069 = Tiling Planes and Driving Planes

Hello, and welcome to A Problem Squared, the podcast equivalent of money, in that we solve a lot of problems, but we also cause a few.

And everyone always wants more of us.

Your hosts are Matt Parker, who is a bit like a million dollars

because he's hard to get hold of.

So true.

So true.

And when you do, you don't want to spend me.

That would defeat the purpose.

That's true.

Yeah.

Yeah, that's right.

I want to be able to hold on to you so I can say, I've got it.

Got it.

You want to invest.

Yes.

If you get me in touch with me, you want to invest that contact.

You don't want to spend it immediately.

Would you say I invest you, Matt?

I think so.

I think so.

Yeah.

Sure.

I think you're getting involved.

I don't know.

I think you tend to feel quite spent.

Well done.

Yes.

And the other host is me, Beck Hill, the spare cash of this duo, because I'm petty.

Hey, oh my goodness, wow, good intro.

Thanks, man.

That's great.

I always thought of you as fungible.

Yeah, putting the gibble in fungible

on this episode.

I've worked out the ultimate decoration pattern for your home or office.

I find out whether it's possible to fly a plane on the autobahn.

And we have any other AOB business.

Ka-ching.

Ka-ching.

Ka-ching.

So, Matt.

Back.

The last time we saw each other was in a tent.

We were in a field, yes.

In a field.

I'm no longer in a field.

No,

we are recording remotely, though.

It's remote this time.

Yeah.

It's a busy, busy point in my life at the moment with

travel and book writing.

Yeah, you're a very busy man.

Oh, it's too much.

I got COVID as well.

That pushed a lot of things back.

Yeah, that's really squeezed my schedule now.

I got better just in time just in time to make a trip to munich i um did i tell you about this i went and saw the next part of a long-term art installation get put in no no i saw some pictures yep of you guys with some concrete that's that's exactly it although i mean this this is just in our whatsapp group i did oh we were haven't i don't think i've shared them publicly alien put a tick tock out if people want to actually go see what we were up to there's a pyramid they're building outside a town called Vemding, which is an hour and a half drive out of Munich in Germany.

And they had the 1200 year anniversary of that town in 1993.

And an artist, local artist, thought, wouldn't it be fun to start an artwork now that will take another 1200 years to finish?

So it's going to be the same length of the town.

So the town was like first recorded in the year 793.

And so 1993, 1,200 years later.

And you think, that's such an incredible amount of time.

And so they're going to build a pyramid out of blocks.

And it's going to be 120 blocks.

And they're going to put in another block every 10 years.

So once a decade, they lift up a massive cuboid of concrete.

It's about 1.2 meters by 1.2 meters.

and then 1.6 i think meters high so it's you know big bigger than a a human.

And they put one every 10 years.

So we saw the fourth block go in.

It was pretty exciting.

It also feels a bit like, like there's going to be a moment where everyone looks at a half-finished pyramid and is like, oh, bless them for thinking we would get this far.

I was wondering about this because my theory is, and by the way, for the record, I love this.

I think it's a great artwork.

I think it's a very good way to make us think about the passing of time because you can see how big it's going to be and you can see now there are four blocks put in and that's taken 30 years.

And so you can see blocks appearing on a human life scale, and you can see how much is left to go.

And you're like, that's an unimaginable amount of time.

But if they'd started it when the town was founded, it'd be done by now.

Like, so it is a reasonable amount of time on the time scale of a town or a city or something.

So I think it's really, really nice.

But I was thinking 10 years is probably about the right amount of time because who's going to be the first person to break the chain when the last one just went in 10 years ago?

and then you don't do that.

I feel I, I mean, I think it might keep going the whole way.

I don't know if, I mean, who's going to break that chain?

Probably just, you know, society collapsing, the overturn of capitalism, concrete being banned, or they'll go old school and just be like a giant block of granite or something.

But I would enjoy it.

So we got to see a big bit of concrete get picked up by a crane and get lowered into place.

And now it's

this for a video or just funsies?

Yeah, a bit of both.

It would be a video.

Yeah, yeah, yeah.

So at some point, if it happened more often than once a decade, I might have postponed going over to film it.

But given it happens once every 10 years, I was like,

I can't miss it because otherwise it's 2033 before the next one.

I'm definitely going to be there in 2033.

While I was there, I filmed, have a conversation between 2023, Matt, and 2033, Matt.

to go out in 2043 to remind everyone that the sixth block is about to go in.

I just need to, I need to, in 10 years from now, record the other half of the conversation.

And then 10 years after that, assuming I'm still making YouTube videos, put out the joint conversation.

And then I did a bunch of takes of just me saying things like, yeah, we did not see that coming.

I'm like, oh, yeah, that makes sense.

And so I can go through and edit them all.

And this person sure got him or herself into some sort of predicament.

Yeah, exactly.

Yeah.

You know the best bit?

They made a mistake.

Yeah.

They made a mass mistake.

Oh, brilliant.

Is the pyramid going to be upside down or something?

No, no, no, not quite.

It's going to finish 10 years too early.

Because an artist.

Oh, fence post problem.

Fence post problem.

Yes.

Classic.

So good.

So they want to.

For any new listeners, this is referring to the fact that if you were to make a fence, every

you count the poles, but if you want the actual fences, the bits that go in between the poles, it's a different number.

Yeah.

Essentially.

There's always one more post.

Everyone forgets the zurith post.

And so they, the artists thought 1,200 years, well, that's easy.

1,200 is 120 times 10.

So we just do 120 blocks every 10 years.

And then they put a block in on the zirth year.

So now

they're not going to have the final post.

So they're going to finish 10 years early.

They're going to accidentally finish in the year 3,183.

instead of the actual 2,400-year anniversary in the year 3,193.

So they're off by.

They'll need to put a slide in after 10 years or something, or like a, you know, a flag or something.

Exactly.

I know.

I tried to engage the organizers in discussion about what their plan is, and they were seemingly quite disinterested in the problem.

They had a real someone else's problem attitude, if I may.

So have you been back?

You've got a new background.

I've been good.

Yeah, it's a dvey cover.

It's hiding the jackets in the cupboard.

I'm back in the recording cupboard.

No, I'm good.

We had some nice weather recently.

We finally had summer.

came a bit late.

Yeah, for two weeks.

And so I organized, you had COVID, so I didn't invite you because I didn't want you to get FOMO when it was happening.

I organized a large game of hide and seek in a park.

What?

I would have gone.

I would have done that 100%.

Yeah, it was really fun.

Yeah.

That's so dumb.

Although what we, it was interesting because we realized, like, everyone was like, so what are the rules?

And we realized that we all had to like remember how to play hide and seek.

And also, like, so we we we did it that i stayed at the base we created a base so that we went by base i mean just like somewhere where everyone could drop their bags right yeah so as as the organizer i i took the bullet and i was like okay i'll sit out the first round because we're at all the bags

yeah exactly the rules were that once you were found you had to then seek with the seeker but you had to always be within talking distance you could

you can't divide off and yell and be like i found them over here yeah yeah yeah so you would seek with them and then the last person to be found would be the seeker on the next round got it just been seeking then watched the bags on the next round and that worked out well because most people seeking found that they got really puffed out

a lot of moving to sit down afterwards yeah yeah yeah it's like the opposite of sardines yes yeah yeah it is it was fun it was really fun

what kind of park yeah well i chose uh caledonian park i think that's what it's called it's right behind sort of the pleasants in London, where

and it's got a big clock tower and it's a good park because it's a reasonable size to allow enough good hiding places for a large group of adults.

It's surrounded by like bush and trees and everything, but there is a big empty space in the middle.

Right.

So in fact, Howard Reed, who you and I both know, his daughter Mabel, her high school was starting back the next day, so she had that day off.

So she came with him and she spent the first round just lying on the grass reading a book in the middle of the open grass and blending right in she was like the second to last person to be found because no one thought to just hide

the people sitting on the grass yeah it was great it was good i tried to climb up a tree

then realized halfway up the tree that I wouldn't be able to get back down so then backed out very quickly.

What I wanted to do was climb up the tree just above where the bags were so that I would just be like above the person who was sitting there.

That's very funny.

Yeah.

Yeah, but it was just a little bit too high for me, sadly.

And who was the undisputed champion of hiding and seeking?

Oh, the real winner was my sunglasses, which I lost in the second round, and no one found

at all.

I'd only owned them for two weeks.

Yeah.

That's excellent.

This first problem comes from Spina, who wrote into the problem posing page, which is at a problemsquared.com.

And Spina said, I think I have a problem that would be good for both Matt and Beck to tackle.

It's my favourite kind of problem.

Every time my mum comes to visit, she complains about my lack of decorations and or how empty my place feels.

So I'm thinking I'll decorate with things that are aesthetically pleasing, but secretly, or obviously, mathematics related.

I'm open to ideas for literally any kind of decoration, from scribbling raw equations on the wall, though my landlord might not be too pleased, to hanging mathsy pictures on the walls, or replacing floors with interesting shapes that tile on the plane.

So in short, what are some neat maths things to decorate with?

Oh my god.

And where should they put them?

I have a lot of opinions about tiling things.

So I feel like if I'm not careful, all of my solutions are going to be tiling related.

Maybe we get a few other options out of the way first and then I can just get into the tiles.

Okay, all right.

I mean, Matt, I've been to your house many times and you've got lots of maths related things dotting around.

Correct.

Do you have a particular favorite without mentioning tiling?

Okay, oh, that's interesting because if you ignore the tiling, the tiling had knock-on effects.

Lucy correctly, my wife said enough conflicting patterns because it was starting to feel a bit like a show, like a tiling showroom.

And so I was like, okay, fine.

So I don't know if you noticed once you're in the house, everything is now either rectangles, which are pretty off the shelf,

or

hexagons.

Yes.

So we kind of just picked some shapes and then stuck with those to try and make things remotely systematic.

But there is one thing I always kind of wanted to do, but I haven't really got the right space for it.

And that's doing a decoration that only looks like what it's meant to be from one specific angle.

And so...

You'll see these done occasionally online where like you stand in just the right place and all these

joint shapes, yeah, exactly, yeah, yeah, so it's called anamorphic art, or sometimes all the bits will line up, like, there's a bit on the staircase, there's a bit on the wall, there's a bit over here, they all line up, and oh, it's Pac-Man or something, right?

Yeah, you can do those pretty easy.

You just get like a projector or something, and you project the shape you want to have, and then you go around, and wherever it hits a wall or a surface, or a ceiling, or whatever.

I mean, if you're in a rental, maybe you gotta

find a way to hang that, like, you gotta then build that shape up somehow.

Yeah, yeah, I like that.

they mentioned spinas They got a 3D printer.

Ah, well, I would okay if I had a 3D printer and I should I can't believe I don't have one.

Yeah, I thought you did

when I was living in a share house in south London when I first moved to the UK I was in a shop somewhere might have even been Ikea and I found a replacement set of cupboard door handles and they were numbers.

It was all 10 digits.

Each one was a door handle.

And I got so excited.

I came back and I was like, oh my goodness.

It's made of the shape.

So, like those magnets that you get for the fridge, they were like in the shape of the number.

Yeah, but they're door handles for a cupboard in the kitchen.

Great.

So, one

cupboard would have zero and one as the door handles that you had to use to open.

The next cupboard would have like two and three, and so on.

I was like, this is amazing.

Because then people are like, you know, can I get a glass?

And you're like, yeah, they're in cupboard four.

Oh, yeah, nice.

I was outvoted.

We did not install them in the sharehouse.

I honestly, I sometimes don't think that's a good thing.

How did you not keep them?

you know, I had them for a very long time after because I was like, one day, one day these will shine.

That would be a lot of fun to do, either do digits for cupboard handles or you could do all the Archimedean solids.

So you've got different shapes.

Instead of having just like, you know, your classic knob, have a mathematically interesting knob for each of the sets of cupboards.

There you are.

No one take that out of context.

I think it's hard to, you know you keep coming back to tiling to to patterns because i've tried several times to have interesting tiling patterns done in the house and wait you didn't ask me if i've got any interesting maths decorations oh sorry beck what are your interesting maths decorations i i don't have any

oh good i'm glad we covered that although your background yeah your zigzag technically triangle wave technically everything is maths so correct answer i do have math things it's just they're not it's just accidentally maths like i do love a geometric print oh yeah yeah got that on my bed sheet one year lucy bought me a print of the original circuit diagram for the apple computer but it's been signed by steve wozniak and who was the designer of the the circuitry and it's in my kind of pile of cool things i one day need to get framed and put up yeah i've got one which sort of counts which was that the beginning of all the horror heights books is an isometric map so it's you know a bit like sim city you know so all the buildings and everything stay this like the same but you get this 3d effect of essentially a 2d map i got that printed as a big print and framed on my wall spima probably has a bunch of maths related a bunch of stuff yeah you know two-dimensional things that you could easily just frame with a cheap frame and stick up with some uh command strips yeah and if you put anything in a box frame it's art so yeah yeah that's why i got all my tiny knickknacks and then mounted them as if they're like butterflies and then now everyone's like wow look at that and i'm like yeah they're just tiny knickknacks but getting onto your tiling your true love so give them a tiling so i really like tilings and we i gave up on the inside part here's the problem if you want to do a cool tiling pattern and in mathematics we use the word tiling the way a lot of people would use tessellation or repeating pattern or something like that.

It just means you're fitting a bunch of shapes together.

Often the same shape, sometimes combinations of shapes.

It's very hard to get interesting shapes off the shelf.

If you want to buy tiles or buy pavers or buy stone or whatever, your options are almost exclusively rectangles.

Occasionally you'll get hexagons or something else, but you're pretty limited.

So if you want to do something inside, you're up against a lot of custom cutting, but it gets complicated.

So I ended up not doing it inside because the sheer number of tiles makes it prohibitively complicated or expensive.

Outside, where there are much bigger stone pavers going in, I'm like, oh, okay, this is my chance.

And so we got our courtyard paved a couple years ago.

And I spoke to the builders and I kind of tried to work out what

the cost per cut is if I wanted to change the shape of the stone.

And one of my favorite tiling patterns is called a snub square pattern.

It's a combination of equilateral triangles and squares.

And because the squares off the shelf already exist, I was like, oh, brilliant.

What you can do is we'll buy a bunch of squares and use them unaltered.

We'll then buy a bunch of rectangles.

And out of the rectangles, instead of cutting the equilateral triangles, we'll cut them out in pairs.

Because if you imagine two triangles back to back, you get what we'd call a rhombus.

Specifically, a square having a rest.

It's just kind of leaning over.

And that wasn't too many cuts.

So I worked out.

the exact measurements.

I was like, here's what you do.

They were like, got it.

And they spent a long time working out with a more straightforward pattern, it's easier to make sure they're all lining up properly because you just make sure the edges line up with a bit of string that you run across the site.

Whereas for this, they're like, well, how on earth do we make sure we're laying them down correctly?

And I was like, oh, if you align a bit of string to go from corner, long diagonal, corner to corner on the rhombi, that'll give you a constant line you can work to.

And then they got that all to work.

So I was very excited.

So, so one of my big recommendations would be lean into what shapes you can get off the shelf, but if you can work out how to alter one shape slightly to get a much more interesting pattern, then you're in business.

I always thought there must be a way to get rectangles, do a single cut on each one to get an irregular pentagon that would then tile.

And I haven't looked into this properly, but I feel like if you rigged up a jig and a tile saw, you could churn through either one or two cuts per tile to get a very interesting, either pentagonal or hexagon-based tiling pattern in a bathroom.

So, that one day, if I ever get to do tiling again, I feel like that would be a winner.

But I don't know if you remember from the Zeeman Award evening where I did a talk at the Royal Society.

Yeah, yeah, and you were there because you the day before, they had an yeah, we talked about the t-shirt tiles on the podcast, you were very excited about that.

I would highly recommend using those to tile a surface.

And you've got a lot of options because there are infinitely many tiles in that family which could tile the surface aperiodically.

So you could pick your favorite one because it's like, you know, there's infinitely many rectangles because you can just change the ratio of the two sides.

Yeah.

It's slightly more complicated for the hat tile.

But there are two lengths within it.

And if you change the ratio of those, you can get different shapes that all still, they'll always always fit together.

They'll be aperiodic, but they'll be different.

And so, the original hat tile was a ratio of one to root three from memory.

And there's another one called the turtle, which is if you do root three to one and you pick any bunch of other ratios, you get a periodic tiles apart from if they're the same.

If they're one, one, you get a tile which can be arranged systematically.

So, that one doesn't work.

And what's happened since the last time we talked about these is I actually organized people to get a whole lot of them and put them together to make a tiling pattern on the floor.

And do you remember before we started recording?

I went down to get a delivery because my mate Alex was bringing my drone back.

He also brought me a box of hat tiles.

I'm holding up a box.

It's got hat tiles written on it.

The box has a picture of a lawnmower on it.

It's also got a picture of a lawnmower.

A hand-push cylinder mower.

So repurposed box.

Shall we?

Yeah.

Oh, look at this.

It's a box of

tiles.

Is it foam?

Foam, yeah.

Foam tiles.

We found a place that would die cut foam tiles for us.

That's amazing.

And I got

over 700 foam tiles in a variety of different colors made.

And so when you're doing the tiling pattern, you have to flip some of them over to go

the mirror image version.

But tiling, so

the people haven't heard me talk about these before.

What's particularly interesting is they never repeat.

so unlike a square pattern or something else eventually the pattern repeats again like you fall into a rhythm whereas these tiles that never happens they never fall into a repeating pattern which makes laying them down a real pain in fact it's provably mathematically difficult like you can't just start putting them down if i just get another one and i'm like oh i'm gonna put that one there or i'll put this one here I'm probably not gonna be able to continue that pattern.

You need to be incredibly careful because they only fit together in a particular way and the way they fit together never repeats, which is, I

find, super confusing, but amazing.

So what we did when we were tiling with these, as at a conference in Newcastle, we had a bunch of diagrams where what you had to do was join a bunch of them into a meta tile made of tiles.

And then you had to get those and join them together into a bigger version of themselves and then repeat.

So it's like if you put, you know, nine squares together, you get a bigger square that looks the same but bigger.

We've found these recursive patterns, like the droster hot chocolate, where you put a bunch of them together and you make a shape that's the same as the original shape but bigger.

And then you repeat that process.

Got it.

And so we did three steps in Newcastle.

So you put a bunch together to make a shape, you put a bunch of them together to make a bigger shape that looks the same but bigger.

And then you put a bunch of those together to make the same shape again, but bigger.

And then part of the way they managed to prove that they're aperiodic relies on that substitution process of putting them together to make the same shape, but bigger, which is very, very cool.

So

that's my advice.

Does that not mean that the pattern does continue at some point?

No, if you keep growing it that way, maybe the squares are a bad example because they fit in systematically.

When you put them together, it's not like they're just like neatly side by side.

They're all arranged at weird angles to each other and the process of enlarging that you never just end up with the same thing again right because then you're re-rotating these super tiles that are made of other tiles at weird angles and you never get the same systematic got it shape repeating at least not it's not from one direction

no

yeah

it's it's it's specifically translational symmetry which is you can't move it to the side and it lines up again got it yeah yeah yeah because i'm like, yeah, but if you're moving it, you've got to move it, like you've got to tilt it, you've got to tessellate that mega tile to fit somewhere.

But then just the fact that it's tilted is what makes it non-repeatable because it's in a different angle.

Because,

yeah.

And once, once you plug it in, it's not like one bit in isolation.

Like, if you pick one little patch, you'll probably find that patch somewhere else.

But what you can't do is globally, the whole thing will never repeat.

Yeah.

If, yeah, yeah, like how in pi, you'll get the same number showing up, but the numbers between them are different.

Correct.

100%.

Yep.

That's it.

Yeah.

Cool.

All right.

You've nailed it.

So

it's a ridiculous tiling pattern.

So that's my, that, that's my one bit of advice was

if you want to do apiotic tilings, you can get them made like I did.

I got them die cut.

I wouldn't put this on the floor.

They're not very hard wearing.

But to bring it all the way around, I keep saying we, I helped plan this and got the shapes made from this die-cutting place with my friend Katie Steckles, who was

organizing the conference where we did it at.

Very great mathematician.

Katie and I worked together to line this up, and then I was going to be there to do the big installation with members of the public in Newcastle.

And I got COVID

like three days before that, so I couldn't go to the build.

So my friend Aileenne filled in for me.

So she was there doing the build with everyone.

Another brilliant one.

We will have a video about this at some point.

Yeah, she's great.

And she's the one, she was also in Vemding in Germany for the pyramid because I didn't know if I'd be better in time or not to go.

So she was gonna go to fill in for me if I couldn't make it.

And I made it just in time.

So we did a joint video together.

Nice.

So I couldn't go.

On top of that, we had a person called David Smith, who's the person who discovered the shape, was coming to the conference.

And I'd emailed with David, but I'd never met the person who discovered the first ever

periodic monotile.

and so they got him to sign a tile for me so

yeah so i've got a signed aperiodic monotile from the person who discovered it and i'm gonna get that framed and that'll be one of my mathematical decorations that i'm gonna put up around the house yeah

i love that i i'll put a few together get them all signed and then i'll get a a section of this tiled and framed.

So there you are, Spina.

Get some interesting bits of of maths.

Maybe get the person who invented them to sign it if they're still alive, which is, you know, some mathematicians.

Get them framed and put up.

That's what I'm going to do.

The video of Alianne doing the tiling will be on my stand up maths channel at some point.

If you can't wait for that and you want other inspirations for mathematical decorations, I can highly recommend Ailian's TikTok and her YouTube channel.

She does Numberfile videos.

People may know her from Numberfile.

So if you want inspiration for cool mathematical decorations, the actual solution to your problem is to go check out Aileen's TikTok.

Yeah, we probably should have just said that and saved a bunch of time, hey?

Ain't that the truth?

Ka-ching!

Our next problem that someone named Jack put into the problem posing page at a problemsqueb.com is,

is it possible?

And then they clarify, legally and or practically, to fly a plane on the German autobahn considering the lack of a speed limit.

So Beck,

you've looked into this.

Can you legally fly your plane down the autobahn because you're not technically breaking the non-existent speed limit?

No.

Oh, oh.

There you go, Jack.

Job done.

Churching.

Yeah.

Yeah, I did a bit of research and found that the rules for driving on the Autobahn are that only cars, motorcycles, SUVs and trucks are allowed on the Autobahn.

It's very clear about what

vehicles, because they don't want people on mopeds or bicycles or, I guess, tractors.

Yep.

So someone's got a souped up tractor that can do 100 miles an hour.

I mean, maybe they could get away with it as an SUV.

But yeah, so there's rules about what vehicles you can have on there.

So unfortunately,

planes didn't go on there but i well i do get a bit curious because i thought how fast can you go in a plane along the autobahn before it takes off because eventually you you take off right i know they did say to fly a plane on the germ on an autobahn and i'm guessing they mean like flying surely like carlo do they yeah like do they mean that otherwise like you're just following the autobahn aren't you you're just above it

yeah and then i guess

adhere to aviation rules so i'm i sort of went through imagine if you were driving the plane along there.

Got it.

And how fast could you go before the plane just takes off?

Or more, how slow can you go?

How slow can a plane go without taking?

Yeah.

Yeah.

How fast can you not fly a plane?

How fast can you not fly a plane?

So the typical take-off airspeeds for jetliners are in a range of 240 to 285 kilometers an hour.

Oh, okay.

That's somewhere between 149 to 177 miles per hour.

That's slower than I expected.

Well, yeah, yeah, because the speeds are usually over 100 miles an hour.

I was on the autobahn because we hired a car to get to Vemding to see the pyramid put in.

And we, on the way back, were on one of the Autobahns because it's not like every road in Germany.

It's not even every

freeway or highway in Germany.

It's specific Autobahns.

We were on one with no speed limit and we got up to...

just nonchalantly got up to 170 kilometers an hour, which is 105 miles an hour.

And we were in the middle lane.

I would say nonchalantly, just because that's the speed the other traffic was doing.

It's not like I was like, I'm going to put my foot down and see how fast I can go.

I was just keeping up with the traffic.

You're just keeping up with everyone around you.

And we were still being overtaken.

I was doing 170k and I'm being overtaken in the fast lane by other cars going substantially faster than that.

But you don't feel the speed.

It's like terrifying how good the roads are that they're designed for this.

Like, they must be perfectly flat, accurately banked, all these things.

It's just phenomenal.

So, I could imagine doing 170 and a plane overtakes me doing 240.

That's conceivable.

Yeah.

But a light aircraft, such as a Sassana 150, take takes off at around 100 K's an hour.

Oh, what?

So that has to be the slow.

62 miles per hour, which is 62 miles per hour is like less than what people do on the freeway and just motorways.

Australia, yeah.

Yeah, and ultra-light planes have even lower takeoff speeds.

So what I'm saying is you could take a, you could drive a jet liner down the autobahn, but if you were trying to drive a Cessna or lighter along the Autobahn, chances are you'll take off before you can match the speed of everyone around you.

That's great.

I suspect the

engine...

I don't know what the phrase would be, but the air being pushed out the back of a jet engine would clear the cars off the Autobahn in their wake.

at least slow them down definitely although that said the amount of cars that might suck up into the engines as well that's a good point there's several reasons why you shouldn't fly a commercial airliner down the autobahn

yeah but uh there you go that's i i thought that was a fun fun tip bit

I mean, I feel like you can.

I guess, I wonder if you could apply wings to your car, then you could, that means you could potentially, with enough

aerodynamic aerodynamics in place, it means maybe you could take off in your car.

There's a prank, get someone's spoiler, turn it upside down.

Yeah,

there you go.

Well, Beck, I feel like you've answered it legally and you've answered it practically, which were the two aspects that Jack requested.

So I think that's a cha-ching.

Yeah, cha-ching.

Thank you.

Cha-ching.

There's time for any other bankable business.

And first up, Beck.

We had several people commenting on the longest word that's one syllable.

Yes.

And you've got a response you're particularly pleased with.

Yeah, so Christian got in contact with us via the problem posing page where that's a problemsquared.com and you can select solution.

And Christian got in touch because they're a linguist from Denmark.

Amazing.

Yes.

And they said when they heard about the problem of the longest one syllable word on episode 067, they knew they had to pitch in with an attempt at a solution.

And they've provided a lot of really fascinating information about how sounds are formed in other languages.

And it's very, very interesting.

I don't have time to go through the entire thing on the podcast, but at some point, we will put this somewhere where other people can read it because it is very fascinating.

Christian...

showed us the steps we would need in order to construct a long one syllable word.

So they said first you need to fill up the syllable.

So they said as you were quick to notice all combinations of three consonant sounds that can start with a syllable in English begin with an S.

Combinations such as SPL or STR are good, but we can do better than three letters.

The word what?

The word SFRAGSTICS, SFRASGSTIX, which is S-P-H-R-A-G-I-S-T-I-C-S,

which is the study of seal emblems, starts with four consonant letters,

and the combination

the combination str, which is s-th-h-r, is documented in the word throne, meaning strand or beach in YOLA, an extinct sibling of the English language spoken in County Wexford in Ireland until the 19th century.

Whoa, that counts.

Yep, so they said I'll go with str.

And if that turns out to be unpronounceable, you can just say the th as in time or Thomas.

So you could say st.

So they said a good word to start with might be thronks,

which has three consonants.

Thronks.

Thronks, which is S-T-H-R,

A-U-R-N-X.

They point out it has three consonants, one vowel, and four consonants.

So we've got the words thronks.

Then they said, step two, use suffixes to extend the syllable.

They said this is where mathematics may come in handy.

You can attach a th to a number to make it ordinal, even if it ends in lots of consonants, such as sixth into sixth and thousandth into thousandth.

So say that our word welcome everyone else.

Say that our word strongs is a number.

Matt can pick his favorite.

If you divide one by

thronks,

you have one thronth.

One strong.

That's great.

You can also make the fraction plural by adding s

to make two thronks.

Ah, glad I've got the punch shield in my mind.

Two strongths

out of ten.

That's great.

You can also make a verb out of an ordinal number.

To quarter means to split into four.

To tenth means to spit into ten.

And a verb can be put in the past tense by adding ed.

So I tenthed the cake means I split the cake into ten pieces.

So what if you split it into throgs pieces?

You throggst it.

That's already 13 letters.

They've said

step three, add silent letters.

Now we use Matt's strategy of adding silent letters to the word.

So far, I've used the most straightforward spelling for legibility, but that won't do for the purpose of creating the longest word.

The X even stands for two sounds, K and S.

So that really has to go.

Here's what I've come up with.

So for S, they've come up with P S, as in psychology.

For

T, they've come up with P H T H, as in

Tithesis,

or

Tithesis.

I think it's Tithesis.

Tithia.

And Tithia.

R, W-R, as in Wright.

Yep, easy W.

Easy silent W.

Yep.

And the A-U sound, or, they've done A-U-G-H-A, as in Vaughan, Vince Vaughan.

So they're just, they're swapping every single letter out

for the longest version of that letter that teams up with a bunch of silent letters.

Yeah.

So R, they've got double R H as in MER.

For the N, they've got NG, as in Ginkco.

K they've got C it's like C Q U E as in SAC the old spelling of SAC I would go as far as to say as barbecue but then I guess you're pronouncing the Q in that S

they've given us a different S to the opening S later on they've given us S C E as in Coles great

for the

sound they've done just TH.

I think it's a hard one to do otherwise.

And for the last one, E D.

so put them together and we've got thronk strongst but it's spelt with 29 letters it's like unpacking a zip file that's what's happened yeah it's exactly what's happened so it's a 29 letter with a letter word with only one syllable meaning to split something into thronkst pieces and you don't even have to pronounce

every single sound do you know what number strongst is Well, he said you should get to choose, yeah.

Well, it's the new word for 29.

Of course it is.

Of course it is.

Duh.

You're right.

Yeah.

So we've shrunked the word by splitting it into 29 bits.

Well, we haven't stronged it, have we?

We've done the opposite of that.

We've like...

We've strung it.

We've split the word into 29 little pieces.

Yeah, actually, you're right.

No, you're right.

We have done that.

Yeah.

We have strung the word strongsters now it's split into 29 pieces.

That's crazy.

Yeah.

29 letters.

One word.

One syllable.

Now we've got a clip that Christian sent us of the pronunciation to make sure that we're saying it right.

So we'll play that now.

Strongs.

Thank you so much, Christian.

That was an unbelievable amount of effort and such an incredible explanation.

It's genuinely up there with my favorite solutions we've received.

I'm going to give them strong stings.

Yeah.

Well, strong strong stings.

Strong stings.

Not in strongs.

Yeah, there's no.

We haven't strengthed it.

It's just strongs.

Strong stings.

We also did, we got a few responses, but another response that I really enjoyed was from someone called Dane, which I find quite incredible considering that Christian is the Danish linguist.

Yeah, but not the Dane Christian.

The Dane name.

The Christian name of Dane, or the Dane with the Christian name of Christian.

The Dane with with the name of Christian.

Yep.

So Dane said in the most recent word, the problem about the longest one-syllable word intrigued me.

I thought I might have a go at a longer one and came up with Skronkst, which is very similar.

It's so similar.

Skronkst.

Skronkst.

What's Dane's logic?

So Dane spells it S-C-H-L-R-A-U-G-H-N-S-T-S.

Now, I think using Christian steps, we could probably get that pretty long as well.

We could probably strongly.

We could unpack that.

But they've said that they think

the plural of scronsts, which is a word that starting as of my writing this, means something that is as large as possible while still being considered small, e.g.

the heaviest possible featherweight boxer would be scronst,

which I really like.

Great work.

Dane and the Dane.

We also want to very quickly apologize to Olaf, who I, when we we were recording in a field last time, I realized I didn't have any internet connection, so I was scrabbling through kind of old pasted notes I'd made about what I wanted to talk about, and I had incorrectly pasted the name of the person who did the incredible spreadsheet about the strawberries.

What do we call them?

I think I called them Eric.

Yeah, that's my fault.

It's Olaf.

So we got in touch with Olaf.

They've sent us their incredible spreadsheet and they're going to get themselves a commemorative bowl.

Slash plate.

Slash plate.

In fact, that should have been our answer to the how do you decorate your house problem.

Yes.

Yeah.

Put up your commemorative

plate slash bowl.

Bowl and a plate.

Yep.

Yep.

I will say, I don't know if we're going to hit our 2 million download in November that I predicted.

Oh, no.

Well,

not as

much as we can.

Yeah.

We're past 1.7 million, but we've really got to exponential those downloads to hit my predicted date.

I'll be close, I reckon.

Yeah.

If you would like, if you would like to hit it, if you would like us to hit our goal of hitting our 2 million downloads in November, then all you need to do is get someone else to listen to this.

Yeah.

If you told 10 people each, we'd have it done instantly.

Oh.

If they all listen to you.

Yeah.

Yeah.

Please.

I mean, that would, that would be incredible.

So if you could tell your friends, followers, family, anyone on social media or through other means to listen to a problem squared, please do tell them what episode you think that they should start from.

In fact, I think on Spotify, you can specifically share a link to a specific episode, which is pretty cool.

If enough people do it, I think it then says on Spotify, most shared, which is interesting.

Really?

Yeah.

So eventually...

I'll see what the most shared is going to be.

We'll see what that is.

And speaking of interacting with you guys, we've had a lot of you coming back.

We're pretty much even in the amount of people saying that they want a Reddit page or a Discord page.

Now, just to be clear, this isn't replacing the problem-posing page.

We'll still be using that for

all of that.

But this was more when we hear from people like Christian, who sent us these incredibly detailed solutions, which are absolutely fascinating, or we want to cite specific sources or websites, it'd be nice to have some.

And to stop us being a bottleneck for listeners interacting directly to solve problems.

I feel like at the moment they have to come through us.

We'd want to be guarding that gate.

We want to let everyone you can workshop stuff together and without us getting in the way.

Someone reached out to say they'd already created a Reddit.

So by the time this goes out, hopefully Matt and I will both be moderators on there.

And that is R/slash a problem squared.

Yes.

Or if you're like me and very new to Reddit, it's reddit.com forward slash R forward slash a problem squared.

We did have someone called Hutton A.

Hull

or h-u-t-o-n-a-h-u-l-l who offered to help uh manage a discord said they'd like they like it when a discord isn't messy and is well set up and we'd love to take you up on your offer but um only half of the email address was filled in so maybe an auto auto great start if i may yeah so we can't email you but if you're listening to this hutton a hull uh then um yeah please uh please get in touch because we could do with some do with some help as we come to the end of another trading day at the Problem Squared Stock Exchange.

I don't know.

I'm trying to go with money.

That's good.

I like it.

Thanks.

On the trading floor.

Yeah, that's

sell.

No buys into the episode.

Oh, yeah, that makes way more sense.

We always like to thank our Patreon supporters who make this podcast possible.

So in no particular order, we're going to thank three of you at random.

And the people we're going to thank in this episode are Lydia H.

I can mispronounce that as Lydia H.

Or Lydia.

Oh, Lydia.

Lydia.

We should strongst all these names.

We should

strongst the.

Or Arn.

Arne.

Timmy.

Ha, man.

Hey, man.

Hey, man.

Yeah, if you would like us to mispronounce your name, then sign up to our our Patreon.

We'll pop a link in the show notes.

And once a month, you'll get a bonus show, which is our I'm a Wizard show, which is very silly.

Sillier than this, if you can imagine.

Unbelievable, but true.

We'd also like to thank my co-host, Matt Parker.

That's me.

Myself,

Cash Money Parker.

Cash Money Parker.

And our wonderful producer, Lauren Armstrong Carter, who isn't in the record this time and yet is somehow going to make this all sound incredible.

Bye!

Beck.

Yeah.

How many dice are in the jar?

Oh, it's not even...

We're not even in the same room as the jar.

No, no.

You got to remember.

what the jar looked like.

Yep.

What did you guess last time?

I can't even remember.

I feel like I went in at 500 just to, I thought I could get like a max threshold or a.

Yeah, that's that was incorrect.

But but then you didn't say whether it was upper or lower.

So it didn't matter.

I did not give you a direction.

No.

No.

Well, it was ruled out one specific number.

I have not changed the number of dice.

Okay.

I did have to borrow three dice from the jar and I messaged everyone on the ProblemSquared WhatsApp group.

to say I'd borrowed three, but I've since put them back.

Oh, good.

The number is still the same.

Yep.

Did Did you choose the number, or is it just how many were in there?

I counted them.

I discovered the number.

I didn't invent it.

So it's not like something, it's not necessarily a hilarious mass number.

All right.

I mean, this episode is a hilarious mass number, and we didn't mention it once.

No, because we are mature.

Yeah, we're adults.

All right.

Well, I'm going to guess.

I know that you didn't choose it, but I'm going to guess 314.

Incorrect.

I think I would have struggled to have contained my excitement if it had been 300.

That's true.

I would have been able to read that on your face.

Yeah, yeah, yeah.

Well, am I just guessing random?

Not there's probably a.

Is there a way?

I mean, I don't know if I'm going higher or lower, so there's no real.

Okay, you know, yeah, do you know what?

Next time we're in the same room, I'm gonna try and do it the way that I would do it if I was actually entering competition.

Okay, I tell you what, if you do the full calculation, I'll then give you a higher or lower if you show you're working out.

Okay, deal.

If I don't accidentally guess it, next record.

Whoa, oh, imagine.