Isnâ€™t the complexity of a randomized Rubikâ€™s cube arbitrary? Shouldnâ€™t you be scored against an average, at least?

I never once solved one of those things, so I donâ€™t even begin to understand the math behind them.

My brother was really good* at these. It did slow him down a bit when I swapped a few of the colour stickers**.

*Not as good as the guy in the video, but waaaay better than me.

**Yeah, Iâ€™m probably going to hell.

I can find it if you like, but there was a proof with regular Rubikâ€™s Cubes that showed that the shortest distance to the solution from any arbitrarily-shuffled cube is roughly the same, no matter how itâ€™s randomly shuffled.

If you deliberately start out with an almost-solved cube, the distance to the solution is much shorter, of course, but in the space of randomly-shuffled cubes, those short ones are a teeny fraction, and are extremely unlikely to come up.

I expect the same is true for a 7x7 cube, though havenâ€™t tried to prove it.

Interesting, thanks!

Wow. Iâ€™ve only got a 3x3 cube, and itâ€™s taken me roughly 17 years and counting

Most cubers are worried about their average but a world record solve is a world record.

There are about 43 quintillion possible scrambles. A majority of about 29 quintillion are 18 moves strong. There are a couple million 20 move strong scrambles. None requires 21. Any scramble is at most 20 moves away from being transformed into any other scramble.

Has a nice distribution table at the end of the page. The number of known 20 move strong scrambles has grown since the page was put up.

The 7x7 is probably something like this but we donâ€™t have the computing power in existence to do the same sort of analysis for a 4x4x4 cube. The 7x7x7 cube has more possible scrambles than their are atoms in existence.

Thatâ€™s what I was thinking of, thank you!

Unless of course we can prove it mathematically, and not rely on brute-force to test every possibility.

I donâ€™t quite understand all the links in â€śA History of Godâ€™s Number,â€ť but I assume that the 1981 proof didnâ€™t require testing every possibility, did it?

Aside from reducing the sets to be solved by excluding symmetries they had to brute force it. The math is rock hard.

The first two papers were simply worked out by hand. Make a somewhat clean technique for solving the cube, plug in a worst case number of turns for each step, show the cumulative worst case number. If it is lower than anything before it thatâ€™s the new upper bound for godâ€™s number.

To keep pushing down the upper bounds was a problem that required brute force and they were throwing that at it back in 1992.

Well thank goodness for todayâ€™s animated .gif, which does not show the gentleman solving the puzzle, and is therefore directly contradictory of the headline.

If they had put the camera on the cube this might have been interesting.

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