104 = Paper Spread and Pencil Lead

Hello, and welcome to A Problem Squared, the problem solving podcast, which is a bit like a cat

in that

it sometimes causes more problems than solves them.

Wow.

I'm

Beck.

I mean, you're right.

I'm Beck.

Are you a bit like a cat in that cats also don't write introductions to podcasts?

Yes, exactly.

That's right.

You guys come to me.

I don't come to you.

That's how this works.

Hi, new listeners.

Normally, we start with an intro, a well-written intro.

where we do an analogy between the podcast and something else.

But I forgot.

Just like a cat would.

Landed it.

Have you cats famously don't write introductions either because of the pause?

But like a cat, you've managed to stick the landing.

So well done.

Have I?

Listeners shall decide.

That is my co-host, Kat Parker.

At least that works.

Oh, well done.

Well done.

Yeah.

Beck Hick Kitten.

Hit nut.

I'm sorry, everyone.

Look, I'll be honest.

I looked around a room.

I'm cat sitting.

There is a cat.

No, you were like a character in a film who had to make up a fake name.

Oh, yeah, yeah.

If I needed an alias, I'd be like, Hi, my name is Cup Table.

On this episode, I've got the measure of some paper sizes.

I've got some leads on pencil lead.

And get ready for any other whiskers.

Yes, that's the one.

Matt, how are you?

I'm good.

It's been a busy couple of weeks.

I got to go to

AstroFest.

That was fun.

Ooh, that sounds fun.

Look, if you enjoy a weekend of current astronomy and astrophysics research while desperately trying to not buy a telescope, it's the place for you.

So, my

dear, wonderful wife, Lucinda Green, is one of the hosts of all the talks, and they get scientists along to do talks, and astronomers, and, you know, amateur astronomers, etc.

And at the same time, they have two floors of like

everything from very cheap reflecting telescopes up to, you know, tens of thousands of pounds on a very fancy computerized one.

And I successfully bought nothing.

But for me, half the fun is hanging out and chatting to

Lucy's science colleagues because a bunch of scientists come along, and I'm there as Lucy's runner, so I'm like fetching Lucy cups of tea, helping with her laptop, and I pitch in to, you know, basically.

You're trophy husband, yes, I'm trophy husband.

And I got chatting to one of her colleagues who is an astrophysicist expert in the radial velocities of the zodiacal dust cloud.

Did you read that off of something just then?

Because I might have.

I feel like that.

I had to have that memorized.

No.

Young upstart astrophysicist Brian May.

This new up-and-coming astrophysicist Brian May.

Yeah.

He's got a side gig and a band, but.

Yeah,

yeah.

But his main passion.

Main passion, astronomy.

Yes.

Astrophysics.

And friend of Lucy's.

And comes along to Astrofest.

So.

Wait, did you say he specialises in astro dust?

Yes, correct.

As in

another one bites the astro dust.

As in another one bites the zodiacal dust.

Please tell me.

The reason I keep looking over here

is I just brought up, because he's done a lot of stuff with space.

Like, he's very big into 3D photography and has done 3D visualizations of asteroids and is a huge supporter of the amateur astronomer community.

but did do a PhD in physics.

And so the reason I keep looking over here is I've got his PhD up on my laptop, which is a survey of radial velocities in the zodiacal dust crowd.

So I thought I'd just get his exact thesis title so I could be specific

by Brian Harold May.

There you go, at Imperial College.

But it's chatting to him because

he's a mega nerd.

Which is a million nerds, isn't it?

Yeah, a million nerds.

And when he was much younger, he wired up his own guitar.

He has a guitar called the Red Special.

And I wrote about it in my book because he

added extra switches to the guitar when he was wiring it up that would flip the phase of the pickups, which basically means it would invert, it would upside down the wave signal coming from the strings vibrating.

And this is a unique feature to the guitar because he made it himself, and it's part of why Queen had such a unique sound to some of the guitars was because he'd wired his own guitar and he'd used his knowledge of physics

to come up with a way of changing the sound on the fly on the guitar.

Which I thought was very cool.

That's very cool.

And I put it in my book because I've spoken to him about it before,

and I put it in my book, Love Triangle, talking about it as a good use of waves.

And then it was nice to report back.

And he said he was originally inspired as a child.

His dad bought him a book called The Physical Basis of Music.

So I've gone and found a copy of The Physical Basis of Music from.

Yeah, Matt is holding up a beautiful

1913 book.

And sure enough, there is a chapter, chapter 3, Interference of Waves.

And there's all these wonderful diagrams, which is showing you the constructive and destructive interference and combination of waves.

So this book, The Physical Basis of Music by A.

Wood from 1913,

this chapter is what then led to Brian and his dad making his own guitar and wiring it up unusually, which then led to the sound of Queen.

So there you go.

The highlight of my year thus far.

Yeah, that's really awesome.

And what have you been up to, young Beck?

I went and visited my dad in Narracourt.

Oh, where's Narracourt?

Obviously, I know, but for everyone who's unfamiliar with...

If you were driving from Adelaide to Melbourne, it's quite close to the border of Victoria.

There's some great fossil caves there.

There is also, it's also not too, it's about an hour's drive from Mount Gambia, which has the lovely Blue Lake, which is a lake in

a volcano.

Also, it has some sinkhole gardens, which are also stunning.

Sinkhole gardens?

Oh, yeah, yeah.

It's in like the garden is in a sinkhole, or you're walking around a garden and occasionally the earth just disappears.

No, it's a sinkhole that is so old that beautiful garden has grown.

Well,

there's some natural garden stuff and then some

landscaping that's happened.

In an ancient sinkhole.

Lovely.

Yeah.

I mean, you had me at Fossil Cave, if I'm being honest.

The fossil caves, well, I did a tour and there was a kid on the tour.

It's about four years old.

And at the very beginning, the tour guide was like, okay, there's no dinosaur.

fossils in these caves.

It's actually the fossils that we found are for these very large animals.

Does anyone know what these animals, what we refer to them?

And this four-year-old, just without even a beat, just went, megafauna.

And she was like, yeah, megafauna.

Oh, damn.

And then the child proceeded through the entire tour.

Like, she would point at something and be like, oh, the bones of the Masupu lion.

And then the kid would just immediately yell out the scientific.

Yeah.

And just knew all of them.

And then it, like, all of us just felt so awful.

And just, this kid was so absolutely on it.

And the thing is, he wasn't even paying attention.

Like, at one point, he was like, Can I have the headphones?

Like, he just wanted to look at his game or his screen or whatever, but like, he was chatting to his dad, and then he just piped up with the answer to a question that

the guide asked everyone else.

Maybe their dad just takes them there once a week, every week, and the kids.

Oh, right.

No, the kid was just moving.

He had a good time.

Oh, okay, okay.

But then, as at the end of it, he was like,

Are we going anywhere else on holiday?

Our first problem comes from Zander,

who wrote into the problem posing page by going to a problemsquared.com.

Do you see how I almost forgot the name of our podcast there?

A problemsquared.com.

You do a lot of podcasts.

problem option

and said,

hi, Matt and Beck.

My second favorite online mathematician hannah fry just recently posted a short where she expresses her love for a4 paper and says that a piece of a45 paper so a45 sorry i thought it was a type of i've realized a45 they do

oh a negative 45 paper would be big enough yes that makes more sense because a1 is very large would be big enough to wrap the entire earth but as someone who has tried to wrap spherical objects before, I wonder if she cut the paper too small, just like I usually do.

How big does a piece of paper actually need to be to fully wrap a sphere?

Lots of love for the pod.

Xander.

Then Xander says,

shots fired.

P.S., my most favorite online mathematician, is James Grime, if you're wondering.

So, Matt, you didn't even factor into it.

And I'm still going to answer Xander's problem.

So, frankly,

maybe I come before you.

Who knows?

Yeah, but he goes, Yeah, it's you, several other people, me.

Yeah.

So, paper.

A4 paper.

First of all, I agree with Hannah.

A4 paper is amazing.

What's particularly amazing about A4 paper for people who are unfamiliar with the paper scale?

A4 paper scale, which is a wonderful paper scale that everyone should use.

And

if you were designing what size a piece of paper needs to be,

you

have to decide what the ratio is going to be, which is like you've got the long side and the short side.

They could be the same.

Why don't we use a square of paper?

That would be fun.

Yeah.

But they're not.

They tend to be a rectangle, as in like one smaller.

The ratio is picked.

So that if you fold or cut it in half, it's still exactly the same ratio,

which is not a given.

Like, if you had a square and you fold it in half, you get a long, skinny rectangle.

You're right.

And if you got a piece of like letter, American paper, and fold it in half, it would be a different ratio.

Like, the ratio between the long and the short side will change.

A4 paper is the only ratio for which if you halve it, you don't change the ratio.

And that's useful because if you want to take two documents and shrink them down and print them both on one bit of paper, it lines up perfectly on an A4 piece of paper.

Yeah.

So the scales designed to be self-similar, which is useful in all sorts of printing situations.

And so each page is just half the area of the previous one.

And in theory, you could keep going.

Every time you fold it in half, it's still the same ratio.

Yeah.

But, in fact, behind me, oh, this is a complete accident.

That's a piece of A4 paper behind me that's framed.

That's full A4.

Now I'm down to, what was this, like A7 or something?

But I can still line it up and it will perfectly match.

Like, amazing, amazing.

But it does mean at this point, you're like, hang on a second.

Well, at some point, it's too small to be a useful piece of paper, but the numbers keep going.

What would an A10 look like, or an A20, or an A.

Like, what happens?

At some point, it's going to be

like smaller than a human cell.

And I looked up, and I'm not saying Hannah did her short completely independent of this,

but almost 14 years ago, back

when the website was still called Twitter,

in August of 2011,

at 26 minutes past midday,

I tweeted, if you continue the A4, A3 paper sizes, a piece of A34 paper would fit inside a human cell.

The question is, what if we go the other way?

Because if you put together two A4s, you get an A3 that's bigger.

Two A3s give you an A2.

You can get an A0.

Like that's like a massive, you know, poster, huge poster size.

Now, back in August 2011, which, by the way, was when I believe we were both at Green Man Festival

doing

what was our first

co-radio podcast thing.

Yeah.

I then said

a negative 47 would be bigger than the Earth.

And so

what I've done is I've gone and I haven't got my original working out from that tweet because it was over a decade ago.

But I then did knock together a quick spreadsheet to just work out what I was talking about.

And A negative 47

is the first paper size

where the long side would be

14 million meters, which is 14,000 kilometers.

And the earth, top to bottom, like the diameter of the earth, is about 13,000 kilometers.

So it's the first bit of paper where if you held it next to the earth, you'd be like, oh, it's a bit bigger.

What Fry has done is different.

She said, wrap the earth.

Yeah.

And this is why Xander's come to us because

wrap the earth could be interpreted two different ways.

Like, potentially, you could just say the area area of the piece of paper is the same area as the earth.

So, in theory, it could cover it.

But if you actually got a bit of paper that size and tried to wrap it, you wouldn't be able to cover it all.

Like, if it was a present, you wouldn't be able to wrap it

because of

completely go around a sphere.

A basketball or a soccer ball for Christmas.

Exactly.

The piece of paper you need actually has to be much bigger than

the surface area of the

wrap.

Just look at it for a rocher

so i was then like oh okay fine so hannah's done one of these she's either worked out the exact area to match or she's worked out like it's big enough that you could use it like a piece of wrapping paper to go around and in her short like the animation that's gone over it shows like a scrunched up bit of paper as if it was around the earth so the visuals imply you could physically wrap it like a ferrero rocher like a ferrero rocher and i was like oh okay great so i was just going to drop her a line and ask.

And I was like, well, you know what?

I could just check.

Like, I could just run the numbers myself before I drop her a line.

And so I quickly ran the numbers and I realized Hannah accidentally made a mistake.

Now, I have spoken to her since.

She did work out

the size of paper you would need to physically wrap the earth

without having to cut it or tear it or do anything else.

Like it was a big enough piece of paper to go around the earth.

Do you mean more like if I were

to

hold the middle of a short end at the equator and then wrap it as a cylinder around

to meet the other side?

Yes, exactly that.

And that's exactly the calculation I did.

I was like, oh, okay, what would I do?

I was like, yeah, but if the short end could go all the way around the equator, you'd basically be turning the bit of paper into a tube, a short end tube that the Earth could fit in.

So, yeah, so if you were holding it in the center of the short end and sort of going horizontally around, so the lot lengthwise you're going around, but that means that you're not going to be able to, if it's just meeting the top wouldn't reach.

Antarctica and the Arctic are going to be cold in their little paper blankets.

Yeah, you'd need the

short edge for that to work

would have to

be

like to go from one pole to the other.

So I, for safety, just went, if the short edge can go all the way around the equator You can definitely wrap it.

Yes.

Yeah.

Yeah.

Yeah.

I think we're both saying the same thing, but we're both thinking about how we wrap things slightly differently.

Now, I ran the numbers and the a negative 51 gets so close.

It's 99.6%

of the way around.

Actually, if you had a negative 51,

that would wrap like the long side would go all the way around the equator.

And I'm pretty sure you'd have enough spare, because the short side should reach from pole to pole.

That should work for wrapping the earth.

Pretty sure that'll fit.

But for safety's sake, if you want to make it easy, go for a negative 52.

That's where you're going to.

Yeah, have some left over.

You're going to be safe.

And I feel like if we overshoot

by a decent amount, then you can just you can just put the earth on it, wrap it up, bum, ba-bum, better take wherever you want, no problems.

If you just want the area to match, that will work at about a negative 49.

But then you'd have to do a bunch of cutting and sticking.

Yeah.

In Hannah's short, she said a negative 45.

And I was like, both of those way off.

That's way off.

So I asked her.

And so she went and checked her calculations.

And she had calculated the size of the A45 paper correctly.

And she'd done exactly what we were discussing, working out if you could get the short side all the way around the earth, which means you could definitely wrap it nice and easy.

Except in her calculations instead of having four times ten to the seven meters circumference of the earth she accidentally used four times ten to the six so it was an order of magnitude her magnitude was off by one is the short answer and it's easy to do i mean i had to triple check what i was doing a couple times because when you're flipping between meters and kilometers and then you're using different big numbers with like you know using scientific notation or less powers It's very easy to slip up.

She was like, oh, it's 5 million meters by 7 million meters.

And the Earth, she accidentally used a circumference of 4 million meters.

It's actually 40 million meters.

And that's where the mistake came in.

Now,

that said, I then messaged her, once we'd cracked this, I then messaged her to say, oh, that would be fine.

if you're using the value of the size of the earth we used when we calculated it by going up the shard because then all bets are off um And she did reply with, Excuse me, how dare you?

Because you can calculate the size of the Earth by taking a protractor up a very large mountain.

And this is how it was done like a thousand years ago.

And so we went to the Shard, which is the tallest building in London, and tried to calculate the size of the Earth from scratch using a very large protractor.

And for the record, there's no subtle way to carry a protractor of that size.

Yeah.

We tried to play it real casual,

but no.

The security thought it could be used as a weapon yeah yeah

so so um so we had to kind of eyeball it it wasn't very accurate and by the time we did all our calculations so our calculations for how high the shard is were pretty accurate because we had the protractor once the protractor had been confiscated and we tried to use like there's like a spirit level app on an iPhone and we tried to use that to work out the angle down to the horizon and that was just wildly inaccurate.

So the Earth has a radius of 6,378 kilometers.

6,000 is what you remember from that number.

We calculated it to be 875 kilometers.

So

and that's why she was offended when you suggested that

she'd been as accurate as that calculation.

But I did then chuck our version of the Earth because maybe that's the real value.

You know?

I'm the opposite of whatever a flat earther is.

I think the earth is more curved

than big globe wants you to know.

Like it's super small.

It's way smaller.

Yeah, exactly.

So I then chucked that into my same spreadsheet calculator.

And on that scale, Hannah's pretty much there.

If you do get the long side of an A negative 45,

it would make it around the equator of small Earth.

And there should be enough to go pole to pole, top and bottom.

So

you can either argue.

Yeah, so it would work.

Like, Hannah's either made two mistakes, or she's really consistent

on how big the Earth is.

And at 840 negative 10,

it still doesn't cover many Earth.

Yeah,

Hannah's way off, then.

I was going to give it to her, but I did what I could.

I can't say it's embarrassing.

I am not a mathematician, nor

everyone, Lorin Arnstrom Carter has worked with Hannah as well.

Everyone is aware of how brilliant Hannah is, but I do get a kick out of pretending that I am superior

when I have the least amount of option to be so.

So, to quote Hannah's final message, was,

what is a factor of 10 between friends?

So, to answer Xander's problem, Hannah did want to work out the size of the piece of paper required to physically wrap the earth so you wouldn't have to tear it or anything.

It would be an easy wrapping experience.

But

she accidentally was off by an order of magnitude, which seems to be a habit when it comes to Hannah and the size of the earth.

Wow, okay.

I know.

Whoa.

Matt, I didn't realize how sassy you are.

You know it.

I'm real sassy when she's not in the room.

Please tell me that you guys are going to start some YouTube video beef now.

Oh, yeah.

I've been needing to get some beef on YouTube.

That's how you get views, right?

That would do it.

Yeah.

I feel like my punches for Steve Mold has gotten stale, so this would be a new one.

I like it.

Yeah.

Anyone listening, if you could start sort of

going into the comments of both Matt and Hannah's videos,

are you Team Matt or Team Hannah?

Join whichever side has the fewer comments at that point in time in the videos.

It needs to be even for it to be in equilibrium.

Escalating equilibrium.

Yeah.

Yeah.

I want it to ratchet out of control.

Yeah, so in conclusion, Hannah was trying to do it right and made a small mistake.

So I don't know.

Do you reckon you can give that a ding or do we need to go back to Xander for that one?

This feels like a group effort.

I would like to hear what Xander thinks about Hannah's frying dings.

Oh, well done.

Frindings.

I feel like we should go to James Grime as the adjudicator, given James Grime.

Yes.

Xander's favourite online mathematician.

I would like to see you and Hannah with beef and James in a referee top.

Well, I've enjoyed this.

I enjoyed this.

Thank you for taking me to Great Heights for a lovely view.

And

it's a wrap.

It's a wrap.

Not doing great on the analogies this episode.

You're firing on some cylinders.

That's not what people come here for.

They come here for sassiness and beef.

Yep, and that we got beef and spades.

Our next problem was also sent in at the problem posing page at whatever the name of the podcast is.com, and Elandress

asks, very concise problem: why do we still call pencil graphite lead?

And Beck, you've got a lead on this.

Nice.

Thank you.

Yeah.

It's because when they found what we now call graphite

in the 16th century, they found like a really large deposit of it in Borrowdale in England.

I mean, it had been used and found in other places.

They found this really big deposit of it.

They were like, oh, what is this substance?

They're like, it kind of looks like a black lead.

And so they called called it plumbargo, which is derived from plumbum.

It can make you giggle.

Which I didn't realize was a word.

It's probably plummum.

I think it's plumum.

But

plumbum.

It's Latin for lead.

Plumbumming.

That's why lead pencils are called lead.

It's actually graphite.

But they thought it was a type of lead.

Lead's just like an element.

It's just metal.

It's in the earth.

Graphite, that's like carbon that's that's been smooshed together, right?

Yeah, and I think we covered this maybe when we were talking about anniversary gifts.

I suggested graphite as the

minus one.

Like a negative diamond.

Yeah.

As a rollover from the diamond, exactly.

Because obviously they're both forms of carbon.

Diamond's famously hard, graphite famously soft.

And the reason is, is because graphite is like where the carbon molecules are are

two-dimensionally connected.

That for me was the easiest way of explaining it, whereas diamond carbon molecules are three-dimensionally connected.

It's like the difference between having a brick, which is a three-dimensional one, and having like a

ream of paper, if you will.

You know how like when

rappers or anyone else makes it rain by like throwing off all the dollar bills off of each other, like

that.

That's That's basically how graphite works.

So when you're writing or drawing, it takes off, like slithers, slides off.

Like if you were fanning a deck of cards.

So if you had like a money gun.

Yes, Matt has produced one of those money guns where you put

fake cash into it.

Yep.

I mean.

Is there a safety?

It might be a safety.

Because we could just say, imagine Matt has a working money.

I'm going to have to keep imagining that.

My money gone.

Anyway, while Matt tries to fix a prop that is absolutely unnecessary for this podcast,

Matt, you're a mathematician.

Are you

friends or do you know of Cambridge mathematician John Barrow?

Oh, I think I met him at a conference.

He wrote a book called 100 Essential Things You Didn't Know You Didn't Know.

Math Explains Your World.

Sounds like kind of guard now.

And he said with an HB pencil, which, by the way, H in HB stands for hard, as in hardness, B stands for black.

2B, like the more black it is, the softer it is.

So he calculated the thickness of graphite left on a sheet of paper by a soft 2B pencil is about 20 nanometers, and a carbon atom has a diameter of 0.14 nanometers.

So the pencil line is only about 143 atoms thick.

The pencil lead is about 1 millimeter in radius, and therefore, if the length of the pencil is 15 centimeters, then the volume of graphite to be spread out on a straight line is 150 cubic millimeters.

If we draw a line of thickness 20 nanometers and width 2 millimeters, then there will be enough lead to continue for a distance of L equals 150 question mark divided by 4 times.

Basically, he worked out a single pencil could draw a line over 700 miles long.

That's assuming you never sharpen the pencil though.

Because when you sharpen a pencil, in fact, another mass mate of mine, Rob Easterway, worked out, and I forget the exact answer, but it's a surprising answer.

When you're sharpening a pencil,

the majority of your graphite is not used for writing, it's just taken away with sharpening.

Because you kind of wear down the apex, but then to get a new apex, you remove so much more graphite

to make it sharp again that actually it's only a very tiny fraction of the graphite ever ends up on the page.

Yeah.

Most of it gets worn back.

And in fact, most of it, well, it's not 100% pure graphite in pencils either.

What?

Yeah.

I mean, if it was, then you wouldn't be able to have a difference in hardness or softness or, yeah.

The modern pencil that we know today, so they used graphite

to

mark things and stuff like that.

That was all very,

very exciting.

And in the 1500s, there was a drawing of a strip of graphite inside a tube of wood that was in a book about fossils.

And so that kind of became the standard writing thing.

And, you know, because England had this huge deposit of graphite, they became like the number one go-to for graphite, right?

But

in 1794, when France was at war with Britain, they were cut off from their source of graphite.

Yep.

And the Minister of War

asked an engineer, Nicolas Jacques Conte, to find a solution.

Conte came up with the idea of mixing impure, low-quality graphite with wet clay.

And then he shaped them into rods and baked them.

And that was how they got to a much closer version of the lead pencil that we know today.

Yeah and so then everyone started sort of doing it where they could

there was Americans that sort of worked on that a bit more and realized that by refining the ingredients of this, you know, mixing it with different levels of clay and whatnot, they could change the hardness, the softness, etc.

I did see recently a picture of an old pencil that was like found

like pre that war found in a roof somewhere in I think France.

Somewhere they found like an old carpenter's pencil.

They did.

It It was the oldest pencil pencil.

It was an ice cream sandwich.

It was found in a timbered house built in 1630.

And it's just like two slabs of wood.

It's like a sandwich.

Two slabs of wood with a slab of graphite in the middle.

Yes.

Back when you could just pick it up off the ground.

Like, no need to be efficient.

Just slap some wood on it.

There's your pencil.

Yeah.

We'll pop it on socials.

Little note for you guys.

I've just put it in WhatsApp.

Have you been

to the pencil museum in Keswick?

I feel like you once started a story with I was at a pencil museum and I laughed a lot.

That is a true story.

That might not have been on the show.

And the thing is, is I don't know why I would laugh at that because I would love to go to a pencil museum.

I went there with Lucy.

We had a wonderful time.

We did a deliberate holiday to the pencil museum.

Highly recommend it.

Learned a lot about pencils.

It's actually quite a fun museum and it's a lovely scenic part of the country.

At the end of the tour, there's like a gift shop.

But one of the things they will do is they've got one of of these machines that's normally used in a factory for pencils, but it can spray text onto pencils.

So you can order a pack of pencils with customized text

put on the pencil, and it's completely run by volunteers, like the whole factory is volunteers.

And so I had to talk to a little old lady about the slogans I wanted on my pencils, and it turns out they will refuse to put f you pens

on the side

of a whole

pack of pencils.

And now, I I desperately hope producer Lauren bleeped that.

It was a naughty word, you pens.

So I do have a pack of pencils where they let me put like characters, F and some other characters, U pens.

And so that's my

favourite pack of pencils.

I thought you were going to come up with some word that has a swear word at the beginning, which you sort of don't really realize until you're sharpening the pencil and you get to the point.

We did make a series of pencils for mass inspiration, and I think you can still buy these on Mass Gear, which are truncatable primes.

So, these are primes, numbers, where even if you remove digits from one end, they stay prime.

And so, as you sharpen the pencil, the prime number remains prime even as the digits get removed one by one.

And we thought we were pretty funny.

That's very we were right.

Yeah.

Did they tell you why

yellow pencils became sort of fairly standard as a pencil colour?

They did.

It's because originally the graphite was encased in the finest quality wood.

So

they would generally paint the pencil to hide bad quality.

Wood was low quality.

If you had good quality wood you'd just have a varnish on it.

But at the 1889 World's Fair in Paris, an Austro-Hungarian pencil company unveiled a luxury pencil that was made from the finest materials, and they'd painted it yellow.

Because of this,

loads of copycats popped up.

That's what a fancy pencil looks like.

Yeah.

Finally, do you want to know about the erasers on the tips of pencils?

I do.

Well, how did you know that's what I was thinking?

I just could tell.

Erasers didn't really exist until 1770.

There was a clergyman chemist, is quite the combination, if you ask me, called Joseph Priestley, noticed that a strange gum harvested from trees in South America was particularly good at removing pencil marks.

Don't ask me how he worked it out.

Vaughn dropped plant specimens on a page of working out.

Yes.

Yeah, that must be it.

And then he went to try and rub it off the page and went, oh, it's taken my pencil with it.

Because it involves rubbing, they obviously called it rubber.

Do you want to know what was used before rubber?

Fire.

I mean, that's one way.

Thank you.

You can't argue with results.

I can't.

You're right.

Look, when I dispose of sensitive writing, I do it thoroughly.

Bold up lumps of old bread.

Bread?

Yeah.

I find that harder to realize.

I guess someone was saying that.

Yeah, they're having a sandwich.

Wait, was this before this sandwich?

And they drop their sandwich, and as it slides down the page, it just leaves a blank streak where there's no writing anymore.

And they're like, hey, that could be useful.

Yeah.

That's great.

I feel like you successfully solved this problem about 20 minutes ago.

So I feel like you dinged it early and you've just been, you know, victory lap dinging it ever since.

This has both been a problem solved and a lot of additional fun information.

And I think the only way to celebrate it.

I don't know if you noticed me very subtly opening the cupboard behind me again while you were talking.

I had, wow.

It was pretty slick.

What?

God.

I know.

Because I happen to own a spare money gun.

Spare money.

Oh.

Oh, that's so broken.

No.

What?

Maybe I've put too many notes in them.

Can you overload a money gun?

Oh, that is the

least

big money gun.

Yep.

All right, let's just bring the music in over the top of this.

It's just sad.

Oh, that's.

And now it's time for any other Bengal.

Did you Google list of cat breeds?

I maybe did.

Cat glossary.

Cat glossary.

Up first, Hugh Thumbs.

Oh.

Brian?

Burn?

No, Burn.

Good old thumbs who had inquired previously about what word has the most valid words if you Caesar cipher it.

I think we did a pretty good job at the time.

And old Thumbsy agrees.

Has

old thumbs

has said

ding.

The semantic Caesar cipher solved smashing.

Yay!

We really enjoyed doing that one.

I think it didn't make the cut, but Spots Dazed was another one where the two words

are very well linked.

Yeah.

You're trying to sneak it in here, thinking producer Lauren won't notice.

You're hiding it in AOB.

We also heard from Jewie Lone,

which are two things you can do in a library, who said, I thought it was going to be a laugh there.

I thought that was pretty funny.

I think we all paused for laughter.

I assume everyone listening is rolling around in whatever way is safest, wherever they currently are.

I would like to tell you that Gleb, Caesar Saved, by nine, is punk.

How did we miss punk Gleb?

That makes it very happy.

Gleb, by the way, is the name of our mascot calculator, just in case anyone's not up to date on all the problem squared rules.

I'm Gleb.

Let's go.

Oh, and now Gleb's got a voice.

Great.

That's how I imagine.

Did Gleb always have a voice?

I feel like that's new.

I thought we vanquished Gleb, but here we are.

We also heard from Stig

on Blue Sky, on the old Bloosks.

That's what they call it.

Yep.

In episode 103, sorry, 103.

Paul may or may not have had the stupidest problem ever.

Now, I will clarify this by saying that Paul started by saying they had a stupid problem.

But you guys definitely had the stupidest solutions.

I was absolute splits over the ideas of magnet walls on one hand and just sitting naked alone in a room on the other.

Loved it.

More of the same absurd nonsense, please.

We had a lot of love for that.

Like, people's

friends message me out of nowhere, go, I've just listened to this episode and I can't stop laughing.

For me, it feels like a fever dream.

Yeah, I sort of forgot until I listened back and then was like, this is very funny.

Listening back to it, Matt, there's so many...

I've mentioned this before.

You're very fast, and quite often I miss your jokes as they're happening.

I think I also especially miss them when we're doing these remote records, right?

Because sometimes on a Zoom call, it might cut out the sound if you're in the middle of talking or vice versa, the lag, etc.

There was a moment in a previous episode where

we were talking about how

dumb numbering systems are because we don't use teens at any other point.

You know, we sort of have teens in the teen point, and then it becomes like 21, 31, 41, etc.

And I missed this at the time, but you just offhandedly said there should be a new number in like the low 3000s.

Like that should just

throw everyone off.

Really tickled me.

It's great.

I think that's a great idea.

So if anyone has any suggestions,

a new one-off number we could have in the low 3000s because suddenly one exception to the rule.

Oh, by the way, 3,125 is pronounced 2 Fuft.

Otherwise,

it's exactly what you expect.

Yeah.

312 Fuft.

That's the one, but then you get back to normal.

Yeah.

And finally, David went to the problem posing page and said that in episode 103, which we were previously discussing about Paul and there are stupid problems,

I was talking about when I was at the MIT mystery hunt, and one of of the logic problems was called Maze of Lies, which we have now shared a link to, and people have gone and had a look.

And David has, in their words, tried their best to turn it into a playable Sudoku.

And they've provided a link.

And oh my goodness, look at this.

There's a pop-up text box with all the stuff from the original puzzle.

Because originally you're like walking around a maze getting messages.

And then they've made the entire map and play it like an online Sudoku.

So if people want to skip to the punchline punchline and have a go at solving it, you can.

I will say, however, well, David's got two points they want to say here.

They're saying that there is a large assumption that we're all making, which wasn't in the original problem.

We're all assuming all the rooms are the same size squares.

I feel like that's forced by the geometry of how the maze is connected.

But I could be wrong.

We'll leave that.

Leave that open.

And they also say it's definitely solvable without programming, at which point I stopped paying attention.

I don't believe that for a second.

I've looked at the thing myself and I don't understand any of it but it looks pretty and might I add have no interest in understanding any of it some things

don't try to explain it as as someone who gets addicted to puzzles oh my goodness don't

explain to me so you're saying clues like in one region with only two doors the digits on the shortest path between the doors strictly increase from one door to the other I mean that's classic Sudoku right there oh Well, thanks, David.

That's awesome.

That was really nice.

We love this stuff.

Speaking of thank yous, I want to thank some other people, namely three of our Patreon supporters.

And on this episode, those names are Valty

Vand Ijk.

Woo!

I thought you were doing yours.

I'm like, hell, you pronounce it in all as woo, but no, no, you're doing Walter again.

Or Walter, I suspect.

All right.

Now I've got to hide what

this one is.

Woo, John's.

Nailed it.

That is mispronouncing it.

And finally,

the a

as in a the a

uh last name team

nice

thank you that would be a great if you called your kid thea team that would be very cool thea team

is team what's the funniest name you've ever heard a friend of mine obviously was a maths teacher and they had um twins in one of their classes who were i forget from an eastern european country surnamed nuss and they were like the equivalent names of Peter and like

Andrew or Andre or something like that but the way the role was called was they had to say first initial surname

role call involved a nus and then p nuss in

in order and that's the funniest true truth because i know the person it's not like oh i heard a thing no i know the person that happened to and it's very funny oh that is very very

Yeah, I may have said this before, but and look, I'm not trying to shame anyone with this name, but my friend went to school with a girl whose surname is Frisbee.

I may have mentioned this before.

Surname is Frisbee, which is a normal surname.

That's where the disc was named after the surname, yeah, yeah.

Yes, yeah,

but her first name was Iona, no, which makes us

which makes it sound like

the weakest boast.

I've got my

Patreon layaway.

Anyway, I want to thank Iona Frisbee

and ANS and Peters

and all of those Patreon.

All of those Patreon supporters.

We love you dearly.

We love you all who are listening as well.

We understand that not all of you can financially support us, so that is completely understandable.

However, we do appreciate it if you tell other people to listen to us because uh, it that is great and appreciated and helps us continue this show.

I also want to thank my co-host

Catnip Parker.

I'll take it.

And I am British Longhead Eck Hill.

I've I've got to try harder after this.

I feel awful.

And I'm on next time.

So 106, I promise

I'll

do my work.

I'll try and do something good.

But you know who's always trying consistently well?

It's our co-host, Lauren Armstrong Catter.

Oh, nice.

No, but is it though?

I've just put the word cat and stuff.

I haven't even.

That's...

Maybe this...

gives away how much my expectations have been lowered, but that was perfectly adequate.

Alright.

Well, I'm sorry to end it this way, everyone.

Bye!

All right, Bec.

We're still playing the remote version of the game.

Yes.

And we left on a cliffhanger.

Yeah.

And I feel like my tactics are failing me.

My tactics are...

You can shoot randomly and hope for the best.

Yeah.

I'm going to go

H8.

Hate.

H.

H8.

Well, I hate to tell you this, but that's a mess.

Dang.

You know, I'm just saving them all up so that I can like go pow pow pow pow pow.

Yeah, yeah, yeah.

you're by a process of elimination, you'll know exactly where my battleships are.

Yeah, that's how the game works.

You're a pacifist playing battleships.

Wow.

Yeah, I thought we're playing the opposite version where I'm trying to hit everywhere that isn't your ship.

Yeah.

Well, I'm not gonna hate.

I'm gonna go

great

with G8.

G8.

G8.

Miss

What

Ooh hoo interesting.

Bum bum bum