A Problem Squared - 104 = Paper Spread and Pencil Lead

Episode Date: March 3, 2025

📃 Is a sheet of A-45 paper big enough to wrap the earth? ✏️ Why do we still call pencil graphite lead?👔 There’s business to attend to. You can find Matt and Hannah’s protractor up the shard video here: https://www.youtube.com/watch?v=ckcdqlo3pYc&ab_channel=Stand-upMathsHere’s Matt’s Truncatable Prime Pencil: https://mathsgear.co.uk/products/truncatable-prime-pencil?srsltid=AfmBOorhZ6qk_IAhKnCjtjoVM3wM-GXMTaFporL13aTjdOokjGG_hkxYAnd the oldest known pencil in the world: https://www.penciltalk.org/2021/02/worlds-oldest-pencilIf you want to know more about that 1889 World Fair and that luxury yellow pencil you can do that here: https://www.artsy.net/article/artsy-editorial-little-known-reason-pencils-yellowHere is the link to David’s MIT Maze turned Sudoku, Go check it out, it’s very cool: https://sudokupad.app/arbp91du01If you’re on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on the ‘Sup ‘Zards’ pinned post!  If you want to (we’re not forcing anyone) please do leave us a review, show the podcast to a friend or give us a rating! Please do that. It really helps. Finally, if you want even more from A Problem Squared you can connect with us and other listeners on BlueSky, Twitter, Instagram, and on Discord.

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 Back I mean you're right I'm back. Are you a bit like a cat in that cat 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 paws. It's true, but like a cat you've managed to stick the landing, so well done. Have I? The listener's shoulder side. That is my co-host Cat Parker, at least that works. Oh well done, well done. Yeah, Beck Hitten? Hitten it.

I'm sorry everyone. Look, I'll be honest. I looked around a room There 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 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 long to do talks and astronomers and you know, amateur astronomers, etc. 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 a trophy husband. Yes, I'm a trophy husband. I got chatting to one of her colleagues who is a astrophysicist expert in the radial velocities of the zodiacal dust cloud. Did you read that off of something just then? Because I feel like that. I didn't have that memorized. No. Young upstart astrophysicist Brian May. This new up and coming astrophysicist

Brian May. Yeah. He's got a side gig in 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 specializes 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, you know, 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 I was chatting to him because, 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 other guitars was because he 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. I thought it 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 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 book and sure enough there is a chapter, chapter three, Interference of Waves and there's all these wonderful diagrams which is showing you like the constructive and destructive interference and combination of waves. So this book, The Physical Bases 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.

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 Narrow Court. Oh, where's Narrow Court? Obviously, I know, but but 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 Gambier, which has the lovely blue lake, which is a lake in a volcano. Also has some sinkhole gardens, which are also stunning. Sinkhole gardens? Oh yeah. Yeah. Is 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 has so old that beautiful garden has grown.

Right. 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 Cave. Well, I did a tour and there was a kid on the tour. It's about four years old. And at the very beginning 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 mega fauna and she was like yeah mega fauna. And then the child proceeded through the entire tour.

Like she would point at something and be like, oh, the bones of these Masupu lion, and then the kid would just immediately yell out the scientific. Like the Latin name. Yeah. And just knew all of them. And then it, like all of us just felt so awful. 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, like, 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, that the guide asked everyone else. Ugh. the answer to a question that the guide asked everyone else. Ah, maybe their dad just takes them there once a week, every week. And the kids like, ah, no, the kid was, let's just move this along time. 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 Xander 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 problem square. You do a lot of podcasts. The 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 a four paper and says that a piece of a four five paper, so a 45, sorry,

I thought it was a typo. I realized a 45. They do. Might be negative 45 as well. Oh, a negative 45 paper would be big enough. Yes, that makes more sense. Because a one is very large. It 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 do How big does a piece of paper actually need to be to fully wrap a sphere?

Lots of love for the pod Zander then Zander says Shots fired PS my favorite online mathematician is James Grime if you're wondering so Zander factor into it wondering. So, Matt, you didn't even factor into it. And I'm still going to answer Xander's problem. So frankly, you know. Maybe I met, maybe I come before you. Who knows?

Yeah. Yeah. It's you. Several other people, me. 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 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 have 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 scale's 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 a Seven 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 gonna 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. Oooh! 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, um, 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, you'd be like, oh, it's a bit bigger. What Frye 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 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. Yeah, if anyone's ever tried to wrap 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 basketball. And then you get some overlap. But just look at her for our Roche.

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 Frere 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 ask. And I was like, well, you know what? I could just check. Like, I could just run the numbers myself before I, um, drop her a line. And so I quickly ran the numbers.

And I realized, um, 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, OK, 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 centre of the short end and sort of going horizontally around, so the 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 blanket. 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. 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 wanna make it easy, go for a negative 52. That's where you're gonna be. Yeah, have some left over. You're gonna be safe. And I feel like if we overshoot by a decent amount, then you can just put the earth on it, wrap it up, bum, bum, 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. 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 10 to the seven meters circumference of the earth, she accidentally used four times 10 to the six. So it was an order of magnitude. Her magnitude was off by one is the short answer. It's easy to do. I mean, I had to triple check what I was doing a couple of 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 on those powers It's very easy to slip up. She was like oh, it's five million

meters by seven million meters and the earth She accidentally used a circumference of four 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 use from when we Calculated it by going up the shard because then all bets are off 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. You know? 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 protector been confiscated and we tried to use like there's like a spirit level app on an iPhone 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 6,000378 kilometers. Six thousand is what you remember from that number. We calculated it to be 875 kilometers.

So that's... And that's why she was offended when you suggested that... Yeah, 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 Earth is. I think the Earth is more curved than Big Globe wants you to know. 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 then A40, negative 46 would definitely do it. It still doesn't cover many. Hannah's way off then. I was gonna give it to her,, but I did what I could. I can't say it's embarrassing. I am not a mathematician nor everyone Lauren Armstrong Carter has worked with Hannah as well.

Yes. Everyone is aware of how brilliant Hannah is, but I do get a kick out of pretending that I'm 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 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 gonna 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 pie towel beef with Steve Mould has gotten stale.

So this will 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 team Hannah? Join whichever side has the fewer comments at that point in time in the video. Yes, it needs to be even for it to be interesting. 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. Are you, 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 Frindings. Oh, well done. Frindings.

I feel like we should go to James Grimes as the adjudicator given James's Xander's favorite 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 it. Thank you for taking me to great heights for a lovely view and It's a wrap it's a wrap

Not to a grant 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 dot com. Broadcastis.com and Ilandris asks, very concise problem, why do we still call pencil graphite lead? And Bec, 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 a 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 it plumbago, which is derived from plumbum, which I didn't realise as a word, it's probably plumbago which is derived from plumbum which I didn't realize it's probably plumum I think it's plumum but plumbum it's a 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 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 diamonds famously hard graphite famously soft and the reason is is because graphite is like where the carbon Molecules are yep 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 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 oh? Cash into it. Yeah, I mean There might be a safety because we could just say imagine Matt has a working money gonna have to keep imagining that. Aw, my money gun.

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 that kind of guy I'd know. And he said with an HB pencil, which by the way, H in HB stands for hard, as in hardness,

B stands for black. Two B, 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 four times basically he worked out a single pencil could draw a line over 700 miles long that's assuming you never sharpened the pencil though because when you sharpen a pencil in fact another mass made of mine Rob Easterway worked out I I forget the exact answer, but it's, 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 is only a very tiny fraction of the graphite ever ends up on the page. Yeah. Most of it get worn back. And in fact, most of it, well, it's not a hundred percent 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, you know, 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. 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 realised that by refining the ingredients

of this, you know, mixing with different levels of clay and whatnot, they could change the hardness, the softness, et cetera. 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 carpeted pencil. They did, it was the oldest pencil in the world. And it basically looks like an ice cream sandwich. 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, you know, 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 Hey, that is a true story. I 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 were on we did a deliberate holiday 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 would do is they've got one 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 Oh fun. Put on the pencil. And it's completely run by volunteers like the whole factory of 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**k you pens on the side of our whole pack of pens.

And now 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, you pens. And so that's my favorite pack of pencils. I thought you were gonna 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. Sharpening the pencil, yeah. We did make a series of pencils for mass inspiration. I think you can still buy these on Masquer, 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 true. And we were right. Yeah. Did they tell you why yellow pencils became sort of fairly standard as a pencil color? 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 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, I could tell. Erasers didn't really exist until 1770. There was a clergyman chemist,

which 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. Ah, Vore dropped plant specimens on a page of working out. Yes, yeah, that must be it. And then he went to try and rub 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. Boiled up lumps of old bread. Bread?

Yeah. I find that harder to realize why. I guess someone was eating a sandwich. 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 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 what I had wow it was pretty slick what gosh I. Because I happen to own a spare money gun. Oh. 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...

Hashtag big money problems. Relatable. Yep. Alright, let's just bring the music in over the top of this. It's just sad. And now it's time for any other Bengal. Did you Google list of cat breeds? Uh, I maybe did cat glossary. Cat glossary.

Up first, Hugh Thumbs O'Brien? Byrne? No, Byrne. 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 gone on the composing page. Old Thumbs has said ding. The semantic Caesar cipher solved smashing.

Yay. We really enjoyed doing that one. 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 A.O.B. 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 laughter. I thought that was pretty funny. I think we all pause 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 Seiford by nine is punk. How did we miss punk Gleb? That makes me 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 law. Hi everybody, I'm Gleb. Let's do some builds. Oh and now Gleb's got a voice. Great. That's how I imagine Gleb sounds. Gleb always have a voice. I feel like that's new. I thought we'd banquish Gleb, but here we are.

We also heard from Stig on Blue Sky, on the old Blue-Sks. 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 in absolute splits over the ideas of magnet walls on one hand and just seeing 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 I had 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 happen. 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, et cetera. 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 we have teens in the team point and then it becomes like 21 31 41 etc. And I'd missed this at the time but you just offhandedly said there should be a new number in like the low 3000s like that just just throw everyone off. It's great I think that's a great idea so if anyone has any suggestions catch people off guard yeah a new one-off number we could have in the low 3000s. Suddenly, one exception to the rule. Oh, by the way, 3125 is pronounced 25th.

Otherwise, it's exactly what you expect. Yeah, 3125th. That's the one, but then you go 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 their stupid problem, I was talking about when I was at the MIT Mystery Hunt, and one of the logic problems was called Maze of Lies, which we have now shared a link to, people have gone had a look and David is 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 can play it like an online Sudoku so if people want to skip to the 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 an 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 open. And they also say it's definitely solvable without programming, at which point I stop paying attention. I don't believe that for a second. 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 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 any 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. Well, thanks, David. That's awesome. That is 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... Valti van IJK Woo I thought you were doing yours. I'm like how are you pronouncing all this woo, but no you're doing welter again or valta All right No, you're doing welter again. Or valter, as I suspect. Alright, um...

Now I've gotta hide what this one is. Uh... Woo, Johns! Nailed it. That is mispronouncing it. And finally... Wooo, yeah. it and finally whoo yeah the A as in a the A 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 like if your surname was team what's the funniest name you've ever heard? A friend of mine.

Ozzy was a maths teacher and they had twins in one of their classes who were I forget from an Eastern European country surname 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-Nas and then P-Nas 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 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 funny Yeah, I may have said this before but and 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've already mentioned this before, surname is frisbee, which is a normal surname, that's where the word frisbee came from. The disc was named after the surname, yeah.

Yes, yeah. But her first name was Iona? No, it wasn't. Which makes it sound like the weakest boast. The weakest boast. I've got my frisbee on layaway. Anyway, I want to thank Iona Frisbee and Anus and Penus and 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 if 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 long-headache Hill. 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 do my work I'll try and I'll just think good. But you know who's always trying consistently well?

Is our co-host, Lauren Armstrong, Katter. 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, back. We're still playing remote version of the game.

Yes. When we left on a cliffhanger. Yeah. I feel like my tactics are failing me. My tactics are failing me. My tactics are- Shoot randomly and hope for the best. Yeah. Uh, I'm going to go H8.

Hate. H8. H8. Well, I hate to tell you this, but that's a miss. Dang. You know, I'm just saving them all up so that I can like a pah, pah, pah, pah, pah. Yeah, yeah. You, you're by a process of elimination, you 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 thought we're playing the opposite version where I'm trying to hit everywhere that isn't your ship. Yeah. Well, I'm not going to hate.

I'm going to go great with G8. Eight. G8. G8. Miss. What? Oh, interesting.