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  • BRADY HARAN: So today I'm going to do something I've

  • never done before, I'm going to phone a

  • Numberphile file viewer.

  • And the reason for that is this viewer has a very special

  • phone number.

  • So while I get ready to do this, let's

  • get on with the video.

  • DR. JAMES GRIME: This came from Brady.

  • So you heard of this type of number.

  • So it was a type number called pandigital numbers.

  • And when you mentioned it, I said well, I've heard of

  • pandigital numbers and I even have a favorite one.

  • So that says start off my favorite pandigital number.

  • I'll show you what they are, as well.

  • 381,654,729.

  • This is my favorite pandigital number.

  • Well, first of all, what's a pandigital number?

  • You may notice from that number it uses every digit.

  • And it uses every digit once there from one to nine.

  • So that's called a pandigital number.

  • This one's my favorite.

  • It has an extra property because the first end digits

  • of it is divisible by n.

  • I'll show you what I mean.

  • The first digit is divisible by 1.

  • The first two digits are divisible by 2.

  • The first three digits, so 381, is a number

  • divisible by 3.

  • First four is a number divisible by 4.

  • That's divided by 5.

  • That can be divided by 6, 7, 8, and 9.

  • And that's the only pandigital number where that works.

  • So this is a unique pandigital number with

  • that special property.

  • -It hasn't got a zero.

  • DR. JAMES GRIME: It hasn't got a zero.

  • So there are different definitions

  • for pandigital numbers.

  • Some are more strict than others.

  • So some definitions allow you to repeat the numbers.

  • So you can repeat the digits as long as

  • you have all of them.

  • Some of you don't allow you to repeat the digits.

  • Some definitions allow you to have zero.

  • So that one would be a zeroless pandigital number.

  • If you like, though, shall I stick zero in it?

  • What I could do is put a zero on the end.

  • And, then, there's a number that can be

  • divided by 10, as well.

  • And that's also unique.

  • So that would be a unique pandigital number including

  • zero, that could be divided by 10.

  • Of course, we can't divide by zero.

  • -Nice improvisation there.

  • DR. JAMES GRIME: You like that?

  • -Yeah.

  • [LAUGHTER]

  • BRADY HARAN: So you've probably figured out by now

  • the person I'm going to call has a pandigital phone number.

  • I found out about it by putting a message out on

  • Facebook and Twitter.

  • So if you don't follow Numberphile on Facebook and

  • Twitter that's something you need to be doing.

  • But before I make this phone call, here's James with a bit

  • more information about pandigital numbers.

  • DR. JAMES GRIME: The smallest pandigital number-- pandigital

  • by the way, it sounds like a radio station on Neverland.

  • Did you like that?

  • There you go.

  • There you go.

  • -No, I didn't particularly like that.

  • I think pandigital sounds like a really

  • modern way of cooking.

  • DR. JAMES GRIME: Pandigital.

  • Yeah, yeah, I agree.

  • I like that too.

  • The smallest pandigital number is one billion--

  • this has a zero in it.

  • So one billion and the rest, 23,456,789.

  • So you can kind of see that that one's the smallest

  • pandigital because you can't put the zero at the start.

  • You can see why that's the smallest pandigital number.

  • Here's another type of pandigital number.

  • This one's going to be a square.

  • So that's going to be 9,814,072,356.

  • That's not necessarily the largest pandigital number.

  • But it's the largest square pandigital number.

  • So that's square because it has a square root that is a

  • whole number as well.

  • Do you want me to check it?

  • 356.

  • And I want to check that's a square number.

  • Yeah, look at that.

  • So 99,066 That's a cool number.

  • Is it 99,066?

  • Or is it 99,066.

  • I'm not sure.

  • I'm not sure what is.

  • -I see what you're doing there.

  • I like the upside.

  • What are they called?

  • Numbers that look the same upside down.

  • DR. JAMES GRIME: Oh, well there must be a name for that.

  • -We'll do a different video on them.

  • DR. JAMES GRIME: I don't know if that was

  • an interesting fact.

  • -Yeah.

  • DR. JAMES GRIME: Oh, but you'll like a prime, won't

  • you?

  • -Oh, a prime pandigital.

  • DR. JAMES GRIME: You want a prime pandigital number.

  • I thought you'd like that.

  • So it's 10,123,457,689.

  • That's one of the looser definitions of pandigital--

  • cause you can see I've used the one twice there--

  • definition.

  • But that's a prime number as well.

  • So how many pandigital numbers are there?

  • If we get really strict first of all, so we use every digit

  • once and once only, then, it's just rearranging the first,

  • well, these numbers here from one to nine.

  • I'll not include zero to start with cause that's going to

  • make things a bit more difficult.

  • The number of ways you can rearrange the numbers from one

  • to nine to make a pandigital number is

  • going to be nine factorial.

  • Nine factorial, which is 362,880.

  • And I reckon if we're allowed to have zero, as well, then,

  • it could go anywhere except the first place.

  • So with zero, it's going to be 9 times

  • 9 factorial, 3,265,920.

  • -This is obviously purely a recreational thing.

  • DR. JAMES GRIME: That's a recreational thing.

  • And I know some people don't like it when we're doing

  • things that are base 10 centric.

  • And this is a base 10 centric little fun thing to do.

  • If we try base 2, which only allows us to

  • use ones and zeroes.

  • Well, then, all numbers are going to be pandigital in that

  • case, except for numbers that are one less

  • than a power of two.

  • Cause in base 2 those are 1111111.

  • So those are the only ones that wouldn't be pandigital.

  • BRADY HARAN: So here we go.

  • I'm going to be calling this number for our viewer, Lara,

  • who is in the Netherlands with a pandigital number.

  • And if you don't include the area code it's a brilliant

  • pandigital number, very pure.

  • Every digit just once.

  • Shall we give it a go?

  • I have no idea what's going to happen here.

  • [PHONE RINGS]

  • LARA: Hello, it's Lara.

  • BRADY HARAN: Hello, is that Lara?

  • LARA: Hi, yes, it is.

  • BRADY HARAN: Lara, it's Brady Haran, here.

  • LARA: Hi, I'm doing good.

  • BRADY HARAN: How are you doing?

  • LARA: I'm just going into the other room because I can't

  • hear you very well.

  • Hang on.

  • BRADY HARAN: OK.

  • LARA: All right.

  • I should be able to hear you now.

  • BRADY HARAN: So I have to say this is the first time I've

  • ever phoned a pandigital phone number.

  • LARA: Really?

  • BRADY HARAN: Oh, I think so.

  • I don't know.

  • It's the first time I've done it knowingly.

  • LARA: I'm always telling people when I give them my

  • phone number, I go, look it has all the numbers.

  • How cool is that?

  • And nobody ever thinks it's cool, but I do.

  • BRADY HARAN: Oh, well, I think it's very cool.

  • And I think a lot of the people who watch our video

  • will think it's very cool.

  • LARA: I hope so.

  • [LAUGHTER]

  • BRADY HARAN: What do you-- tell us about you, though.

  • What do you do and stuff?

  • LARA: I'm a student.

  • I study psychology.

  • BRADY HARAN: Psychology student.

  • LARA: Yeah.

  • BRADY HARAN: What are you doing

  • watching Numberphile videos?

  • LARA: I really like maths but I'm very bad at it.

  • So Numberphile is sort of a comfortable in

  • between spot for me.

  • BRADY HARAN: Well, we're obviously not going to tell

  • anyone your phone number, but thank you for sharing the

  • glory of your pandigital phone number with us.

  • LARA: Yeah, it is glorious.

  • Isn't it?

  • BRADY HARAN: Yeah, thanks so much for being part of, I

  • guess, bit of a silly video.

  • But, hopefully, when you watch it you'll learn lots of other

  • stuff about pandigital numbers, too

  • LARA: Yeah, I'm really looking forward to it.

  • BRADY HARAN: Excellent.

  • Well, you're the star of the show, now.

  • So I hope you're looking forward to it.

  • [LAUGHTER]

  • BRADY HARAN: Alright.

  • All the best.

  • Have a good evening.

  • LARA: Yeah, you too.

  • Bye bye.

  • BRADY HARAN: Bye.

  • [PHONE DISCONNECTS]

  • BRADY HARAN: There you go.

  • Pandigital phone number.

  • How cool was that?

  • A special thanks to squarespace.com for supporting

  • this video.

  • Squarespace is this all-in-one platform for designing

  • websites and blogs and online stores.

  • Why don't you check them out?

  • These are some websites that have been designed using it.

  • They're pretty slick looking.

  • Much more impressive than the Numberphile website.

  • So go and have a look.

  • It's free to join up.

  • And if you decide to use it and purchase anything from

  • them, you can actually get 10% off by using numberphile5 as

  • the voucher code.

  • I actually contacted them and asked if we could change it to

  • numberphile and then a pandigital number, but I think

  • someone decided that'd probably be a bit complicated.

  • So we're going with numberphile5.

  • Anyway, enough about that. squarespace.com.

  • Free to join up.

  • If you buy anything, use the code, numberphile5.

  • And thanks to them for supporting us and helping us

  • make videos.

BRADY HARAN: So today I'm going to do something I've

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