a newborn healthy child or a blind child, recently operated ,catching the first glimpse of the gifts of nature.’

     I truly find what I had come here for,’ a source of livelihood along with universal satisfaction’. Ram Sharan’s eyes are enough moist by now that he cannot hide them. They manifest joy and peace. With this begins Ram Sharan’s short homily on his boat, with his hands forcing against the gusts of water and words against the momentary pleasures of philistinism. What religion you follow or which deity you worship, is immaterial. The important thing is the will to reach the almighty, the will to offer a helping hand to the needy, the will to indulge into good practices.

     The person who understands these aspects is a true disciple of the almighty.He is the true servant of the lord.That is why, I often ask people not to come here, the holy pilgrimage for the wipe out of their own miseries but the miseries of the world. Because,it is rightly said that sacrifice itself forms the basis of humanity.’Jay Ho Ram Ji ki’,he cheers as the boat births along the east coast. What astounds is the level of philosophy Ram Sharan speaks and what is revealed is the importance of peace and satisfaction. The silent image oars back across the saffron-red horizon of the setting sun, carving a deep mark of inspiration and determination in the heart.

True Self

‘True self ‘ when I say this what comes to your mind ?

 is it your image, your personality, your thoughts or the way you act.

What decides us to say that “   this is my true self  ? ”

is it the way we look or the way we act?...

 And how many of us know ourselves well enough ??, Well the answer would be few.

For example, when we are asked  questions  like  “What are your strengths and weaknesses?”

Though the question appears to be easy but the moment we start looking for answers it becomes difficult to find it and why’s that?

Don’t we know about our own self well enough to answer this question in just few seconds??... the real reason for that is that we don’t spend  time in knowing about ourselves, knowing what we like and what we don’t. Has it ever occurred to you to sit in a quite place and think about what you are and what you aspire to be , what you want from life and how can you achieve it . You may think that it appears to be lonely but I think that lonely hours are the best hours to know one self. I am not saying to just sit alone all the time… nope , not at all. But what I wanted to say is  that why not give ourselves few minutes each day to know about our own self more and in a better way so that in future we are ready to move ahead with our own goal and aspirations and not what our friends or others are doing or want to do.

After all knowing about your self is the best way to discover what  you  are good at and succeed in it.

Think different, be different and act different.