August 19th, 2007
You are presented with a Rubik’s Cube, disordered, and ordered to solve it. You twist and turn the thing for hours through thousands of rotations but get nowhere – it’s just become random and frustrating. As if only to make the defeat more cutting, a new bit of research has proved that at any given stage you are no more than 26 turns away from the solution.
But what if you were God? God would, for every Rubik arrangement, know exactly which twists to make – he’d be able to solve it in the minimum amount of moves. It’s this piece of speculation that has led to the number being called “God’s Number” – the minimum moves needed to solve any Rubik’s Cube if you are omniscient. Whilst the new proof tells us God’s Number is below 26, the truth of the elusive number remains to be discovered.
Why the number is so tantalising a prospect to figure out is anyone’s guess, but perhaps it’s the sheer difficulty of the problem compared to the simplicity of the solution – just an integer in its “low twenties”. Contrasted to the low solution are the 43 billion billion possible Rubik arrangements to plough through to get it – far too much even for a supercomputer.
Graduate student Daniel Kunkle and Gene Cooperman from Northeastern University in Boston thought of a clever way to get round cracking the problem. By telling their computers to only solve the different cube arrangements half-way – arriving at points where they knew only a few more moves would be needed, they came to the half-proof that most arrangements took 26 moves or less, but some were taking 29 or more. They were then able to focus all the computer’s energies on the problem cases above 26, which numbered significantly fewer, finally being able to resolve all of these cases.
Whilst the 21st century’s Rubik counterpart is something like Su Doku, easily solvable by most computers, the Rubik’s Cube of the 1980’s remains firmly mysterious and yet as ever a tantalisingly simple puzzle – if only you knew…