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MALE SPEAKER 1: The number I want to talk about is 6,174.
And it doesn't seem to have anything which is
unusual about it.
But Kaprekar showed that if you carry out a procedure,
which I'll outline for you, it always comes to this number.
The conditions are that it has to have four digits and these
four digits mustn't be the same.
So you have to choose maybe three the
same and one different.
Or all different.
It doesn't really matter.
But you don't choose 1, 1, 1, 1 or 0, 0, 0, 0.
So I asked you to choose one at random and you said 9,218
is your starting point.
Now the first thing you do with this is to put that in
the order, the largest number first, then the next largest
number, then the next largest number, and then the smallest.
And then the other way around.
1,289.
I've rearranged these digits in the order, highest to
lowest, lowest to highest.
And then what you do is take this away from that.
And when you do that you get 2 and then you carry 1, 9 into--
and I get 8,532.
Now this is the new number that you
put into this machine.
You arrange that in order with the highest to lowest, which
it turns out to be right straight away, and then the
other way around, 2,358.
And you take one away from the other.
And there we are, 6,174.
So you've been really kind to me because I've only had to go
through this iteration twice and I get to the number.
Well if I'd got to this number and I do it again I would
have, let me see, 7,641.
I've got to get this right.
And then 1,467.
And I take this away from that.
And I get back to 6,174.
And if I were to do that again, I would get this and
then that and that.
And it would go on forever.
The whole thing with this procedure always converges,
always ends up with this number.
And when it's got to this number, it's stuck in a
perpetual loop that will always bring you this number.
MALE SPEAKER 2: Any four digit number is going to?
MALE SPEAKER 1: You can't have 1,111 because if you rearrange
that into the other order, you get 0,000.
It doesn't work if all the numbers here are the same.
All zeros, nines, whatever.
That would not work.
But anything other than that, it's going to
converge to this number.
This is the one that's known as the Kaprekar constant, if
you want to look it up on Google.
That's the number that really is associated with this work
of an Indian mathematician, who must have had more time on
his hands than anybody else, if he's going to be playing
with numbers to try and find something like this.
But that's what mathematicians do.
And I think it's beautiful.
MALE SPEAKER 2: I see you've got some spare
room on your paper.
I'm going to give you another random four digit number and
let's see if it works.
I'm going to make this up off the top of my head.
MALE SPEAKER 1: You haven't got anything on
the top of your head.
But that's a wig, isn't it?
MALE SPEAKER 2: 2,984.
MALE SPEAKER 1: 2,984.
So I have to first put it in the order of the numbers and
then change them around and take one away from the other.
One.
One.
Two.
I've got the Kaprekar number in three goes.
So you just chose one at random and it took three goes
to get to it.
It's very appealing.
Not everything has to be useful to be
appealing and fun.
And this seems to be fun.