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.
-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?
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