Topic: Rubik's cube
Ernő Rubik started this discussion 2 years ago #114,630
There's a surprisingly large amount of complexity hidden away in such a simple toy.
I came across a 2x2x2 cube and thought I could just intuit my way into solving it. Turns out even this small cube is far from trivial. And from looking into it more, it seems no one intuits their way into solving even cubes of this size, at least not how I thought they would. It's all about recognizing which algorithms to apply and not as much about spatial reasoning as I thought it would be.
I can now solve it pretty quickly, but believe it or not you can speed solve these things without having much insight into what's actually happening, since you just plug and chug through the algorithms.
In some ways it's kind of a disappointment, but in other ways I have more respect for the cube because it's such a difficult problem that no one can think through and keep track of all the rotations that are happening, except for a few rare exceptional configurations.
Even the best speed solvers are far from solving these in the optimal number of moves. No one knows of any algorithm even for the 2x2x2 cube that's optimal, without resorting to exhaustive computer searches that is.
One thing that probably makes this all so difficult is that if you are just two cubes transposed from the solution, you are actually the maximal number of moves away from bringing it to the completely solved state. Looks are very deceiving here.
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