Black Hole Fun - Exploring Kaprekar's Constant

So why don't we jump right in? You started talking about something called Capricar's Constant.

Get us started with that, Pete.

What is it?

Yeah, well, as you know, I spend most of my free time just sitting around, thinking about what Noah and I might talk about in another episode.

And I was kinda running some number theory through my head, and I saw a little video that got me thinking about a little trick that you can do with four-digit numbers.

And before I tell you exactly what's going on, I thought, why don't we take a four-digit number and do a little math on it and see where it leads?

All right, I'm game.

How do we get started?

Why don't you pick a four-digit number, anything you want.

Any number I want?

[gasps] 23, 19.

We have a 23, 19.

All right, because I have a super huge ego, I'm gonna pick my birth year.

Let's pick 1971, one, nine, seven, one.

Dude, I don't wanna, like, contradict you, but you picked my birth year.

Oh, well, that's because you also are a huge ego.

Oh, I forgot.

I for- you're right, I forgot.

Okay, 1971, that's a totally good starting number.

Now- That number has four digits, and what I would like you to do is to rearrange them so that we create a new four-digit number where the largest digit comes first and then the second largest comes second, and so on down the line.

Okay, so 1971 has a 1, a 9, a 7, and another 1.

So I'm gonna arrange this 9, 7, 1, 1, 9,711.

Awesome.

So let's put that off to the side for a second.

Now, do the same thing, but arranging the digits from least to greatest to create another four-digit number.