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Googling the Cube

Posted by Big Boo on August 16th, 2010

solved-rubik-cubeWhen it comes to iconic items from the Eighties they don’t get more iconic than the humble Rubik’s Cube.

It may have caused many a gnashed tooth and uttered profanity, but there’s no denying that when someone wants a picture to illustrate the decade of the 1980s, they go straight for the cube. There are countless compilation albums and books featuring the cube on the cover, and a fair few websites too (hey, I’m as guilty as the rest of them!).

Whilst most of us would just fiddle and twiddle with the thing for hours, perhaps completing one side and then giving up, boffins around the world have been trying to work out what the maximum number of moves required to solve the cube is. This magic number, nick named a God Number, is a surprisingly low twenty – yep, a maximum of 20 moves is all that is required to solve any combination of the cube!

So how did they get to this number? Well, firstly the scientists took every single possible mixed up cube combination (a mere 43,252,003,274,489,856,000 possibilities!) and dissected this up into groups of similar types which would all be solved in the same way. These groups were further wittled down by taking symmetry into account, which left just 2.21 billion groups to solve!

A computer program was then devised to solve each combination in the most optimum manner. On a reasonably powered desktop PC this took around 20-30 seconds to solve a single combination. Not bad, but 2.21 billion groups would still take around 35 years of non-stop processing to complete!

cat-with-cubeSo how did they solve it in a more timely manner? Well, they trained an army of cats to solve the Cube!

Only kidding… To the rescue comes Google, who offered to run this program on their high tech super computers (so if you’ve found Google slow to respond recently, maybe it was too busy wasting time on a Rubik’s Cube solution) and managed to churn through all the combination groups in just a matter of weeks. Ouch, that’s some serious processing power they’ve got there!

Turns out there are around 300,000,000 combinations that need the full 20 moves, but the majority can be solved with between 15 and 19 moves. Even with solid scientific evidence though, I still find this very hard to believe!

Then again, given that the world record for solving a scrambled cube is just a little over 10 seconds, I guess there can’t be that many moves required as I reckon it can’t be humanly possible to do more than 3 or 4 moves per second, and certainly not on my inferior quality Rubik’s Cube copy off the market, which had to be aligned exactly before you could twist the damn thing.