What makes the regular 3x3x3 cube so intriguing to so many people is that it looks simple and people think they might be able to solve it given enough time and patience but then after a short while they give up in frustration, maybe having at least completed their so called 'one side'. Some persevere enough to try to solve a 2nd side, not realising just how stupid a method this is, especially when the pieces of the first layer aren't even positioned correctly with the centres.

Very few people have figured out how to solve a cube by themselves, and of those who have, the vast majority have had to study a fair amount of maths to understand things like group theory (which I do not), there was one maths teacher at my secondary school who I remember telling me that he figured out how to solve a 3x3 with group theory.

But what makes it so difficult?

The 3x3x3 has 43,252,003,274,489,856,000 possible combinations, we can make some estimates for some interesting statistics here:

If we assume that there are 500 million people who have played with a 3x3 cube at some point, obviously some speedcubers will have done millions upon millions of moves, while others will probably have done a few hundred and given up. But if we assume an average of 100000 moves applied per person, of which 40000 cycle through cases which have been seen before because they are either the solved state or close to the solved state with common solving methods, that is 60000 cases multiplied by 500000000 people which is only 30,000,000,000,000 cases ever seen by anyone in history!

so, yes, we can estimate that 99.9999% of possible scrambles of a regular 3x3x3 have never been seen by anyone in history. If you had to learn a different solution for every case then no one would be able to solve it.

But how can speedcubers solve it then?

Methods, steps and algorithms.

Most people who learn to solve a cube learn by following a solution guide or video tutorial, there are so many out there today (and of course, I even have my own), they learn to align the edges of one colour into the cross, then insert the first layer and then the second layer and then finally various algorithms to solve the last layer (note layer, not side, no speedcuber solves cubes by sides, that would be ridiculous). To solve it faster, they learn more algorithms and have to recognise the various cases and instantly know to respond with a particular algorithm that they have ingrained into their muscle memory. But what keeps it exciting is that no two cube solves are ever going to be exactly the same, there is still some thinking involved, even if it happens in a tiny fraction of a second to decide how to solve that cross.

So if you want to get into speedcubing, then I would advise you not to go down this idea that following a tutorial is cheating, you can buy a decent speedcube here (you really are spoilt for choice so if you can't decide then get this one). And yes, once you can solve a normal 3x3 you can try and figure out bigger cubes and smaller cubes and different shaped twisty puzzles and because you can solve the 3x3, that knowledge can carry over and maybe you will be able to figure out some other puzzles yourself!