093 = Game Solutions and Neil Distributions

Welcome to A Problem Squared, the problem solving cod past.

Cod past.

Oh my.

You can't get any cod past you.

That's the most PG response you could have given me to.

Thank you.

That's a teacher.

Yes.

I was going to say a podcast much like a duck.

Oh, like a duck.

In what way would you say, Beck, a problem-squared podcast is like a duck?

In that

it seems very calm.

It does.

But underneath, we're scrambling.

Scrambling to write intros.

Love it.

Yep.

You're Matt Parker.

That's correct.

And mathematician and comedian.

Oh, yeah.

And

big fan of Drake.

Which is

both very funny and

topic.

No, I get the.

Also, you're not actually.

That's the half of the joke I'm worried about.

I realize that Drake might be problematic.

So

that was a joke.

Matt is not a fan of Drake.

He hates Drake, in fact.

Recreate the Drake meme.

You did.

Yeah, that's what I was thinking of.

Less problematic version of it, if anybody wants it.

Yes.

And I am Beck Hill, a comedian,

podcaster.

And if I tip my hat, I would say, Maladi, what?

Malad?

You duck around all the obvious, like anything easy, and you're like, what's an obscure.

Yeah, like I'm quackers or something.

Yeah, exactly.

Yeah,

you're buoyant.

Yeah,

things roll off you.

Heck Bill.

Oh, yeah.

Yeah, you're always.

I was going to try to get like a comedy Bill.

Order for duck's Ducks beck.

That's the one.

That's the one.

We got there in the end.

Look,

this show is more collaborative than it.

We assemble the show in front of you.

Yeah.

Yeah.

We're the Huston Blumenthal of podcasts.

Exactly.

We come out to the table.

Yeah.

Other podcasts are out the back, planning ahead, rehearsing,

writing, not us.

This is a deconstructed podcast.

Yes.

It's an open podcast.

And on this episode.

I've worked out if tic-tac-toe can be fun.

I'll be looking at sizes of Neil.

Oh, of Neil.

Yeah.

And we will conclude with any other beakness.

Because ducks have a beak.

Yeah.

Well, it's a bill, isn't it?

Is it a bill?

Which is a different to a beak.

Any other billness doesn't work quite as well.

No.

Oops.

We'll solve this problem in any other birds.

Any other birdness.

Birdness.

There we go.

hey matt back how are you i'm good

and i'm aware of the pressure here because last time we had a catch-up previous episode you had a lot of news i had a lot of news we're recently in the states

and lucy had work in boulder colorado ah wonderful place better than the lesser known uh shire colorado

Because if you're boulder, you're boulder.

Oh, oh.

So shire, like you're shy.

Yeah.

But you said shyer, like a location.

That's good work.

Yeah, thanks.

Yeah, yeah, yeah.

So she was in Boulder, which people haven't been.

Wonderful place.

I'd not been before.

Lucy's been there a lot because it's kind of the center of massive solar physics to some extent in the US.

Is that because there's mountains there?

It's because a lot of physicists, and particularly space scientists, are into outdoor activity.

Yeah, they love skiing, they love mountain biking, they love all this stuff.

So their conferences are like in Hawaii and all this kind of stuff.

I'm in the wrong wrong wrong industry yeah so a lot of them live and work in boulder

and so there's like obviously the well there's a university there university of colorado is in boulder you've also then got the southwest research institute and the northwest research institute which are completely unrelated institutes oh wow so lisa was out there working with her colleagues and i thought i would hire a bike We're going to be there for a week and there's phenomenal cycling in the Rockies.

Like you're right in the Rocky Mountains.

Yeah, nice.

Because we landed and went straight to one place where we were staying over the weekend.

And I went from sea level.

I'd been New York and San Francisco, all on the coast,

to

a place in the Rockies, which is 8,500 feet altitude.

Yes.

And we got there and we're like, why have we got headaches?

Right.

It turns out we had our mild altitude sickness.

I never even considered that.

Just slightly, I mean, Boulder itself, like Denver, the plane, is already 5,000 feet altitude.

Wow.

And then you got the Rockies.

But the cycling, once you got over feeling ill, was absolutely incredible.

Except when we picked up my bike, because we flew into Denver and then I got the higher bike from Boulder, then we drove into the Rockies.

I forgot to get the helmet.

And we had driven a reasonable distance.

Lucy went, oh, have you got a helmet?

And I was like, oh, I forgot to, because it comes with a helmet.

And at that point, it was right on the cusp of, can I be bothered?

going all the way back to get a higher helmet or not.

And Lucy very correctly said, we should go back and get the helmet.

Turned around, we drove all the way back, went in, and they're like, oh, what size are you?

What helmet do you want?

They got like a rack of them.

And they happen to have the exact helmet that I have at home.

Oh.

That I'd recently purchased.

It's like one of the safest rated helmets.

I like my brain.

My brain's

career critical.

You're either, can I be stuffed to wear a helmet?

Yeah.

And if I am going to wear a helmet, it's the best.

Yeah, yeah, yeah, yeah.

It's all or nothing.

I don't want the illusion of safety.

I either want to know I'm not being safe.

yeah i'm just wearing a hat or i'm as safe as possible yeah because i go all out so you might think was that the coincidence no it wasn't i was initially startled that they had the exactly the normal helmet i have at home different color but otherwise identical and i was like that's amazing got it got back in the car we had to retrace our steps driving out go all the way to the place where we were staying in the Rockies, several hours drive later, pull up, roll the bike into the garage, hanging on the wall in the garage of the place we had rented was the identical helmet.

What?

Yeah, wow.

Right there.

And so I took a photo of both helmets.

We'll put that on the socials.

And that's my story.

Oh, wow.

Yeah.

So I feel like we're maintaining the high caliber of story people have come to expect.

What we've learned from this is that you

like a very popular helmet.

Yes, yes, yeah, yeah.

Chances are that any place that you go.

Anywhere you go will have this helmet.

It's the gyro, gyro helmet.

We'll put a link in the show notes.

Good helmet.

That's how I've been.

Lovely.

Thank you.

How have you been?

I've been good.

I went to an antique toy fair.

Oh, yes.

You sent me various photos from an antique toy fair.

Yes, there were a few things I thought might tickle your fancy.

Oh, yeah.

There was a display case.

It looked like it was for one of the original slinky displays.

Yes, it was a slinky set of display steps.

Yes.

There was a calculator of Lego that was still working.

Many cursed objects.

Oh, I can imagine.

But I picked you up something because they didn't just have toys fair.

They had other sort of collections.

Because you sent me a bunch of photos and I was like, where is this toy fair?

And you named the suburb it was in.

Glendale.

There you go.

You're like, Glendale.

I'm like, ah.

I was there for, I think, about four hours.

Wow.

I just zigzagged

amongst all the tables.

I was in my element.

I was very happy.

I didn't really buy anything because I packed very long.

Did you buy anything for you?

I bought a troll.

A troll, of course.

Yeah, I bought a troll, doll.

Great.

Yeah.

But I picked up.

I'm a world expert on trolls.

Yes, exactly.

And you got me something.

I got you something.

Oh, my goodness.

I bought this within seconds of walking in.

Oh, really?

And this is not something you sent me a photo of.

No.

I walked in.

I went, I wonder if, ah, they do have that.

All right.

I'll get that.

You've handed me a small bit of card that seems to have a coin in the middle.

a coin that says

one cent and on the back is

is it in is it the Indian cent it is it is it's the Native American

if you remember on that episode that we talked about how when pennies would be worth the most yes wondering what was on it before Lincoln yeah

Washington whatever Lincoln cent yeah Lincoln yeah we're trying to work out what it was and looked it up and went, oh, it's a Native American.

That's what it looks like.

And there, I went, oh, I'll pick that up.

It's a 1902.

That's quite late in the game.

This is definitely a bit more worn than some of the more collectible ones.

Okay, I've got an adequate photo.

We'll put that out on the socials if people want to check out the gift Beck bought me that's worth one cent.

At least.

At least.

Face value.

Thanks, Beck.

You're welcome.

While I was there, though, I bumped into Grant, better known as The Toiley.

Ah!

Who did

Grant?

Yeah, he did an evening of undressed redetail at Flappers in January.

I bumped into him and his partner, Susanna.

Yep.

She was there because

she's working

or doing a favor for a woman who bought the house that was being used for the external shots for the Brady Bunch.

She bought that house and then as part of some TV show beforehand, they'd done a thing where they made the inside look like oh it actually looked like the inside the inside of the bradybunch house the sets look like yeah and the owner of the house basically it's their life-size dollhouse that's how much money they have so they're like they just bought a house they were like oh let's preserve it as if it were the bradybunch house so let's fill it up with

contemporary toys and bits and things and yeah so susanna was there picking up her job is to buy old stuff to put in a life-size model of the bradybunch house.

Yeah.

Love California.

I know.

Anyway, meanwhile, I'd like a mortgage so I can get a studio flat.

So, if anyone wants to lend me some money, if you could be sufficiently

period accurate, you could live in the house.

I mean, yeah, if I can.

I would, I would, I would happily.

You have to research like lingo to make sure you don't use any anachristic words.

Yeah, Daddy O.

See, you're in.

Our first problem comes from Alec, who says, it is well understood that tic-tac-toe is a solved game.

That is, all of the possible game states can be brute force crunched through to determine how to win all the time.

This is because the total number of game states is a small enough volume that is trivial for modern computers.

My question is, what variations or combinations of variations of tic-tac-toe are necessary to design a game that isn't solvable by brute force?

Examples, playing the game in three dimensions, which would be three by three by three instead of just three by three,

or super tic-tac-toe, where each cell contains a smaller game and you have to play in the super cell corresponding to the sub-cell that was just played in.

Alec, I don't know what that last sentence was.

I'm sure Matt will explain that.

Well, get ready.

Yeah, here we go.

So, first of all, Alec is talking about the notion of solving a game.

Yes.

And that means that it's no longer a game.

So, for example, knots and crosses.

you can play knots and crosses as a game, but if both players know how to play, it's no longer a game because it's guaranteed to end in a draw.

Yep.

And optimal play in knots and crosses isn't that difficult.

So we say a game is solved if we can prove that the person who goes first,

or sometimes second, is guaranteed a strategy that means no matter what the other player does, they win.

At that point, no longer a game.

We're not playing it.

We've solved it.

Job done.

If you go first, you're most likely either going to win or draw.

Well, if you assume both players play perfectly.

Yeah.

The options are either for any game like this.

And this excludes games where there's like random chance, because obviously that changes things.

And it's separate to saying there are good strategies.

It's saying there's an ultimate way to do it.

You follow the algorithm.

You'll definitely win.

Or if everyone follows the optimal play algorithm, it's definitely a draw.

So those are generally the options in games like this.

Either it's definitely a draw or it's definitely a win.

Interestingly,

I would argue that it's a psychological game in that you keep playing until one of the people playing either gets bored enough that they just try somewhere else to see whether you're going to go somewhere else differently or they just lose concentration.

Well, that's what happened two nights ago after a talk.

I was signing books.

Someone said, oh, could we play a game of tic-tac-toe or knots and crosses I should say

I'm flipping between the two actually in the UK it's knots and crosses in America it's tic-tac-toe I forget Australia which one's that dingleberry dingleberries a big game

it involves shit well you said knots and crosses great okay right

so hugs and kisses I hope

you call it really I guess circles and crosses yeah fair enough So,

I did a weird open, I opened in a corner, and then they didn't take the centre, They did a weird move, but we were deliberately larking around because it's not fun.

If you play it properly,

it's boring.

Because it's soft.

Is there a way to play where both parties deliberately try to avoid winning?

Yeah, there is.

There's anti-knots and crosses

where you have to play such that whoever makes three in a row loses.

Yeah, that's fun.

But again, that's also, there's so few states, and actually, Alex, right here, that these sorts of things are solvable.

Yeah.

Chess.

So chess is not solved.

Oh, okay.

Because partly there are just so many possible states the game can be in.

Yeah.

Partly, it's just a very complex game.

So you don't have to have analyzed every single state for a game to be solved because you can just come up with

a strategy which guarantees a certain outcome.

Let's say there's a game where you play by putting a mark on some kind of massive grid, and as player two, you can just always do the exact symmetric move or whatever player one did

and guarantee a draw by the end of the game because you stay in lockstep with them for whatever the rules may be.

That's now a game where we haven't analyzed every possible state, but we can say it's solved because we know there's an optimal strategy for player two such that they will always draw.

Yes, however, one way to do it is just to analyze every single state.

And in anti-chess, so that's chess where you win by the other person taking your king.

Oh, wow.

Now, anti-chess is interesting because normal rules except if you can capture a piece, you have to.

Okay.

And that means you can force your opponent to do a certain move.

That's much more doable, yeah.

Yeah.

And that's why anti-chess has been solved to an extent.

There's a winning move.

I think the first player to play moves the fifth pawn from the left in.

And with that opening move this like it's quite complicated but there's a series of other moves no matter what the second player does the first player will win anti-chess okay and the reason we can analyze anti-chess but not regular chess is that forcing element because you can control several moves of your opponent in a row by just constantly feeding them pieces

and that makes it possible to solve whereas regular chess forget it

Now, knots and crosses solved.

You can actually buy, you can play knots and crosses against a book There was a book written by Dennis Gurio

called Solo Norts and Crosses.

Okay, where you just look up the current game state you look up the board in the book Yeah, and it will tell you where it's moving what move the the book wants to play.

Okay, and then you do your move and look up the next one.

Oh, I like that.

There was a more modern version called tic-tac-tome.

So the idea is like

very boring choose your own adventure book yeah well that's what i was gonna say

when you when you were describing a solvable game that's where my brain went i went oh it's a choose your own adventure yeah 100 yeah yeah and you'll never beat the book i can't remember off the top of my head if either of those have deliberate mistakes where you can win um my friend james grime owns a copy of both of course and uh he brought solo knots and crosses along to a show one time to show like we played it with the audience it was that evening of a necessary detail of course it was huge amount of fun.

Yeah.

And my friend Matthew Scroggs built a computer out of matchboxes and beads that learns to play knots and crosses.

I've got a video on my channel about this because it's basically machine learning, but again, there's one matchbox per possible state the game can be in.

And it's such a small number, you can

just have a box for each.

And then there's this complicated system where you train the match boxes to play by adding and removing beads if it wins and loses to reinforce bees bees yeah yeah so regular norths and crosses very simple very boring

people have come up with a bunch of other variations on a theme

you can do norths and crosses where instead of having just the three by three grid and absolute edges you have it where it wraps around

so you can use what are called the super diagonals yeah big fan of a super diagonal you talk about it in your double talk i do talk about it in my double talk yeah i love the super diagonal you used a super diagonal in your graph for time in the last episode we did there you are yep good old super diagonal where the line went from zero to twelve and then wraps around comes back on perfectly good diagonal one of my favorites they're super so at super diagonal knots and crosses or you're playing it on a cylinder you can't draw anymore you gotta win so it takes out the draws which is nice fun because there's no way to arrange all the

hugs and kisses such that there are not three in a row.

Before we go any further,

Connect 4 is like a bigger version of tic-tac-toe or notes.

Is that a solved game?

Connect 4 is solved.

First player wins.

The first move is they have to play in the center.

And then no matter what the other player does, it's a guaranteed victory for the first player.

But it's such a complicated strategy.

I was going to say, because I've played against you.

No, I don't know.

I don't think it's human doable.

It's really complicated.

You actually say that, but I mean, you've seen me learn stupider things for more ridiculous reasons.

There was a paper called A Knowledge-Based Approach of Connect4, which was written by someone called Victor Ellis, I think in the 80s, from memory.

Yes, 1988.

They were the first person to crack it

and solved first person will win with optimal strategy.

Wow.

And you know what?

Interestingly, you've now pointed out, because Connect4, if you ignore the gravity aspect, if you imagine you can just put the pieces wherever you want.

Oh, yeah, I forgot about gravity.

Exactly.

That makes a mild difference.

I forget the exact ratio of a connect4.

But surely the gravity element then actually makes it more solvable because you're being forced.

It changes it.

So connect four

is played on a six by seven grid.

And you have to get four in a row.

Yep.

Whereas tic-tac-toe is on a three by three grid.

You have to get three in a row.

And all three of those numbers, you've got a something by something grid, an M by N for two numbers, M and N grid.

And then you have to get some number K in a row.

Yep.

That's actually, that is the generalized version of tic-tac-toe.

It's an M by N

grid with K in a row to win.

And there's a whole family of these.

They're called MNK.

Is it MNK?

Yeah.

Is there a reason for those letters being used?

No,

there's a bunch of conventions in maths for different letters you use to mean different things.

So X and Y are often used as

real values that continue between numbers, whereas M and N are often used as whole numbers.

As is K.

Yeah, I know about N.

Yeah, so we have to use N for number.

Once you've used N, people would also use M.

For bumba.

For mumba.

I forget why.

K?

But K, I, J, and K are often used as whole numbers.

L is not often used because it looks like a one.

So

M and N is a common way to do a grid, and K is a constant that you might include.

So,

but there's no hard and fast rules.

You can do what you want.

But if you follow the vague conventions, it makes it easier for other people to understand.

Yep.

So it's called an MNK game.

Why does that sound?

It's making me think of multi-level marketing, MLM.

MLM, yes.

Like an MLM game.

Whoever starts playing first is most most likely to win.

So different combinations of M and N and K

either give you solved or unsolved versions of the game.

Yes.

So 333, as we know, is solved.

There's another version that's called, I'm going to mispronounce this, Gomoku.

That's...

That sounds Japanese.

It probably is Japanese.

Almost certainly Japanese.

That's five in a row on a 15 by 15 grid.

Sometimes bigger grids.

But that's a 15, 15, 5 game.

Oh, it looks a bit like Go.

It's played on a Go board, yeah.

Huh.

But different rules.

Well, there are different versions of how you start the game.

But then it's basically Connect 5 on a Go board.

So no gravity, which distinguishes Connect 4.

Yep.

So Connect 4, which is our 6, 7, 4 game, but with gravity.

And different games can have different additional rules.

Like Connect 4 has gravity, Gomoku has sometimes you start by placing like two whites and a black at the beginning because the first player had such an advantage, they changed it.

So you've got to put two whites and a black, and then you're the second player.

You can now decide if you're white or black.

Ah, and there's other rules like you can either add an extra black or you can add one of each and send it back to me to decide what I want to be.

Okay, so you can add all these extra twists.

15155 5 is solved.

First player will win.

Actually, it's impossible for these sorts of games to have a strategy for the second player.

So in this entire family of games, if you're playing second, your best case scenario is a draw, assuming everyone is playing with optimal strategy.

And the reason for that is these are a category of games where there's no downside, there's no penalty for making a move.

So it's not like you can put an X somewhere, if you're X, and later on it gets in the way or causes you a problem.

Like in chess, you can move a piece forward, but that piece can be taken out of the game.

You can be taken out of

it available to go somewhere else instead and all that.

Whereas in Knots and Crosses,

all the symbols are equivalent for each player.

You've got an infinite supply of them.

Yeah.

And they're indistinguishable.

So for these games, if you imagine a massive grid, an N by M grid, we're playing some crazy version of it, and I get to go first, but you're like, you're player two, and you know there's a winning move for player two.

You're like, got him.

I could get my first one and decide, you know what, I want to be player two.

And I just put my first move in some arbitrary, far-flung corner of the board.

And I'm like, surprise, jerk, now you're player one, because I've thrown away my first go.

Okay.

And hypothetically, even if I did later have to use that spot, it's great.

It's already there.

And then instead of doing that move, I can put that one in some arbitrary other space.

So, because player one could opt to become player two,

and which makes the other person player one, yeah, you could then throw away your spot and back and forth.

So, there's it's impossible to have an optimal strategy for player two

because player one could co-opt that strategy instead.

Got it.

So, we know for all these games, either it's guaranteed draw or it's guaranteed player one win.

So, to answer the problem as stated,

for completeness, they wanted to know at which point is it not solved?

Is it fun again?

And I can confirm that if you're playing on a board, which is something by four

of any size by four,

and that something is between nine and twenty by four.

So if you're between nine by four and twenty-nine by four, and you're playing connect four, first of four, but without gravity, so tic-tac-toe but four in a row wins

all of those boards are currently unsolved

so there you are so if you want to play a version of the game where you're guaranteed nobody's going to have the perfect strategy a four by nine board of knots and crosses four in a row wins have at it

there are other versions where you keep playing and you just get a point for each time

You get four in a row or whatever it may be so then you have a score by the end.

Yeah, and you have to agree in advance, if you, like, if you're playing this where it's four in a row to win,

and you put in a symbol and you complete a row that's like five or six at once,

does that count?

And some versions of the games, it's four or more, and others are exactly four or whatever the number may be.

Okay, so for instance,

if you had three going up,

and then

a diagonal

what I mean is if you've got like one, two, three in a row,

not gravity.

I keep forgetting there's no race.

Yeah, no gravity.

That's what it is.

One, two, three in a row, then a space, then another one, two, three, and you put one right in the middle.

You've just made a row of seven.

Does that count if you're playing connect five?

Yeah.

Yeah.

Agree in advance.

Changes the rules.

Yeah.

But if it's exactly four,

anything between a four by nine to a four by twenty-nine grid, connect four,

no gravity.

Your opponent cannot have a built-in strategy because it's, as we are aware, unsolved by humans.

So this might also be a fun way for people to display their collectible coins.

100%.

Pennies.

If your friend has bought you several pennies, you can do that.

You can build a little

rack.

You would have to...

Or like a little game board.

Little game boy.

Yeah.

Game board.

Finally, ultimate tic-tac-toe.

Ultimate knots and crosses.

which Alec referred to in the original problem.

We're going to have a quick game.

So do you want to describe to the listener what I'm setting up here?

Matt seems to be drawing a traditional tic-tac-toe 3x3 grid.

Yep.

Like a hash.

He's now just got a different coloured...

He's just got a different coloured pen and now he is putting the same thing into each of those squares.

So here's the way the game works.

There's a pen for you.

All right.

So first of all, you've got to pick a cell and then you make a move on the game within that cell.

I'm going to do a circle because I like circles, and I'm putting it in the very center.

Middle, middle.

Of the

one in the middle.

Now, the bonus rule that makes this interesting.

So to win this, you've got to win three games in a row.

Okay.

So by forming a line is winning all three of those games.

Yeah.

Except you have to go in the equivalent game that matches.

the smaller spot the previous person just went in.

So on this sub-game, you went in the middle.

Yeah.

That means I now have to play the middle game.

Okay.

But if I go top right,

you now have to play top right.

This game.

Oh, got it.

Okay.

So you can not only are you putting your move in to win each sub game, there's the meta strategy of you're directing where I have to play next.

Now, what happens if I go, so if I go middle again.

Then I've got to play back over here.

Yep.

So I've gone back.

I've gone in the corner.

I've put a zero in the middle.

Matt has put an X on the other side.

For the sake of symmetry, I've gone in the middle on the other diagonal.

Ah,

we see what has happened here.

Yes, but you've got to give me an.

But you might.

So on the center one now, I've set it up so there are two places that would win for me.

And in a normal game of knots and crosses, game over, because you can't block both.

Yes.

So I wouldn't send you do not want to send me back to the middle because I'm going to win if I go back there.

I see.

So now you can't take any more center spots.

All right.

I am enjoying this.

We will.

get edited down.

Now, best I'm aware,

this version we're playing has been solved if once someone wins a game, you still have to keep playing in that now pointless game if you get directed there.

But there's another version where if you direct someone to play on one that's already finished, it's a free move.

They can go anywhere.

I see.

And that's not solved.

Okay.

To the best of my understanding.

And that was a lot more fun than regular knots and crosses.

But even if it like, even if this was solved, it's like Connect 4, the optimal strategy is not human-doable.

So we know that

you've got no friends to play with.

No, if someone's got like a massive encyclopedia of instructions they're referring to.

Yeah.

Yeah.

So even if you know things like Connect 4, it's still fun to play, even though it's solved.

And this falls into that same category.

So I highly recommend if you do need to play knots and crosses in a pinch, go for ultimate knots and crosses.

Alec, I hope that solves your problem.

I'm going to give that a

ding from Dingleberry.

From Dingleberry.

Yeah.

Other game of dings and dongs.

Yeah, there you go.

You don't want to see what

the symbols are.

They take longer to draw.

Our next problem comes in and they've started hi Beck, hi Matt.

Really covering their bases there.

So Matthew Smart says they're a big fan of the podcast and of you guys in general, they're still hedging their bets.

So Matthew's problem.

They have two work colleagues, both named Neil.

They are father and son.

I bet they're American.

Americans love reusing the same name for different generations.

To differentiate them, we call them Big Neil and Little Neil.

That could be workplace bullying.

Matthew complains that's not particularly original and they were wondering how many nils could you have with ever decreasing sizes and what would the smallest of all nils be called?

They pointed out they hurt the parameters will stop the problem from taking infinitely long to solve.

It's not a not a concern most problem posers have to be honest.

They want to say here are the rules.

You can only put one word in front of nil.

So you can't have smaller than the previous nil.

That's good.

I guess it rules out kind of, you know, recursive nils.

Yep.

yeah,

you can only use words in the English language, so you can't generate gradually bigger and bigger nonsensical words to describe the nils.

Kind regards, Matthew Smart back.

By the way, first of all, Matthew said hi.

Hi, Matthew.

Secondly, have you found a way to work out

how many nils there are and what would the smallest one be called?

Uh,

yes, good,

Maybe.

Maybe.

Well, no.

I backed down real fast.

I liked this one because it reminded me of something that I've mentioned on the show before.

My

grandparents on my dad's side, we called them Nanan and Dad Dad.

That was actually because that's what my dad used to call them when he was a baby.

Oh, wow.

And that stuck around.

And I think they were like, oh, we'll call them.

Generational nicknames.

Yeah, to differentiate from grandma and grandpa on the other side.

So like, oh, nan and dad, dad.

And that meant that my great-grandparents, the two who were still alive when I was born, were big nanan and big dad dad.

Got it.

I realized there's something missing from this, which is they've got a big nil and a little nil.

Yep.

They don't have a zeroth nil.

No.

It reminded me of in Bob's Burgers.

They've got a character who's called regular size Rudy.

Yes, yeah.

I really like that.

Out of context, that's just what they call that that kid in the show.

Yeah.

Because there's a bigger or small one out there, right?

Well, yeah, because I don't think they ever introduce the other sized ones.

No, yeah.

Not that I'm aware of, which is even funny.

Yeah, well, first, you need a default Neil.

Yeah.

In order to.

What is your standard issue metric Neil?

Yeah.

And then you can have a bigger Neil or like a bigger

little nil.

Yeah.

I realize that you

I feel like this is cheating, so I'm going to say it, but then immediately discount it.

You could

have.

Obviously, it's words in the English language, so you can't have numbers.

So you wouldn't have...

Numbers have words.

One nil, two nil, three nil, as in.

Also, then it starts to sound like you're doing very poorly in a game.

I like to add that numbers are also apparently valid words.

Yes.

And

I'm the first person to solve most problems by using numbers.

Sure.

But I do agree we should discount just numbering the nils.

Because then, even if you are spelling it with letters,

when you get to 21, if you were to say you're not going to allow dashboards,

squash it all together.

You could say it's two words.

And then you're limited.

Five, five, five.

So I think that's potentially out.

You could do divisions.

So you could do.

So rather than little, you do half-nil, quarter-nil,

eight-nil.

Okay, yeah, yeah.

I think we're also going to discount that for the same reasons as the numbers.

Okay.

I think it's all, it is on, it's slightly in this area.

I think it skirts into being over the line of being allowed.

Right.

I think we should go into metric kneels.

Well, like a mega kneel.

Yeah.

A kilo kneel.

Yeah, exactly.

Exactly.

So I think it should you start at just kneel.

Regular kneel.

Yeah.

And then above kneel, deci kneel.

So you could do kilo Kilo-Neal?

Kilo-neal.

You could buy a thousand.

If you're just doing thousands, yeah, kilo-neal, mega-neal, giga-neal, tetraneal.

Yeah.

Yeah, it's very funny.

Going down.

Pentenal.

Yeah, milli-neal, microneal, nano-neal.

Nano-neal is a nice thing.

Nano-neal, that is lovely.

Yeah.

Yeah, yeah, yeah.

Who doesn't want to meet nano-neal?

Nano-neal sounds like...

It should be a nana.

It sounds like a nana.

Yeah.

Yeah, so.

Hey,

check out who's here.

It's nano-neal.

Hey, hey, everybody, what up?

Oh, you just missed Giga Neil.

Liquid measurements.

Right?

Yeah.

You could have like a millennial, which is almost a millennial.

A millenil.

A millenneal.

Nice, nice.

Yeah.

So I need to ask,

how many words do we have for,

let's say, length or...

Or size or something.

Yeah, in metric.

Oh, a metric.

Well, we can just keep generating them.

You just take the, is it Greek prefix, chug it on?

But I guess, because they've got to be in the English language.

We can't start inventing

no, but you're getting dangerously close.

You basically go back to what we've just discounted, which is numbers.

Because after a while, you're just going tetroneal, pentroneal, sextoneal, septonal.

Yeah.

Octoneal.

We get a little bit lazy after a while, don't we?

Oh, yeah.

Like a lot of things in counting, we start creative

and then really phone it in.

It's like once you go past 10,

11, whole new number.

Great name.

Love it.

12.

Okay, pretty creative.

13.

It's basically just three with 10.

And then 14, 15, 16.

Come on.

Crazy.

But then we go the other, like,

I've been learning French and the numbering is interesting because

in French, when you start to get to like 20s and 30s,

it starts to be like maths.

Now, I got some bad news.

Everything is maths.

But yes, the French numbering requires more arithmetic than you would expect if you're not already fluent in it.

Yeah.

In French, up to 69,

it uses a base 10 system.

But when you reach 70, it switches to a vigesimal system, which uses base 20.

Yep.

Which is annoying.

Super annoying.

In Japanese, I like Japanese.

Japanese is sort of similar to English in that when you're counting, you get up to like ju for 10 and then it's uh juic ju ni ju san juyon so that's like ten one ten two ten three and then you get up to niju which is twenty that's two ten so then you go nijuich niji san ji ju niju so yeah it's just you're saying it depends if the nils are french or japanese yeah well in english i'm just saying the teens are dumb oh yeah because we we go up to 10 fine 11 what we never use 11 ever again hate that one i love it 12 one off one off name 13

we should have more of them all of the numbers then all the numbers another number in the low 3000s that just has a name i'm so glad i don't have to learn english because the more i learn other languages i'm like wow

so i did

play around with whether you could have little nil yeah smaller nil tiny nil

micronil teeny kneel Yeah

the problem with that is that then it really comes down to the

Perception of the other person as to whether teeny is smaller than micro or vice versa Yeah, my next question was because what you could do is just get a set of all the words in the English language that mean size So you got gargantuan nil you got big nil you got all that jazz, right?

Do they need a ranking?

Does that matter or they just need to be different?

Well, I think it needs to be ranked because if it's different, then you might as well just assign a different word, right?

So you might have to do it.

You might as well just start at the dictionary,

do our drag meal,

and then whatever the next one is.

Whatever the next one is, you know, the other words.

Yeah.

And so on and so forth.

So, what you'd need to do is get a set of all the words that mean a size.

Then you have to get a lot of volunteers and you'd give them all pairs of words and say, which one's bigger?

And then you do enough of that.

I sense that you're writing some terrible Python code.

No, no, no, this would be like a big online survey.

We're not going to do this.

It'd be a lot of effort for no discernible reward at the end.

But if anyone out there listening,

we will promote it.

So, how many people would we need to fill out the survey to work out what is

depends how

much everyone's in agreement?

Would you do it that you give everyone a pair of words and they decide what's bigger and do it that way?

Or would you just give them all the words that mean big, large, enormous?

You give them all, and then each person ranks them and then you work out how many or some are.

I think it'd be easier to do a pairwise comparison.

And there's already a bunch of maths done for how you would then combine all those results into

honestly.

I don't have an answer.

I was kind of hoping we'd come out in this conversation.

Oh, really?

I love your approach.

I feel like we've broken the.

My suggestion was to go

metric.

I think.

That's great, but I feel like it does revert to being just numbers.

Yeah, it is.

Just a different version of that.

Yeah, it's just a different version of that.

Yeah, I think this is going to be not yet to be dinged, but potentially, if anyone is looking for a project to do in their downtime.

I mean, how many...

You know what?

I'm not saying you haven't done this.

English words which mean a size.

I'm just getting a lot of words that are synonyms for the word size

that don't.

I want words that represent a volume.

Yeah, so I'm going to look up large because I'm assuming we can go up in Niels as well.

Yes.

And this is the thing: I'm working on a show at the moment, a kids' show at the moment, where I don't want to say too much because I don't know what I'm allowed to say.

There's always an NDA for a new show, but essentially, the main character's parent, so let's say the main character is called Matt.

Yep.

Their parents are called like mum Matt, Matt.

And then going up the mother's side, it's then grandmum matt.

Yep, great-grandmum Matt, great grandmat.

And then it's very similar to what we have now.

However,

we were talking about this in the writer's room, and we think, because we haven't decided, but

this might end up being sort of show Bible stuff.

But when a new generation is born,

they all switch names.

Everyone shovels up names.

Everyone shovels up, yeah.

So you would then become

dad Matt Matt.

And then you'd become granddad Matt, granddad Matt.

So, yeah, and that would just be your name.

That's how everyone's

exactly.

Yep.

Yep.

So I did just find on a website a worksheet for kids with size words.

And I can confirm if size words is to be trusted, there are 27 nils.

That's so specific.

Some of them feel pretty, at least 27, let's say.

Some of them are pretty straightforward.

Little Neil, itty-bitty kneel, gigantic kneel, enormous kneel, humongous kneel.

Some you might have issues with.

Deep kneel,

petite kneel, oh, that's fine.

Low kneel, hmm.

Skinny kneel, that's a different dimension.

Long kneel.

I take my kneel's long.

Long nil is long.

Wide kneel.

Yeah.

Yeah.

I mean, I put the word large into word hipposaurus.

Now, some of these are

conjoined words or something, but it's got a dash in between.

I'm going to say no to dashes

because it's meant to be one word.

But even so,

it's over 500 words.

That's just for large.

And are they all

big nil, colossal nil, enormous nil, giant nil, gigantic nil, huge nil, great nil, massive nil, monumental nil, humongous nil, sizable kneel, grand kneel, immense nil, super nil, astronomical nil, cosmic nil, elephantine nil, gargantuan nil, ginormous kneel, titanic nil is

Neil.

Serious Neil.

Serious Neil.

Now that is a serious amount of Neil.

Unwieldy Neil.

Prolific Neil.

Stately Neil.

Great.

Phenomenal Neil.

Or Phenomenal Neil.

Phenomenal.

Phenomena Neil, definitely.

Kingly Neil.

Cracking Neil.

Cracking Neil.

Increased Neil.

Increased Neil.

I'm going to disallow that one.

There's also lengthy Neil, which is a bit like long.

I'm good friends with long Neil.

Yeah, exactly.

Also, economy, Neil.

Economy, Neil.

If you can't afford,

can't you and Neil?

Yeah.

Theatrical Neil.

Oh, yeah.

Then we're getting back to issues we've had in previous problems where it kind of comes into the eye of the beholder as to what's big.

What do you think is a reason?

Opulent, Neil.

Opulent, Neil.

Unfathomable, Neil.

Neil,

beyond the comprehension of the human mind.

Noticeable Neil.

Which also suggests that the other directions are

unnoticeable.

Like, I'm just looking at the big ones.

Let's have a look at small ones.

For every kneel, there is an equal and opposite kneel.

Neil is such a great name for this, by the way.

This must be good.

For people listening at home, Becca's laughing too much to even read out the Neil names to me.

I love these.

Okay.

Yep.

Toy-like kneel.

Toy-like kneel.

Becca's just going to take a moment and we will resume the kneels.

Portable kneel.

Good old pocket-sized kneel.

There is also pocket kneel.

Shrimpy kneel.

Shrimpy.

Bantam kneel.

Some of these are unavoidably an insulting name for a Neal.

Reduced Neil.

Reduced Neal.

Sounds like one of a recipe.

Yeah.

Oh, gosh.

Concise Neil is a

peanut kneel.

Peanut Neal.

Travel Neal.

Now, we wouldn't be able to use this one because

it's two words, but one of the options in here is not big.

Not big?

I thought you put the word not in front of all the big words.

Embryonic Neil.

Embryonic Neil.

Lesser Neil.

Yeah.

Lower Neil.

Neat Neil.

Trim Neil.

Dainty Neil.

Cute Neil.

Oh, that's all Neil's.

Handy Neil.

It's a convenient Neil.

Yes.

Dinky Neil.

Dinky Neil.

Narrow Neil.

I feel like there's no limit.

Yeah.

Me a Neil.

Mia Neil.

He's but a mere Neil.

I mean, look, there is a limit in that at some point.

There's a finite number of words.

There is a finite number of words.

Yes.

How many of those you're happy to class as a size-based word is also limited.

Yeah, but there's at least hundreds.

Yeah.

I would say...

I'd say not thousands.

Yeah.

But I would say at least a thousand, both going up and down.

Up and down, down.

Agreed, agreed.

So I think you could get many, many generations of nil out of this if you could agree on the scale of these words.

Well, I would say, first of all, going back to Matthew Smart here, we do need a ranking because they want ever-decreasing sizes.

So, we'd have to solve that problem, but we have a mechanism by which we can do that.

They also do say these are work colleagues.

Now, we're pretty confident, push comes to shove, we could whip up a thousand nils.

It now comes down to how big a workplace

does Matthew Smart work in?

Because if they've got fewer than a thousand colleagues,

we're done.

If

they work somewhere bigger than that, we might have issues.

So I think we might have to throw this

back.

So I can't yet give you an ever-decreasing series of dings,

but

I feel like we go back to Matthew and say, look.

At a pinch, we could find and rank a thousand nils.

Yeah.

How many do you need?

Otherwise, you're looking at just big nil, bigger nil.

Yeah, big nil, bigger nil, bigger row nil, bigger rural nil,

etc.

Deflated nil,

as opposed to inflated nil.

I'm sorry, these are very fun.

So I think you have brought us a colossal solution.

But we'll throw it back to Matthew to find out if it's adequate.

Yeah, you can ask epic Neil.

We've reached any other birdsness.

I think we decided on birdsness.

Yeah.

Well, in the meantime, I've looked it up.

Oh!

Beak.

But beak and bill, yeah.

The difference?

Yep.

There is none.

What?

They are cinnamon?

They are cinnamon.

They are cinnamon.

You can tell I'm a bit hungry game.

They are synonymous

with each other.

So all birds have a bill.

Or a beak.

But most people have chosen to use beak for the more pointy types and bill for the flatter rounder types.

But that's not a strict definition.

No, it's not.

It's just something that we've kind of started to vaguely use.

Right.

One day it might be codified and become...

Well, because I wouldn't say that a platypus has a beak.

I wouldn't say it has a bill.

I wouldn't say that a platypus has a beak.

I would say it has a bill.

Yeah.

And now I'm...

Because it's a duck-pill platypus.

Yeah.

Is that just why?

I don't think it's a is it a bird.

But I feel like platypus's bill evolved separately to beaks or bills.

Whereas bird, beaks and bills have a common ancestor.

Technically.

Technically.

They don't have.

Technically they don't have a bill.

No, because they've evolved a flappy thing on their face.

Yeah, because it's a leather.

It's not bone in the same way that a bird's beak or bill is technically bone.

So there you go.

So in conclusion, any other billness

is acceptable?

Yes.

Because it's duck fat.

Obakness.

Beakness would be equally correct.

Any other beakness?

Beakness is a better part.

Got it right.

In any other beakness, also animal related.

In episode 089,

we discussed if dogs have four legs or two legs and two arms.

Because a fantastic listener named Tim was arguing with their partner.

Their partner was adamant arms

and Tim was adamant legs.

All legs.

Now we made a lot of fun of Tim.

We may have come on a bit strong.

Tim, good sport.

Yeah.

We decided, and we've already done this in any other business, so people think this sounds familiar.

We decided definitely arms.

Dogs have two legs and two arms.

Bunch of biology and evolution reasons.

Made a lot of fun of Tim.

Tim took it very gracefully, gave us the ding.

Yeah.

Thanks, Tim.

Good sport.

Yeah.

I would just like, the reason we've circled back to this is I just want to tell everyone, we're done.

Yeah.

People are still using their front legs to type.

And they go to the problem posing page at the problemsquared.com.

They choose solution and they keep adding more votes for arms.

and some people even supplying more reasons.

Yeah.

Now, it's been a long time since we've had to forcefully close a problem.

Yep.

The what animal would form the longest line if they all queued up.

We're done.

Dogs have arms.

Leave Tim alone.

Closed.

End a problem.

Yeah.

Good.

This is very cathartic.

It is, isn't it?

We should enter the closed zone more often.

Technically, that's what the ding is meant to do.

The ding is meant to ding is the dingfinitive.

Yes.

That's why some

games don't have dings.

Because they're still open.

Yeah.

Dinged.

Done.

Let it go, guys.

We appreciate you all getting involved, except in

these few specific cases where we're done.

However.

However.

If you're a Patreon supporter, you can

message us up.

You're paying for the right to keep going.

We might not read it out loud.

No, but we will read it.

And we won't mind.

Yeah, we won't mind.

If you're a Patreon supporter, you are welcome.

If you're a patreon.com slash a problem squared, go nuts.

Yeah.

Speaking of Patreon supporters.

Oh, I just was.

We like to thank three of our Patreon supporters at random at the end of each episode by mispronouncing their names.

For example.

On this episode, we'd like to thank B N.

That's it?

That's it.

C.

Handler.

Oh, that was good.

Or C.

Handler's myth.

Myth.

They are a myth.

I've noticed since we started mispronouncing names, people's names have been getting longer.

And sometimes easier.

I feel like people are going in and just making sure we've got their full name to mess up.

Yeah, and some of them have been a real challenge.

Yeah, apart from BN, these ones are all pretty full.

Okay.

C.

HALS.

I'm just doing what you did to me.

Yeah, you are, yeah.

Yeah, but it works.

C.

HALS.

C.A.

Elkins.

Kai ends.

C.

L.

Cow Kai

ends.

What about Charles Calkins?

Charl.

You love moving the space.

I do.

Charl Leska

Elkins.

Lescal.

Lescale.

Lescalkins.

Traditional pronunciation.

As in the family of Lescale.

That's the one.

Thank you.

Also, did you know that show Kath and Kim is a pun on

Kith and Kin?

What?

What does that mean?

Kith is friends.

Kin is family.

Friends and family, Kith and Kin.

Oh, really?

Did I know that?

Kath and Kim.

Kathy and Kim is

Kath and Kim.

New to me.

Fun fact.

It's a little fact for everyone.

Just when you think the podcast episode stopped giving.

I know.

Now just wait forever.

No, it's not.

Yeah, everyone, pilot on that.

That's fresh.

I'd also like to thank Matt Parker.

Myself, Beck Hill, and someone who I wouldn't even put in the category of ducks.

I'd like to thank our once was an ugly duckling and is now a beautiful slum.

I don't know if that's 100% compliment.

I'm nagging her.

I think so.

Our producer.

Before you worked with us, you were nothing.

Yeah, that's right.

Lauren Armstrong Carter, who is infinitely patient with us.

Correct.

I would like to thank

infinite Lauren.

Good old infinite Lauren.

The biggest of all the Laurens.

In Biggins the biggest Lauren.

All right, I got my battleship open again.

Oh, mine hasn't fallen out.

Oh, mine did.

I fixed it because I took a photo last time.

Okay.

Oh, it's my turn is done.

Yeah, yeah.

Okay.

We've hit a rhythm where you go first, I go second every time.

Unless I throw my move and then you become

player two.

Yeah, I have two.

Player one.

Yeah.

Yeah, player one.

That was.

I keep the end of that wrong.

All right.

Um

J6.

J

six

miss

now I said A1 last time

because I'm systematic.

Yep, but this time I'm gonna say B2

Miss.

You can probably extrapolate my next

eight moves

based on that.

All right,

till next time.

Just them falling out.