Reply to post: Re: Hey, Bishop. Do the thing with the knife

How to solve a Rubik's Cube in five seconds

Michael Wojcik Silver badge

Re: Hey, Bishop. Do the thing with the knife

I wonder how long it would take to arrange the each side of the cube in every possible combination, one after the other, using only the human hand and mind.

Well, that's easier than arranging a cube in every possible combination simultaneously.

Anyhoo...

Let's assume Etter can in general iterate overy 27 configurations in 5 seconds. That's the starting configuration, plus 26 quarter-turn moves at worst to reach the solved configuration. Etter presumably uses half-turns as well as quarter-turns, but half-turns pass momentarily through their intermediate quarter-turn configuration, so we can assume quarter-turns with no loss of generality.

We can assume those 27 configurations are distinct, because if he reached the same configuration twice then he has a loop and he's not using an optimal path.

There are roughly 4.3e19 configurations. (4.3e19 / 27) * 5 gives us ~ 8.0e18 seconds to complete, or somewhere around a quarter of a million million years, plus some time for pee breaks.

If anyone's curious, a little back-of-the-envelope shows a Rubic's Cube has about 65 bits of entropy, assuming all configurations are equally probable. (They are, mechanically, but since RCs are sold in solved form, and many people manage to solve them and then leave them that way, at any given time the solved configuration probably appears disproportionately often across the entire state of extant RCs. So don't use the solved configuration as your Rubic's Passcube.)

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