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

perfect, most efficient algorithm.

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

could be five or so on.

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

the Rubik's cube was this huge number.

It was 43 quintillion.

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

number of combinations you can reach is less than this

massive number, 43 quintillion.

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

definitely more than 17 because there's so many you

can't even reach.

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

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

closer and closer.

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

not too slow, either.

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 often called God's number.

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

need to do these 12 moves or whatever.

But there are people who can.

So they do Rubik's cube solving competitions.

And they have, obviously, speed challenges to see who

can solve it the fastest.

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

solve competition.

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

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

The world record for that is 23 moves.

And obviously that was for a particular

scramble of the cube.

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

solve that was fewer than 20.

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

23, which I think is probably more impressive than people

who can solve it really quickly.

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

How do we know that?

Did we just check all 43.25 billion billion different ways

of solving it?

And we effectively did that.

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

quarter turn the other way, or half turn.

That counts.

So anything that you move counts as a move.

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

turn, those all counts as one.

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

look at all the possible combinations.

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

mixed up that way.

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

have to check.

And this is one of those wonderful things where you do

a proof by exhaustion.

JAMES GRIME: They found a very difficult position.

It was called the superflip.

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

superflip, in 20 moves.

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

less than 20 moves.

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

So 20 moves.

So they thought, great.

Maybe 20 is God's number.

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

two things.

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

need to check as much as you can.

Secondly, you've got to get very clever

ways of checking them.

And so they got better and better computer programs and

also more and more powerful computers.

So they just crossed.

So they had reduced the number of cases far enough.

They had a fast enough computer with a smart enough

program to check that many.

And they could run it.

I've been to the place where they actually did the

computation.

It was at the Google headquarters in San Francisco,

just outside San Francisco.

And Google, because it's run by benevolent nerds, let

people use their mind bogglingly powerful computer.

The amount of computer power that Google has is phenomenal.

They don't use it all of it all the time.

And so if you come up with an interesting enough reason,

they will let you come and play around on their

incredible computer processing power.

You've got prove that your code's not going to

run amok, et cetera.

And that's what these guys did.

They had their code that checked the

reduced number of cases.

They ran it on the Google servers.

And they did.

They exhaustively checked.

And we know now, for a fact--

JAMES GRIME: --that God's number is 20.

Every Rubik's puzzle can be solved in 20 or fewer moves.

MATT PARKER: I'm actually involved at the moment in a

attempt to set the world record for the most people

solving a Rubik's cube simultaneously.

So we're going to try and get 2000 school students into the

O2 venue in London.

And we're going to try and break the simultaneous solving

world record.

And it's for a charity.

So the DePaul charity has organized this.

Rubik's is sponsoring it.

And any school in the UK can enter.

It's on the 21st of November.

So if you go to the DePaul website--

Or I imagine, this is the internet.

We can probably hyperlink this information beneath the video.

Schools can get involved.

I'm involved.

It's the charity I do charity work for.

It's to stop young people from becoming homeless, which I

think is fair enough.

I'm hosting the event.

So I'll be there on the 21st wandering around talking about

math and how wonderful it is.

And I'm developing resources.

So I've developed videos and worksheets for teachers to use

to teach students how to solve the Rubik's cube.