# Rubik’s Cube: Fun, frustrating, or both?

**History of the cube**

The Rubik’s cube is the brainchild of Ernő Rubik, a sculptor and professor of architecture from Hungary. Originally designed in 1975 as a way of solving and studying the structural problem of being able to independently move individual parts without causing the entire mechanism to disassemble, he soon saw the potential of what he had made as a toy when he scrambled his newly made cube and faced difficulty trying to restore it to its original state. Originally called the Magic Cube in Hungary, it was re-branded as Rubik’s Cube, the name we all know and love (or hate, depending on how much time you’ve spent trying to solve one) when it was released worldwide. As of 2009, there had been around 350 million cubes sold.

Just to recap what the puzzle actually is to everyone, it is a 6 sided cube (as all cubes are), with each face made up of 9 coloured stickers, with each face being able to rotate independently. When it is solved, the colours on any individual face are all the same. The difficulty comes in the face that, unless certain techniques are known, it is extremely difficult to return the puzzle to its solved position.

**Why so difficult?**

Well what could make a seemingly simple puzzle so hard? Well the answer lies in the fact that there are so many different ways of arranging the cube, yet only one of them is the solved arrangement. So how many possible ways can you arrange the cube then? To answer that, we’re going to have to use some maths! There’s some pretty complicated things that are needed to be taken into account to understand the figures arrived at, so this is shamelessly copied from the Wiki page on the Rubik’s cube. Also, any number followed by an exclamation mark (like 8!) means the factorial of that number. So 8! is 8x7x6x5x4x3x2x1. Anyway, onto the explanation:

*“There are 8! (40,320) ways to arrange the corner cubes. Each corner has three possible orientations, although only seven (of eight) can be oriented independently; the orientation of the eighth (final) corner depends on the preceding seven, giving 37 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, restricted from 12! because edges must be in an even permutation exactly when the corners are. (When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation.) Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 211 (2,048) possibilities.”*

Altogether this leads to 8! x 3! x (12!/2) x 2^{11} = 43,252,003,274,489,856,000 combinations! That’s 43 quintillion ways of arranging the cube And only one of them is the solved state. Surely that may offer some perspective as to why solving the cube generally requires some knowledge on certain techniques.

**Speed-solving**

Yet people can solve these cubes quite easily, and some people can solve them really, really, fast. The world record is 4.22 seconds by a fellow named Feliks Zemdegs. How do they do it? Through the use of algorithms, sets of particular moves to follow to solve each particular stage of the puzzle. Using these algorithms, rather than trying to solve the cube intuitively, is much quicker as they can be memorised through repetition, and muscle memory comes into play allowing for the moves to be done super quick. There are some other crazy records though. The fastest non-human solve is 0.38 seconds, performed by a robot called the Rubik’s Contraption. The fastest blind-folded solving done in 17.33 seconds by Jeff Park, and even a 17x17x17 cube solve completed in one hour and six seconds by Douglas Shamlin. Think of how many combinations there would be for a 17x17x17 cube!

I learnt to solve the standard cube back in primary school, though I was never that fast at it. Having not touched one for many years, I bought one about 6 months ago to see if I could still do it. And though I’m not even close to a competitive speed-solving time, here’s a video of me using the so called ‘beginners method’ to complete the cube!

Let me know if you can solve the Rubik’s Cube, and how fast you can do it!