Name: 上帝的數字和魔術方塊 - Numberphile(數字愛好者) (God's Number and Rubik's Cube - Numberphile)
Uploaded: 2021-01-14T04:33:25.000Z
Duration: 6 min 16 s
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JAMES GRIME: They wanted to find out the number of moves

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it would take to solve the most difficult combination.

And this number would be called God's number.

If you have perfect knowledge of how to do the Rubik's cube,

you would be able to solve the most difficult position in its

MATT PARKER: Obviously if you get a solved cube and you

twist one bit, you've just got to twist it back.

So it could be one, or it could be two twists, or it

But what's the most you're going to need?

It turns out, for a long time we didn't know.

JAMES GRIME: So they knew that the number of combinations for

And if you turn a piece 17 times, if you do 17 moves, the

number of combinations you can reach is less than this

So if you want to be able to solve all combinations, it's

definitely more than 17 because there's so many you

And they managed to work out that there was less than 30.

And over the years, they started to whittle this down,

TONY JIANG: As you can tell, I'm not really fast, but I'm

MATT PARKER: It was 2010 was the first time we actually

knew for sure no matter how much you scramble up a Rubik's

cube, you can solve it in 20 or fewer twists.

It's called God's number because you have to be some

kind of omniscient being to work out those 20 moves.

It's so difficult to calculate what those moves are.

KATIE STECKLES: I couldn't look at a cube and say, oh I

So they do Rubik's cube solving competitions.

And they have, obviously, speed challenges to see who

But one of the other things that they do is a efficient

And the competition there is look at a Rubik's cube and

then just write down a list of moves that will solve it.

And it may have been that the actual, most efficient way to

But a human can look at it and actually write down a list of

23, which I think is probably more impressive than people

MATT PARKER: You might think, well how do we know?

Did we just check all 43.25 billion billion different ways

JAMES GRIME: A move, by the way, is a quarter turn, or

quarter turn the other way, or half turn.

So anything that you move counts as a move.

All right, so a quarter turn, a quarter turn, or a half

MATT PARKER: So guys got the Rubik's cube and they try to

And they realized that actually you don't have to

check all of them, because some of them are the same.

And so they used arguments from symmetry, saying, in

fact, being mixed up this way is actually the same as being

It's the same way to solve it and so on and so on.

And so they managed to whittle down the number of ones they

And this is one of those wonderful things where you do

JAMES GRIME: They found a very difficult position.

Now the superflip is essentially completely solved

except each edge position was flipped over.

Now that would be a very difficult position to solve.

They realized that you could solve that position, the

And they proved that you couldn't do it in anything

So you couldn't do it in 19 or 18, nothing less.

MATT PARKER: And to do a proof by exhaustion, you have to do

You've got to first of all reduce the number of cases you

And so they got better and better computer programs and

So they had reduced the number of cases far enough.

They had a fast enough computer with a smart enough