Cards are available for these are better on this.

Okay, so just Well, you know, we know what number five playing cards.

There's me.

Of course, I always itself.

In fact, Brady there is there, is you?

Of course they can watch.

They're just here to watch.

I'm also gonna let Matt watch because Mark is Thea, is this king of number five card tricks, right?

So Okay, so what?

I've just taken nine cards, Okay?

The first, all the clubs, basically all the numbers clubs.

Here's the challenge to you, Brady.

I want you to put them in any order you like.

I'm not even going to pay attention.

Let's go.

That will do, mate.

Yeah.

Okay, so we read off.

What number that's gonna bay 945,136,872.

Do you know anything about that?

Numbers?

Anything.

You you know, it's about it.

It's even.

It is even.

Yeah.

You think it's something not prime.

Then do you think these numbers in the nine times table probably not.

Don't feel like it is?

Yeah.

I've been wanting nine numbers is in the nine times table.

Right?

So it's you might think it's unlikely.

Sure.

We should.

We have a bet.

Okay.

I'll bet you're fired, right?

You're saying it's not?

I'm gonna say is Okay, so should we check?

Okay, let's stick.

Right.

So Okay, so we put the number in divided by nine, see if we got a whole number.

Oh, yes, we do.

Okay.

Do you want to go again?

Don't try again.

You can even take it.

You can take a number out of you.

Any number you take on him, right?

All right, let's take out.

Double.

Quick.

Straight together.

Top number.

Okay.

You think out something, mister, You've been left with this number, okay.

To recognition.

You can write.

What, you want to move them around a bit.

Yeah.

Let's swap the five on the fourth day with you and show you.

You done?

Yeah.

Okay.

You think this is in the nine times table?

Yes, I did.

You did idea.

Okay, well, you might have won your battle.

Okay, I study.

Check it.

Divided by Let's see nine equals.

Yes, it is.

Well done.

Well, you removed the nine, which made it a lot easier for me if you'd removed.

Say, let's let's put this back.

If you removed the five, my next step is gonna be so It's only fair I get to move on out, take one out as well.

And I was gonna take out before we'll come back to.

Why, that that work later.

Try another trick.

Okay.

Slightly different one.

They've got the 1st 4 cards now wants pulls.

The three are quite common, right?

I mean, one in three numbers is a multiple of three after new four cards.

All right, you can put him in any older just just make me a multiple of three.

Well, you just try it, I guess.

All right, let's get with it.

21 for three.

Okay.

You don't sound confident.

Radio like, save it confidence like a 2 to 143 when divided by three.

Oh, dear.

You need some help?

I can get health.

You?

Yeah.

I'll just I'll just gonna put one card and card in for you, right?

This one.

I know you can put it whatever you like.

Let's put it in the middle.

Okay, let's put it in the middle right.

You wanna put right in the middle?

You sure you don't put over here now?

I'm over in the middle.

Okay.

All right.

Well, air, let's turn this car over.

Okay?

Now, let's see if this helps the situation.

Okay, let's try it now to 1543 has tried Divide in that way.

Three.

It worked.

Okay, so what is going on Radio?

What is going on?

Well, these little tricks Well, I kind of inspired by actually my own incompetence.

And because in our last video that you and I did together, which was about Belle figures Prime.

You remember we asked the following question we asked, Is this number?

We had a one and then lots of zeroes.

And then a 616 And then another bunch of zeroes.

And then one.

We asked if this number was a prime number or not.

We said it, you know, reporting enough zeros.

Can we Can we find a prime number on?

I ran a little computer code and got up to 100,000 zeros and didn't find any of them.

If you remember this, I saved up to anything.

100,000 and no prints.

And, of course, our super smart number.

File viewers immediately saw that this was never gonna be a prime number.

And the reason?

Waas Well, if you calculate the sum of all the digits, okay, so the cross, some of this object, then you'll get one plus lots of zeros.

Six plus one plus six butcher zeros again, plus one on that Totals 15 now 15 is divisible by three.

And if that number, if the cross some is divisible by three, then it guarantees that the original number is divisible by three.

So you were you were running this code checking every number when you would never It was never gonna be There's never gonna be They're wasting waste of confusing time.

Break time.

I should have just been smart number five years, right?

You think I just I just, uh to be honest, if I'm honest, I was trying to load the different things because I wanted something that might sort of cool in the video.

And I got so sort of, you know, sort of hung up on on all the different things I was trying.

I sort of lost sight of, of the beauty of maths Because this explains what went wrong with the with the with your your attempt of the att The number earlier, right?

Okay.

You took the 1st 4 numbers.

Whatever.

No combination you take these in.

I mean, these numbers 123 and four They add up to 10.

So whatever order I put them in the cross song is always gonna be 10.

But 10 is not divisible by three.

So whatever number I create cannot be divisible by three.

And now I at the five and it doesn't matter where I put it.

The cross Some is now guaranteed to be 15.

Whatever number I create is guaranteed to be divisible by three.

Okay, If the cross so Mr Visible by three the number is divisible by three.

It's also true for nine's.

If the cross, um is the visible by nine.

The number is divisible by night on that comes back to this one first nine numbers What?

Today?

Something they sort of 45 45 is the visible by nine.

So wherever combination of these numbers, I take whatever order a take guaranteed to be divisible by known.

This isn't true for other cross sums like if the cross some is divisible by four.

No, it doesn't mean the number.

I don't know.

It's just 33 and nine.

It works for Okay, It works for three and nine.

Okay, there are this or the rules that you can apply to other numbers, and we'll get into that.

But for this, this cross, some rule, it works for threes and nines.

Let's see if the roof Okay, let's see the proof.

Let's write down the kind of number that we might be interested in.

Let's just write it down as follows.

So the number and that's just right.

It's and it's gonna be an M plus one digit number.

Okay, Which we might write like this.

Okay, so we got a zero in the ones they won in the tens and so on.

Let's actually write down what this number is sort of algebraic.

Lee.

So what?

This means that end is really tend to the end times A and plus tens of the n minus one times and minus one plus 10.

A one plus a zero.

Okay, so that's what this No Berries.

Okay, Any number in principle at this stage now, Let's write down the cross.

Um, okay, so the cross comes easy to write down.

Let's call it tear, then.

Okay.

That's just gonna be the sum of all these individual positions and plus and minus one plus two.

A little toe, a one plus a zero.

Okay, Now let's do that.

Take away that.

Do that.

We can end minus tear, then, Okay, let's see what we're going to get.

So in this position will get tensed.

The end minus one and plus 10 to the N minus one, minus one and minus one.

You'll get similar things all along here.

You'll get 10 minus one, a one and then the a series of counsel.

Now look what you've got.

You've got This is nine, right?

The next one in the sales will be 99.

This one is going to be a whole bunch of nines.

This one's gonna be a one more nine.

You'll have another nine there, So there's gonna be all the nines, all the nines.

There are gonna be nines.

So they're all divisible by nine.

Okay.

So I can pull out a factor of nine.

So this is always gonna be nine times some whole number.

If the cross, um, is divisible by nine, this is the visible by nine in this better be divisible by.

And similarly, if the cross, um, is divisible by three this is definitely divisible by three.

Then this number, the original number must be divisible by three.

That's the proof.

That simple.

Right, then easy to prove.

Okay.

Why does that any work with nines and threes?

Precisely because the fact that you take the factor that you take out is nine.

Okay, that's why So, you know, basically, you need it for threes and nines.

So they're a bunch of these rules, some, some of which are easier than others.

And we can go through them, right?

And so one.

Okay, that's he's pretty.

He's the second.

Something's divisible by one tear is easy.

It just has to be an even number three's.

We've done about fours.

OK, what's the visibility rule for four.

Okay, I'm gonna write you down a multiple of 4145632 viewers can check of.

That's a multiple of four directly.

We know it is.

How do we know it is the way you do the full check is you just look at the last two digits, okay?

And you ask yourself, Are the last two digits divisible by four?

If they are, that's enough.

So here it's 32.

That's divisible by four.

I don't need to worry about the rest, and it's easy to see why.

Because these air hundreds thousands tens, thousands 100 is divisible by 4000 divisible by four.

And so on all the all the higher powers of 10 of the visible by force and the only thing you need to check of the last two.

So four they're easy as well.

It's a really easy test.

Five Pretty easy things.

Ending 5006 is well, there you have Thio do the two tests on the three test.

Okay, so you check is even in any deal.

You across some test for threes and it has to pass both.