I wanted to tell you about the number 2084.

It rises at the end of a little story.

This particular one came about on a chess board, for this is a really big chessboard.

This is an infinite board.

And so I'm gonna number the squares, so I'll start off.

I'll pick any square and number at one.

And now we work in a spiral around it and we number thing.

It's called a square spiral.

We row around around around till we filled up the whole board.

Now what we dio is we take a night on ordinary chest night and we start him off at square number one.

And now we look at all the squares that he could jump to the night could move from 1 to 12 or from 1 to 18.

The rule is we always go to the smallest square, and we can't repeat a square.

We have to always go to a new square.

So from one, it looks like to me like, um, we could get to 10.

They're eight squares and tennis the smallest.

So we're going to get a sequence, which is the sequence of squares where the night goes to.

So it starts off.

It won.

Its first move is to the smallest number that it can go to that it hasn't already bean too.

So it could go to 10 from 10.

Ah, it could move back to three.

So 10 goes to three.

So the third term in the sequence is three.

Then from three, we could go to 66 is obviously the next number and then 94 So that's the sequence.

We do that forever.

It will be nice if we could do it forever.

But something strange happens after we've been going on for a long time.

It gets trapped.

In fact, after 2000 and 16 steps, it must.

It gets stuck.

It cannot move every square, every one of the eight squares around it that it could move to.

It's already bean, too.

So it does.

The sequence dies at that point after 2016 steps, and the last number that it reaches is 2000 and 84.

And I have in my notebook here a picture of the spiral so you can see it starts off here and the colors it gets lighter and lighter is.

It starts off fairly dark, and then we have blue and green and yellow around.

They're very strange, long lines of points when it moves in a straight line this night, moving, too, and 12 and one and so on.

But eventually it gets to this red dot, and there it gets stuck.

All of the eight squares could possibly move to it's already visited.

It's deliciously Erba treason and unexpected that it could.

You would have thought some pattern or system had emerged where it's gonna go for ever now, is it?

It's It's It's wonderful.

Yeah, that surprises me.

I think it's wonderful.

It's It's uh yeah, it's a strange sequence.

The missing numbers.

That's another sequence.

So if we look at the ones, it doesn't visit there infinitely many.

That's an infant sequence and the smallest one that doesn't get to his 9 61 You can do it with other chess pieces.

You can do it with a castle, a rook.

You could do it on a chess board of the different shape.

You could do it on the kind of chess board that you get.

If you just just one quadrant once 1/4 of the infinite bull.

So let's pretend we have our chess board.

We number the squares.

Justus.

We did in the spiral here.

We're gonna number them in a long diagonals.

More precisely along Auntie diagonals too three and so on.

What?

Same game you play the same Game one.

And what's the smallest square it could move to?

Well, it can only move to eight or nine, so it has to go to the smaller of them.

So the sequence goes 18 and now from eight.

We could move to some big numbers here, but the smallest number is obviously six.

So 186 and then to two and then Thio 12.

It looks like so so 186 to 12.

Again.

The sequence is finite and step 2402 it reaches 1378 and there are no squares.

It could move to it dies that point again.

It's color coded.

It starts off in the corner.

And as the trajectory moves along, get the colors get lighter and lighter and you see that red X there.

That's where it gets trapped.

You love it, don't you?

I do?

Yeah, yeah.

Um, So you could do the same thing with Brooke with a queen.

It doesn't get stuck.

Keeps going.

Do you play chess?

No.

Not anymore.

I retired.

I retired at the age of 14.

It was taking up too much time.

So you did this instead?

Well, I didn't start this till I was in grad school.

Everyone have a look at this and this.

And how about this?

The's just some of the quizzes and puzzles and questions you'll find on Brilliant, which is a sponsor of today's episode.

Now I've met some of the people that work of brilliant.

They're real science math people.

And they take it really seriously.

These courses, these quizzes, these questions they're designing, they're really well thought out.

They really think about how to design these in such a way that people like you who were doing them they're gonna be smarter.

They really wanna change the way you think.

Now there's lots of stuff on the brilliant sight that's free.

But number five years can also get a 20% discount on a premium membership, which has got even more good stuff by going to brilliant dog slash number fire.

And now, thanks to a brilliant for supporting this episode when you go and check him out, there's also a link down in the description.