I remember my first Rubik cube. It was early 1978 before I started my studies at Cambridge. I had been into Edinburgh in the morning and stopped off at a puzzle shop in the grass market. They had all kinds of mechanical puzzles that you would never see anywhere else. That morning the new Rubik’s cube caught my eye. How could anyone have missed it with its brightly coloured sides. So I took my cube home and spent the afternoon playing with it. By the end of the day I found that I had enough moves to convince myself I could solve it from any starting point, so I put it way and more or less forgot about it.
According to Wikipedia, Rubik’s cube was not available in Western shops until 1980 when Ideal Toys started to market it (obviously that is not quite true). At that time a massive craze for the toy developped and some people made a small fortune selling booklets showing solutions. I never would have imagined that people would want to be shown how to solve it! While some people competed to see how quickly they could do it, other people tried to analyse it to see how few moves are needed in the general case.
Now the upper bound on that number has been reduced to just 20 moves using a horific amount of computer time donated by Google. As it happens, the lower bound is also known to be 20. For more details and history of the developments you need to read “God’s Number is 20“. There you can learn that there are about 300 million positions that require 20 moves to resolve and see a video of the hardest position they found. God’s Number? Are mathematicians trying to outhype the particle physicists now?