I have a card trick.

I'm gonna show you this card trick.

Here we go.

Just a bunch of cards and I need someone to pick a card.

So let's so randomly pick a card out of there.

There's your card.

I haven't seen it.

You're memorizing it, and you can stick it back in the pile here, anywhere, anywhere you like.

All right.

And just to be extra careful that I didn't see anything.

It's really mixed up in there.

There's no way I could know it.

I'm gonna shuffle these cards.

And then now I'm going to deal them out into three piles and for show.

I need youto remember this card so that you can mentally pass along that information to me, and we can help that card rise to the top.

Okay, so you point to which column you see your card.

This this one here.

Okay.

Perfect career.

So we're going to divide them up again.

I hope you remembering your card, because otherwise this trick might not work.

All right, Now, where do you see it?

It's in this one here.

Okay, That makes me a little nervous.

That's all right.

All right, one more time just to be safe.

Okay, So you think hard about this card.

And where is it now?

Is this one this one?

No.

All right.

I think that's okay.

All right.

Okay.

So 0.24 piles for me, please.

Uh, let's go with that.

These four here, These four here.

Okay.

Great.

And now, how about two piles from these ones?

Left?

These two in the end.

The two on the end.

Okay.

And one more.

The one closest to you.

This one.

Okay.

Oh, no.

I'm feeling nervous.

Okay.

One of these cards, please.

Um Mita, One little one.

How did we D'oh!

Did we do it?

Why did I not make it?

You got it.

I got it.

I think I was going to get a little nervous.

We're gonna have to do this again.

Okay.

That was investments.

That was very good, right?

I imagine the people in the audience are probably a little more excited.

I think maybe I'm a little more relieved.

Let's let's break it down.

So the first thing we need to know is the name of this trick is actually the 21 card tricks.

So the one piece of information I kept from you is how many cards I have.

So I have 21 cards in my hand.

And so you can really start thinking about this in terms of modular arithmetic.

So I'm thinking about numbers.

And when I divide that number by some fixed number, like three, I can ask for which remainder does that number have?

It can have remainder zero.

So maybe it's like six.

Divided by three.

His no remainder seven has remainder one So seven divided by three.

I can get three times to a six plus one so I can get one.

And then I can also have to sew like eight.

Divided by three has remained or two.

So I can think about dividing up my numbers.

Any integer divided by three into these three groups.

Where the remainder zero remainder one remainder too.

Okay.

So you picked and we picked a card.

That was the first thing we did.

Yes, please.

Whatever time.

So here this time, two of clubs.

Okay, so everybody knows, and it's okay, because eventually I already was gonna know that, but okay, two of clubs.

So we stick it back in and just for show.

I mixed them up.

This was This is a legitimate.

This was a real shock.

Yeah, this is for sure.

I'm not doing anything special here.

Just tow toe.

Add to the enjoyment of the randomness of it all.

You certainly my my dog could have shuffled them.

I guess so.

Two of clubs, That's the one we're looking for.

The second step was to divide them up into these Collins, so it could have been anywhere.

At this point, the card condemn finitely be anywhere.

But now I'm dividing them up into three columns.

If you recall, we discussed Modelo arithmetic.

So we're thinking about dividing up 21 cards by three.

So one of those cards has to be in the column where you could think the remainder is one.

The remainder is too, or the remainder is zero.

And so we see our card here.

Okay, So the first thing we want to do is make sure that this column has to be sandwiched between the two other columns.

And the reason I'm going to do this is because this one has seven cards in it.

I don't know which card you know, Supposedly I don't know which card it is, but I know now it's somewhere in positions, so they're seven here.

Once I put this one on top of these cars, it's got to be positions 89 10 11 12 13 or 14.

So in positions eight through 14 lies your card.

And then I'm gonna add the rest of these cards here, and so that helps me know for sure.

It's right in this section 8 to 14.

So when I separate them up again or divide them up into these three columns, here are the 1st 7 Those were the ones that I stacked on top of my group.

No, I'm no in there.

Right.

Here comes eight.

So maybe all kind of go like this so we can see eight, 9 10 11 12 13 and 14.

So there's that collection of cards where your card has to live, and then I just do the rest of them here.

And what happened is I took a 3 14 divided it up by three, and those numbers have to have remainder 12 or zero.

And so it did spread them across my columns.

And now the rose that they live in his shrunk.

So you can see that Whatever your whichever card we know that we need to find has to be in row.

So this one goes in.

And here, just to make it clear, has to live in row three, four or five.

Another way you can think about it is a soon as I do this, the same thing of sticking, whichever call him you say your card in which is here after seven cards, that means it's in position.

89 10 11 and possibly 12.

Because this one had three rows involved.

Okay, so now I'm looking at positions 10 11 and 12.

That might contain your card.

So now I'm gonna pick up this column where your card lives.

I'm gonna put it between the two columns of seven cards.

And now we were remembering positions 10 11 and 12.

That's where your card should live.

Okay, so here are the 1st 7 eight and nine.

Here comes 10 11 and 12 and then the rest of the cards.

So I knew your cards should be somewhere in positions 10 11 12.

And once I've divided those cards up, I've spread them across the columns.

And so now when you point to the column, I know exactly which card it is.

It's this one, and now Thio to make it more exciting.

Instead of just saying appears your card, What I'm gonna do is again take a pile of seven.

I'm going to stick it in front of the pile that contained your card and then the other seven.

Afterwards, that means 1234567 89 10.

Here's your card.

It will always be in position 11.

So all I need to dio in this second the last part of the trick is to count.

So there's 3456789 10 11 12 There's your card.

So as long as I have counted and I remember where the 11th card goes now I can finish out my trick and make sure that I remove all the groups, remove all the cards that are not the Elevens card, and at the very end, you'll be amazed.

You told me to pick groups.

That's right.

What were you doing there?

I was making sure that whichever group you picked or didn't pick it, it never removed the card that I wanted you to find.

So if you said I said pick four groups and so you pick for maybe you picked these for I take them away.

You don't tell me before.

If you're gonna keep will get rid of it.

Not at all, because it because you're picking it.

So you told me that you first saw this trick as a result of learning it.

Like with your Children?

That's right.

Did you look at it in straightaway?

Think mathematics?

Or did you like, How long did it take to you started thinking This is This is mathematical Now, I'd say immediately, I mean, it didn't help that the person who showed me the trick is also a mathematician.

And we were with a group of mathematicians.

So it's already embedded in my brain that there's math involved.

But I know that there are 21 cards.

I see three piles and there are seven cards in every pile and you're doing it three times.

I knew immediately math was involved.

Your youngster who doesn't?

Does she appreciate the mathematics, or has she just memorized?

I have to know.

You know, this is just like she loves the response.

Yeah, she she knows there's math, but she's much more excited to get the people toe shell.

Oh, my goodness.

When when she pulls their card out, she's just running for sure.

She's She's a star, She's a superstar.

She wants to be on TV.

That's her.

That's her goal.

Think so?

I almost actually almost kept one home today from a school distant case.

I know what you're thinking.

You're thinking G.

I could really do with some number file playing cards, but that's the case.

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