Thursday, February 19, 2015

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

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