A Problem Squared - 127 = Labelling Consumables and Conceivable Numerals

Episode Date: February 2, 2026

🫘 Can we come up with some fun names for common pantry items?🔢 What's the smallest number that has never been written down in human history?🧂 And there’s a sprinkling of Any Other Business.Numberphile’s take on a number NOBODY has thought of: https://www.youtube.com/watch?v=KdZrxkix9MkEvery Time "67" Has Been Said on Numberphile, if you dare: https://www.youtube.com/watch?v=LlJMJfPPnVAGoogolplex Written Out: http://www.googolplexwrittenout.com/If you’d like to see Bec at the Adelaide Fringe in March, you can get tickets here: https://adelaidefringe.com.au/fringetix/bec-hill-creates-the-perfect-show-work-in-progress-af2026 And if you’d like to see Matt on tour, all the dates, venues and tickets can be found here: http://standupmaths.com/shows Join us on Patreon for early releases and our monthly bonus podcast I’m A Wizard! If you’re already on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on our pinned post!  If you want to (we’re not forcing anyone) please do leave us a review, share the podcast with 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.

This is a problem squared. The problem solving podcast that solves problems. And stays on top of trends. We've been going for six, seven years. I am joined by Beck Hill, who does a number of funny things. And I am the mathematician Matt Barker. I'm looking at me like that. Why are there so many pauses?

Just to remind everyone, the previous line was and I am mathematician Matt Parker. Someone who focuses too much on numbers. And on this episode, we shall. Am I going to ruin it now? No, no, no, I'm done, I'm done, I'm not doing that anymore. I'll be renaming some pantry staples. I am going to help us think of a whole new number.

And there'll be some any other business. All right. The intro, I'm trying to be down with the kids. every sentence alternated between six or seven words. What's funny is... I don't think any of that was funny, but carry on. Kids don't use six, seven now. They're well past...

I know, I know. We are only catching up. That's why I refuse to do it until it's not cool. I knew it was over. You can do anything and it will be not cool. By definition, I am the death now. I've never seen a meme race that fast through

descending through the ages of kids through a school and then dead. I feel like it was around way before. I feel like it's like when you have an overnight success. I would say that 6-7 is probably going along for quite some time before it was memeified. Once it was memeified, it burned bright and fast.

Yes. Yeah, like a supernova. I had someone describing to me, they had to help out on one of their kids, like a primary school kid's like field trip, like excursion. And there was still one kid, six, sevening everything. And all the other kids were like, you've got to stop. I know you've made this a load-bearing part of your personality. Yeah.

But you've got to let go now. The other kids, you're getting so annoyed. That would have been me. Yeah. I'm that. Yeah, as soon as people said it was annoying, I'm like, great, doubling down. Lock it in. I used to say, I used to not know how to respond to compliments.

So I just started going, I know. And then I remember, I specifically remember my friend saying, stop saying that. It's really annoying. Wow. And then now I was like, all right, well, you better believe I'm going to be really leaning into it. And now I have no idea how to respond to compliments. As an adult, it's very hard to say, I know. But yet somehow.

That's right. I actually should have listened to her. I've just learned to go with a concise thanks. Then I yell by and I walk away. I feel like we're a fair way into how we're doing. Just for completeness sake, so we can tick the box. How are you doing? I'm all right.

I've started reading Terry Pratchett. Oh, wow. Finally. Wow. Yeah, I was gifted Mort, which is the fourth book. in the Discworld series. Yep. And it's the first fiction that I've actually read from cover to cover in a very quick amount

of time for a long time. And it's got the lifetimes in it, which people mentioned to us when we were talking about the hourglasses, which is an hourglass that lasts for a lifetime. So finally I got that reference. There's so many references that I finally got from our listeners. I'm under-patcheted as well. It's really good. Yeah, I know.

I'm great. Now I got you saying it as long as well. When people say go to the gym and you're like, I'm not going to the gym. And then you finally go to the gym and you're like, oh, yeah, I should have gone to the gym. That's exactly how I feel about Terry Pratchett. And, yeah, because people would be, like, people would be surprised when they found out that I hadn't read any. Because they're like, that's very much your jam. And I think it was the fantasy element that put me off a bit because I'm more of a space guy rather than like fantasy.

But the type of writing is, nah. Yeah. It's great. I've read bits, but like books, but I think there's just such a daunting amount of it. I've never sat down and read stuff, like all of the disc world, like series or whatever. I've just picked off books here and there as they've happened to float past me. Yeah, I think now I'm going to have to start from the first one and work my way through. Yeah.

Great. Yeah, and we did an evening of unnecessary detail. We didn't even in the necessary detail. Which was great. That was a lot of fun. Yeah, I talked about the Tooth Fairy and managed to. not go on a massive rant about the film with Dwayne The Rock Johnson.

No, but you did dangle it in front of the crowd. Because I wasn't sure how long my set was going to take. Right. And then I finished like perfectly on time. Yeah, you nailed it. And I was like, well, there's no time to talk about the film. I have a whole, that film, anyway. Wait. You can come back and you can do a whole thing.

I just like, and then there's maybe something you talk about, it's from that rebranding era where the top of the poster has to. to have Dwayne and then The Rock in quotes. And then Johnson at the end of it. I found that I have to say the full Dwayne the Rock Johnson. There's something very fun about saying Dwayne the Rock Johnson as if that's his full name.

Yeah. I always, if I'm in a restaurant, order food using the entire title the restaurant have given it. Because if they've gone to all the effort to name their dish, I use the whole name. Yeah. I don't just be like, can I get the burger? I'm like, can I have the? and then the extra Super Smash name of establishment burger or whatever they've called it. Yeah.

I'm like, can I have 12? Can I have number 12? Whereas I try to make it sound as natural as possible. Yeah. So I don't want it to be a, like, they're like, this guy's doing a bit. But I am doing a bit. I try to do it as subtly as possible just to get it. So it's a joke for you and you're alone.

100% Like many things in life I remember quite early in our relationship I forget the situation But Lucius went Wait, you just do this stuff when you're by yourself As well I'm like yeah I'm only ever entertaining me

Just because there's no one else here Stop doing all my You're your greatest audience Exactly 100% Great audience And how are you I'm good And your audience

Yeah well we did detail on Monday which was a lot of fun. Thank you to everyone who came along. Full House, which is great for a new venue. First time in a new space, like we show up and the venues used to like single human in a microphone shows. And we're like, okay, we've got this many laptops. And we've brought our own, you know, a projector and vision mixer and all this stuff.

But up the creek were great. They rolled with it and they got it all working. So which was lovely. And thank you to everyone who walked up and said the secret code phrase, blah, blah, blah. and were issued with a salt of the Perth sticker. I left mine at home, but thankfully was in the green room so much that no one had a chance. Everyone got to me first. I'm always there walking around.

So I think everyone got their blah, blah, blah, it's out of the way with me before they found you. And early on, I forgot that they're all on one big sheet. And so for the first two people, just got the sticker peeled off and handed over. and so it was just a sticky sticker they then, the clock was ticking on using that. Yeah. I think the third person had bought and brought

a container of salt. Wow. But just like the cheapest salt that let's say Sainsbury's does. A little bit of me was like, what do you think this is? First of all, I'm offended, you're paying money for salt as we've established. It's free. It's in the ocean. Go get it.

Go get it. Secondly, I'm putting my face. Yeah. And growing brand. Someone's going to sprinkle that and go, hang on. Hang on. This is too granulated.

This sprinkles way too easily. Why am I getting such a homogenous seasoning? This isn't salt of the Perth. This is a normal salt. This isn't clumping at all. Where's the caking? So I stuck straight on the salt for him. And then I managed to wrangle some scissors.

So by the end, I was cutting them off and out of the math. So success. And I got to talk about the maths on the Kellogg's, Frosties, Glazed Donut holes, which was a lot of fun with the audience. Yes. And then the very next day, I filmed a YouTube video about it. I will have a video soon about Kellogg's claiming a sphere as the perfect shape to hold sugary glaze. And I got a whole thing about that, which is a lot of fun.

It was very pleasing. Yeah, it made me remember that I want to. revisit my oven chip. Yes. 100%. Right. So in conclusion, this is a podcast where we entertain ourselves. Yes.

Shall we do the podcast? I suppose so. First problem comes in from Adrian, who went to the problem posing page, which I believe most people find at a problem squared.com. Adrian then typed in, Dear Beck and Matt, my girlfriend and I, store most of our pantry items in glass jars. Ooh la la. Anyway, Adrian, I don't think that's the big problem here.

They try to give each jar a fun name, which is describing what's inside. Some English examples are Drummond Basmati. Okay. Jazzmin, but that's jazz like the genre with two Zeds. Sugar Hill Gang. Wait, are they all? music? Oh no, the next one's Sesame Street in Linseed Graham. Now so far they've just been showing off both their fancy jars and their funny names, but the actual problem, that's it,

the end. Our problem is not enough people appreciate. The actual problem is they want more fun names for common items and as examples they say pasta types, flowers, beans, lentils, dot, dot, question mark. Thank you for the amazing podcast, obligatory blah, blah, blah, Adrian. Beck, this feels like a perfect problem. Yes, I've come up with a list of things that you would commonly get. And they've got to be dry things. They're things you put in jars, right? It's got to be jarrable.

Yeah. I'm going to read out what a thing is. Okay. And then you're going to guess what it's supposed to be. Got it. So I thought I play a little game with you and producer Laura. Oh, great. Called Name That Pantry Item.

I may have just named it just then. Let's see if you can guess this first one. Okay, I'm ready. Spaghetti about it. Would that be the spaghetti? Ding. I feel like we're going to split the point on that one. Flaude powder.

Like flower power, but for flour. Yeah, exactly. FLO you are. Yeah, it's flour, yeah. Flower. Okay, next one's a bit harder. Orphan powder. Orphan powder, like a ground-up orphan.

Yeah, it doesn't sound like something I want to eat. No, give me a second. Give me a second. Orthin powder. Yeah, I got nothing. Or-or-or-an. So it's not a play on the word in terms of how it sounds. I'm trying to work out if there's like a type of flour. I've got it.

What is it? Self-raising flower. Because orphans have to raise them. Oh my goodness. Unbelievable. We try to give each jar a fun name. Rowan Atkinson's. That could be any type of bean, right?

Mr. Beans. It's just beans. Just beans. All the beans in one big... I was thinking black adders would be black beans. Okay, that's kind of freaky. Yankee doodle noodles. Yankee doodle noodles?

Yeah. Mac and like macaroni. Yeah. Pasta? Oh, okay. Yeah. I would have called them like baby got Mac or something. Oh yeah. That's good. Cooked cane.

Cooked cane. Yeah. Now, my instinct is like brown sugar. Yeah. I liked it because it sounds like cocaine. Right. And if you had it on like white sugar, then. That's very funny. Yeah, thanks. Karaoke cane. What do you do when you're doing? Self singing. Self.

You're really close. Singing sugar. It involves singing. Sing. I sing. I sing. I sing sugar. I sing sugar.

I sing sugar. Baking bad or in brackets, water white stuff. Baking bad is great. Thanks. And it's pretty obvious what that is, I think. Meth. Otherwise known as. Baking powder.

Yeah, it's baking powder. Oh, baking powder. Okay, that's great. Erecting. Now this is, I will, I'll give you a hint, it's a dried fruit. Erectings. Erectings. Erectings.

Raisins? Yes. These are less like puns and more cryptic crosswords. Yes, we're a plus. This is why I turned into a game. Yeah, no kidding. Queen of spades. Queen of spades.

This one's a tricky one. Queen of spades. It's type of grain. Okay, here we go. Queen of Spades. A type of grain. Type of grain. Cus-couce. Keynoir?

Yes. Keenwa? It's like Queen Noir. Yeah. Oh my goodness. You may have heard me go as I thought of it. Sanders. They're probably kernels or something.

Yeah, that's right. Popcorn kernels. Nice. Nice. And then I've just got Doctor. Is it pepper? Yeah, it's pepper. then Doctor Who? White pepper? No, it's a herb.

It's a herb? Yeah. Is there a herb that lives forever? Because we never actually use it. Is it Oregona? No. Just naming herbs now. Is it basil?

Is it fennel? No. You'll get there if you name herbs. I know, it's naming. It's one of the big ones. One of the big players on the herb scene. Mint. No.

Parsley. No. We're going to... Hang on, hang on. We're going to do it. We're going to... I refuse to do it by exhaustion. What is the doctor in Doctor Who?

An alien. Or more specifically... It's time. It's a time, Lord. Oh, it's time. Come on, guys. This is making some listeners very angry. I feel like...

In both directions. Correct, correct. I feel like... You could have just put... Time Lord on the jar with... Yeah, but it's too easy. It's not supposed to be a challenge. They've said, a fun name.

A fun name, which... I hate to quote Adrian back at you, which is describing what's inside. Not leaving breadcrumbs. I mean, to be fair, you could call Time Lord. You could call Popcorn Colonel's... Colonel Sanders. Yeah, yeah.

Like, I'm giving you two. things here. I'm giving you a game and an answer. There's two more left. All right. Urine balls. Urine balls. Yeah. This is a play on words. Peanuts?

Yeah. Peanuts. I hate the fact you're making me try and be good at this. I'm forcing in order to solve the problem you have to be really Immature. All right, last one.

This one's very easy. I'll both get this. I believe that when it happens. Matt Parker. Better be delicious clumping salt. You bet your sweet butt it is. My butt is salty. Well, Beck,

like you've really close the lid on that one. Some people tune in for in-depth research. and tendons. But you know what? I feel like sometimes you need to have something really dumb to really appreciate all the other ones. Good work. Excellent.

This is a palate cleanser. Yeah. All right. Well, Adrian, you... You asked for it. And your girlfriend are the only people who can decide. If what just, if what just happened, solves your problem.

please report back of any of these that end up on glass jars on shelves in your kitchen. Our next problem comes from Rafe Rhyrhymes was safe. I'm assuming the entire name is that. So Raph Rhyph Rhymes with Safe has also written a short version and a long version of the question. Very much appreciate that. Me too. So the short version is, what's the smallest number that? never been written down in human history.

Slight caveat, integers only. So, Rafe watched a number far video from a few years ago, done by Tony. Which is a YouTube channel which you have featured on. YouTube channel that I've featured on many times over many years. And in the video, Tony went through the concept of how big a number would you have to think of to, with some level of certainty, be confident no other human had thought of that number before. Now, Rafe slightly changed it to be written down, subtly different. We can try and solve it either way, to be honest.

But they're not 100% convinced by the argument put forward a number file, and they're curious to know my take on it. Now, just this alone has raised many questions. Yes. If you can imagine the number or write it down, then it already exists. Yep. Which means that someone else has...

Ah! Ah, maths, we discover it. We don't invent it. All numbers are already there. Do we have a highest, you know, we've got like Google. Oh, yeah, yeah, good work. So I knew about Google. I don't know how that ranks.

You're pronouncing the gold bit so specifically. I'm so specific. I don't know where that, it rhymes with Smeagold. I don't know where it goes in terms of like your, your zillions and whatnot. But like what is the largest, you know, thing with that many zeros that has been named? That's great question. So suddenly different question is what's the biggest number? Humans have used as such.

And Google is actually pretty small in the biggest scheme of things. It's 10 to the power of 100, which means it's like a one with 100 zeros. Yeah. It's like a million has six zeros. Billion's got nine. Google's got 100. not big more than the number of atoms in the universe, I'm pretty sure, but not outrageously big in terms of numbers.

A Google Plex is when you've got one and then a Google of zeros after the one. So there are much bigger numbers. Famously, the biggest number ever used is something called Graham's number. I always forget how much of an anti-climax that is. When you're for the first time, it's like you got your plexers and your genoma and your billions. What's the biggest one? Graham. See, the problem with the patriarchy is that because there haven't been enough women of like who've been given the same level.

Yeah. I would love there to be like a Susan. Susan's number. Yeah. Yeah. Barbara. Now, there's an ongoing debate in mathematical circles. that nothing should be named after a person because it's a terrible way to describe something.

Yeah. It tells you nothing. Yeah. And I agree with that like 95, maybe 96%. Except for when it comes to certain... Money names. Yeah, no, exactly. Exactly.

If you're going to name it a minor planet, name it after this white guy. So, no, it's because like not everything can be a description. That's why we have names. So I'm not saying it's going to be named after dead white guys. But sometimes a name is a catchier way to summarize something. Yeah, like Kelvin. But that's a day. But often, like, calling it Graham's number tells you nothing about what it is.

Whereas if we called it the hypercube coloring number, you're like, oh, okay, it's not a full explanation, but I understand where it's coming from. And it sounds more impressive than Graham. Yeah. Okay, I get that. I mean, Graham's number was the, interestingly, so it's. It's touted as the biggest number ever used. And it was in a maths paper by Graham. I was going to say, yeah, I bet I know who said that.

Yeah, Graham was talking about this. And Graham was trying to work out. And it's like this classic theoretical math question where there's no reason why you want to know this. It's just an interesting question, can we solve it? There was a question about how many, don't quote me on this, something like how many vertices would a very high dimensional cube need to have such that if you colored the vertices, some number of colors, you wouldn't have

two touching the same color. It's something in the ballpark like that. And because it's combinatorics, basically, when you're looking at combinations and arrangements of things, the number of options explodes hugely. And so Graham's number was just a case of saying, oh, we think there is an answer to this. and it's definitely smaller than, and the upper bound they gave was then named Graham's number. And at the time, I think the lower bound was six. So somewhere between six and the biggest number ever used by humans, the correct answer is in there.

But it's not infinite. Like, it was just trying to show there's a finite answer to this problem. Right, yeah. And with no interest in being efficient about it, they didn't care how big the threshold was. They just wanted to prove it exists. But you wouldn't say like Graham's number is a one followed by however many zero. We haven't got a way to articulate that, no. It is, it is a certain number of digits.

Yeah. But we don't have the machinery in all the brains. It's a bit like algebra. Like it's a placeholder for the number that we don't, we don't have a specific number. But Graham's number is a specific number. And we've gradually been working out some of its digits, but we have no idea what it is. Yeah. So it's not algebra where it's.

placeholder for possibilities for numbers. It's a specific number. We just don't know what it is. Which, you're right, a form of like a pronumeral, we got something to represent the number we don't know. In that regard, it's exactly like algebra. So you are correct. So what is the highest number that has been named

where it would be like, this thing with this many zeros? Oh, that's interesting. where it falls into a rhythm after a while of just putting Greek, whatever they are, words together to describe. Yeah. Because once you go past trillion, you then just quadrillion, quintillion,

sextillion, you're just, you're working your way up. There's an algorithm by which you can generate a name for any number of zeros. Because I think that was like the way that I thought, and I know this isn't even the question, but like to understand the question

I needed to understand. the original one it was stemming from. Because my first thing was, well, then you just take the highest number we've named. Yep. And I'm just going to say a million as if it was. As a placeholder, I agree. As a placeholder. So say it was a million.

So then you'd just go, all right, well, it would be nine million. Yep. Nine's all the way down. Yeah. Like that would be, because once you get one more, next number, we haven't named it yet. That was my least thing of it. Yep, yep. Because it was like we can't name the number, so that must be the biggest one

that we've been able to write down or think of. The thing is, naming is just a handy convention for small numbers. It doesn't really hold for bigger numbers. Although people love reading up big numbers, doing the full name. But I understand now that it's more like what's the biggest number that would have come up in. Yes. Yeah, because even like your calculator might, depending on what sort of calculator you use, might have the like E where it just like.

Yeah. Oh yeah. It just rounds it off and says it's this big. Yeah. So even a calculator can't go beyond a certain amount. So it's interesting that now we're talking about numbers we're likely to use because they're a big obscure math numbers like Graham's number and there's other ones. There's tree and all these things.

True. The tree numbers. You know. I swear, the more I find out about math, the more it sounds like when people talk to me about numerals, like, like horoscopes. Oh, when they're just like, oh, yes. This number's in tree. Retrograde. What you're kind of touching on is when you've named big famous numbers like a billion or a trillion, they're going to get used to a bunch.

Easy to say, people are aware of them. But like a number that's basically the same size as a trillion, but there's a couple off and looks like a bunch of random digits, maybe no one's ever used that. Maybe they have. Like if I gave you a bit of paper and said write down a number you think no one's ever written down before, how many digits would you have to write before you're confident you're the first person to write that number down? Yeah. That feels like a possibility to figure out. Well, we can try. What? Now, there's a similar question, which is with a deck of cards.

So famously... Wow. Matt just snapped his fingers and a deck of cards appeared in his end. famously, if you shuffle a deck of cards, you will end up with an arrangement that's never been shuffled before. Yeah. The deck of cards, I just shuffled them. No one's ever shuffled a deck into that arrangement before because there are just so many ways you can arrange 52 cards.

The probability of someone else having done it exactly the same is basically zero. No, I refuse to believe that. I know. I thought you might. Because there's a lot of people out there and a lot of card games happening all at the same time constantly. So what's the maximum number of shuffles humans could have done? Does it involve a shouty sign? No, it doesn't involve a shalti sign.

The number of ways you arrange the deck is 52 shalti sign, which is actually, we get the exact value of that. 52 shouty, I think it's like 10 to the 60s. Yeah, eight times 10 to the 67. So it's eight with, well, it's a number that starts 80658-175-170-9-43 and then carries on for a total of 68 digits. Could we estimate an upper bound? Like what's a number we're confident humans have shuffled a deck of cards that many times or fewer? I mean, I'm thinking about all the casinos around the world that have games going on constantly. surely there's like millions a day.

Yeah. Well, you could say there's currently like 8 billion humans. Yeah. A billion or fewer are playing cards at any point in time. Yeah. Definitely 8 billion or fewer, because that's the number of humans we got. Sure. That's the upper bound.

If you really want to go nuts, you'd say, tell you what. Let's say everyone has a pack of cards. Everyone's got a pack of cards. Let's say there's 10 billion humans. Everyone's got a pack of cards and they're shuffling it once a second. Okay. And they've been doing that since cards were first invented or something like that, right? That would pin a very, very high upper bound on what that could be.

Should we try that really quickly? So let's put in 10 billion. Yeah. 1, 3, 456, 7, 8, 9, 10. Okay, 10 billion times. That's people, everyone shuffling cards. Yep. But they're shuffling it once a second.

So I'm going to do 365.25. for days of the year, times 24 hours in a day, times 60, that's once a second. And how long do we reckon, what would we say? Like, when were cards invented? It feels medieval. Like dice are older because there's Roman dice. We don't have kings and queens on them, so I... Yeah, maybe they could go way back.

Producer Laura says... Playing cards were most likely invented during the Tang Dynasty around the 9th century. Okay. and far off. Well, let's check in 2,000 years just to be safe. 1,000 years. Okay, here we go. Maximum number of shuffles, 6.3 times 10 to the 20. Oh. So a number with 21 digits.

The 10 to the whatever is how many extras plus the legal. So even our upper bound is like a third at the very... It's not even a third because each time you go up a digit is 10 times bigger. Oh, yeah. Oh, cranky. Yeah. This is the same as a birthday problem. Instead of having a birthday and you're choosing from days of the year, this is your shuffling cards and you're choosing for more possible shuffles. So what we're asking is if there are 10 to the 67 arrangements and we've shuffled 10 to the 20 times, that's like saying there's 10 to the 67 days in the year and we've got 10 to the 20 people with birthdays. What's the chance two of them have the same birthday or not? That's what makes cards so good for bedding and gambling, right? Yeah.

Because if there was a chance that it would be in the same order as it has been before, yeah. Okay, I'm just going to very quickly, I've written some Python code that now working it out the proper way, because with a birthday, the numbers are small enough, we can actually work it out completely in detail because it's only 365 days. And it ends up being 23 people. For much bigger values, there are approximations. and so I'm using approximations for much bigger ones, but they're very accurate within what we need. So we just said there's 10 to the 20. Let's even do six times.

It almost feels pointless, but why not? Six times 10 to the 20 shuffles out of 52 factorial. And I'm going to print the probability that the same shuffle happened twice with those assumptions. Zero. I haven't got enough precision. I'm sorry. Come on. I was hoping I'd get like the whole thing. It's just, it's, it's too small to even calculate. Wow. Yeah. Yeah. Okay. So that, yeah. So now we can do the same thing with numbers. So we have to work out how many numbers people have written down. Okay. And then we can work out. how big a number you'd have to write down such that there's like a 99% chance

no one's never written it down before. Yeah. That would be the way we'd do it. Yeah. And shall we just use the same number? So instead of 2,000 years, we bump it up to 10,000 years. Sure. Because that's going to get us way back before people were writing numbers, how we'd understand it.

That only puts us up to 3 times 10 to the 21. So now it's 3 times 10 to the 21. Okay. So we're going to assume humans have written down a maximum of 10 to the 21 numbers. And there's a big bound. What level of confidence would you like that no one's written down the same number as you? 99%. 99.9.9.99. I don't know how many nines.

I mean, how big can we get? Tell you what, let's do 99.9.9.9. Lufth balloons. 9.99%. There we are, basically way out. I'm basically, I'm just plugging in a bunch of values and waiting until, I'm not even close to it yet. Okay, 70. Now, I could have written an equation to try and solve this.

Ah, there it is. Okay, so, yeah, 50. Okay, there it is. 50 digits. If you write down a number with 50 digits, there's a 0.000000-1 probability. that assuming 10 billion humans for 10,000 years doing one a second, someone will have written on the same number as you. So 50 digits is an upper bound. But I'm happy with that. The number file working out got 67 digits. But they answered the subtly different question

of how big would a number have to be, that it's 99% likely no one has ever used a number bigger than it ignoring trivial examples. So actually the number five video is subtly different. The moral of the story is a bit like if you shuffle a deck of cards, you'll get an arrangement no one's ever shuffled before. If you write down 50 digits, no one has ever written down those 50 digits before. And almost certainly you could get away with far fewer digits. We've just made some big assumptions.

Can I swoop in with a back way of solving this problem? Yeah, because you're looking at something on your screen there. Yeah. In 2013, a PDFE book and then a multi-volume set of soft cover books, both with their own ISBNs, was self-published by Wolfgang H. Nietzsche. The volumes were called Googleplex written out. Hey, all right. Where it is a multi-volume of books.

It consists of a Googleplex, which is 10 to the power of 10 to the power of 100. Correct. Which is a one followed by Google zeros. Yep. And they have been writing out that as a series of books. Writing? Or is it like type? Is it been programmatically generated and typeset?

Or is this someone actually writing it out? The copy is, in 1940, the mathematician, Edward Kassner, published the book Mathematics and the Imagination in which he popularized the words Google and Googleplex. Oh, that's where they come from. Nephew suggested his names for big numbers. The number Google has been defined as one followed by 100 zeros. A much larger number, Googleplex, has been defined as one with Google zeros. While this number can easily be written as Googleplex, or you know, you have 10 to the power 10 to 100.

Using exponential notation, it has often been claimed that the number Googleplex is so large that it can never be written out in full. However, in this Googleplex written out multi-volume set of books, I am doing just that. Ah, work in progress. It consists of a Google volumes. and each volume contains a thousand zeros of the number Googleplex. The first volume also contains the initial digit one with which Googleplex starts. Okay, so if it's Google volumes, then it must be a Google divided by a thousand volumes if there's a thousand zeros in each volume. And it looks like that volume is here.

Right. And by writing out, is this person set at a keyboard tapping zero? It doesn't specify. Because a human lifetime. Yeah, because even the seconds that would take to add out the numbers. Yeah, it's not long enough. Yeah, so he must have, he must have written some, it's Googleplexwrittenout.com. Catchy.

Yeah. Yeah, because a century is roughly pie billion seconds. Yeah, so there's no way that. No. So if you do something once a second, your absolute upper bound is ones of billions. Yeah. Yeah. So there you go.

That's the highest anyone could have written out, is if they started writing out a number from birth. You go, yeah, zero. It's just the easiest digit to teach. Or ones maybe. Go. But there you go. There's a little bit of extra. There you go.

I mean, Wolfgang's a liar. Honestly saying that they're attempting it. Yes. And there's someone who's printed out. the at the time largest known prime numbers, I'm not one to diss this project. So those are big numbers. Big numbers. But this question was about smallest.

The smallest number you could be confident is 50 digits. Now actually, we could tighten our assumptions up a little and maybe 50 is too many. Maybe we could bring the threshold down. But I'm happy to say 50 digits would be unique. Well, we could do that right now. We could do that right now. Do you want to write out 50 digits? No.

Oh. Do you know what? That was both really interesting and not. It's just another adventure and big numbers are big. Did you catch that the number of arrangements of a deck of cars is 10 to the 6'7? Oh, no. Wait, are you, have you reverse engineered this? Did you make the theme of the episode 6'7?

because you knew that 6-7 was going to be involved in this. Which came first, the 6-7 or the... Which came first, the 6 or the 7? No, it's because I knew it was going to be 10 to the 6-7 for the... Oh, that's even less cool. Someone yesterday, actually was Keith Stackle sent me, someone's made a super cut of every time we said 6-7 in number file over the last like 15 years. It's pretty funny.

You can even place I'm in. Six plus seven. Six, seven. Six, seven. Six, seven. Six, seven. And don't. Now, it's time for any other business.

And I had forgotten what we're doing for any other business. Yeah. I was reminded right then. You made a big fuss about this the last episode. Oh, my goodness. If people who haven't heard the last episode, I was excited about what I assumed would be the wave of salt-related chat. And there was basically zero.

Yeah, I realized that we referenced at the top of this episode about... My salt. Your salt. And actually, for any new listeners, we have not explained that whatsoever. My side hustle. Yeah. How would you summarize it? Matt's attempted to make his own...

Well, Matt has made his own salt. I harvest fresh seawater from the Indian Ocean. Oh, but this means you could harness like sweat salt and tear salt. I feel like no one's taken my salt. I'm going to start saving my tears. Every time I cry, I'm sitting in a jar. Yep. And we're going to see how much salt you can build up.

The point is, I'm not harvesting the salt from my own. It is the result of the sweat on my brow, but it's just the effort it takes to carry the water home from the beach. So I made my own sea salt. I was very proud, and Beck made me a logo. Yep. Sold to the Perth, printed a bunch out. And that was mainly so I can get it back through customs and make it look like a real product. It did not look like a real product.

It did the opposite. It made it look like I was smuggling a suspicious white powder. Yep. I had a surplus of stickers, and I offered to give them away to anyone who came up and said blah, blah, blah. Yes. And that has begun. I think the audience have ascertained all of this from context by now. I'm just putting it all together. This is what we should have said at the beginning.

I feel like we're about to have so much salt chat deep in the salt law of a problem square. Salt mines. In the salt mines. But I just want to make sure we're all starting with a rolling stuff. Okay. All right. Do you want to read them out? I haven't even looked at them.

I wanted to come in fresh and salty. All right. Well, I will say that I appreciate the fact that people have been writing in with their credentials. Oh, no. My favorite, my favorite salt. So we heard from Andrew. Hi, Beck and Matt. I have a proposed solution for your salt question.

Yes, they've put solution in quotation marks to show it's a joke. That's how I do my jokes. You do. As an analytical chemist with several years in mineral and environmental testing, I feel my input is warranted. Oh my good, yes. 100%. There is little cause for concern consuming the salt you made.

Well, good. Thanks for telling us now. Because, mate, I've been going at it. In that quantity, any of the likely suspects, arsenic, lead, etc. Wouldn't be present at sufficient concentration to cause harm. Right. I wouldn't make a lot of it and use it as your primary seasoning of choice just to be safe. That chip has sailed.

Boiling slash filtering the water should remove anything else of concern. Maybe some microplastics slip through, but they're already a part of you now. Yeah, exactly. It's too late. I would also be happy to analyze yourself for you, primarily for metals and composition. I'm in the US, so that might pose a problem. It's crossed international borders once. But you're the experts on problem solving, so I'll leave that to you.

I'm happy to answer any more questions about analyzing salts for chemical composition. Thanks, love the pod. I'm not doing the blah, blah, blah thing. Thank you, Andrew. I like the cut of Andrew's gym. Yeah, me too. To the point, no messing around, no blas. Great.

You know what, Andrew? I'm going to smuggle some salt into the States for you. I love to get it analyzed. That like, if you had it analysed and then you'll court it customs, then you can be like, I've had it analysed, here's the breakdown, here's the official. Trivel amount of lead. But the fact that you don't have that yet.

Now, here's my big issue. Because what I'll do is, I'll wait till the next time I go to the States and take it with me and then post it internally. I don't want to post it in the mail and feel like that's a whole other problem. I think international mail, they're probably looking for drugs. What should I do? Should I take the entire jar with me? I think you should put it in a big, you should brick it up and a big plastic with tape.

Exactly. And then you take it to your stomach as you go through the... Because my instinct is I'll just put a little bit in a zip-lock bag and take it over for it. Okay, Andrew, Andrew, we'll talk. I'll send you an email. We'll work something on that. But you know what? I've leapt straight in to picking Andrew. I assume there's, there's, you know, multiple chemists have offered their services. Finally, you should say that. Oh, my goodness. No way. We heard from Tristan, who said, hi, Matt and Beck. I do work. I do work. I do work. I do work. Look, I do work. Yeah, whatever you say, Tristan.

geology lab. In a geology lab in which one of my main jobs is identifying minerals in small samples of powders. The suspiciousness and colour of the powders varies widely. Yep. They're used to working with orphan powder. Oh yeah, yeah, yeah, classic. Flauda powder powder. It is fun to say.

If you were willing to part with a small sample of the salt, maybe an eighth teaspoon to be safe. Oh, look, minimum serving is a whole teaspoon. But I can make do with pretty much anything visible to the eye. I would be happy to get back to you with a thorough composition and analysis featuring pictures, graphs and best of all numbers. Tristan. I am in the US. Oh, this again. So I recognise that shipping costs would be statistically significant.

I don't think it's a shipping cost. I'm worried about. Not the problem. Sure, there are places in the UK with same or similar equipment. I agree with you, Tristan. And Tristan does say blah, blah, blah. They do say blah, blah, blah. We heard from Kahn.

And I love this Kahn. Kahn has put A-O-B salt. Great. So the producer Laura, you knew where you put this. Boom. Love that. Hey Matt and Beck, love the pod.

Listening from episode zero one. Great. Take that zero zero two. Today I learned that salt, sodium chloride, form square-based pyramid crystals. What? What? And my mind was blown.

I didn't know that. That seemed like the perfect intersection between Matt Salt Guy Parker, Matt Geometry Guy Parker, and Matt Science Lab Coffee Maker Parker. Everything at once. Apparently it involves a shallow pan, heating the brine to precisely 70 degrees Celsius, alum powder. Alam powder?

Huh. That must be like to seed the crystal flowing. And harvesting the pyramids promptly with tweezers before they sink. This sounds very labor intensive. Could salt pyramids be another exciting product of Matt Parker's Perth's salt enterprises? All the best, love your bans. Now, I'm tempted. I don't know if I could do that at scale, but I'm tempted to see if it works.

We also heard from Dr. Alastair, no indication, what type of doctorate or whatever, maybe medical, because they're talking about iodine. They're pointing out that since 1924, iodine has been added to most commercially available salts to prevent a host, all caps of problems caused by iodine deficiency. Great point. And I'm kind of aware that's one of the most successful medical public health things that has ever been. done. So they're pointing out, I can enjoy my free perpetual salt, and I assure you, Dr. Al, I shall, but maybe try the brand name stuff once in a while to get my iodine. Okay, that's a valid point. Maybe you just need to mix some iodine in with your salt. Yeah, I could iodize my own salt. Can you know, I just take a tablet once a year? Would that do it? There's no, Dr. Al.

A few people have been a bit sassy, per specifically, has pretended they're sending you. in a genuine problem in good faith, but they're not. They're one of the people pointing out that what I did to get my free salt involved a bunch of energy. No comment. Finally, lazy Tom wants to know why I'm importing salt from Australia. The UK has salty oceans as well. Yeah, but have you seen British beaches?

I mean, there's probably a lot more sewage you've got to deal with. Yeah. I wanted pure, pure water from the Indian Ocean. ignore the fact we're pretty close to a large shipping port in Fremantle. And Cannon, they say they have a solution, about how I can transport my handmade salt from the UK without getting flagged for transporting suspicious white powder. They say, before I leave Australia,

I should rehydrate my salt by pouring it into the sea. And then when I arrive in the UK, it's a simple matter of picking it up at my nearest coast and dehydrating it back again. You're welcome. No, you're welcome, Cannon. I think that's a good point. I think, in fact, if Tristan and Andrew do want to test Matt's salt.

Pour it in this side of the Atlantic. Jerks, everyone. Look. Otherwise, it would be called Sold of the Perth. The motto is it tastes like being dumped by a wave at Scarborough. Well, you know what? It's like being dumped. It's a great tagline for your product.

Then you're going to rotate the jar to keep. reading it. Oh, by a wave. I mean, being dumped can be a very salty experience. You want to make sure the label doesn't get like wrinkles. It doesn't just say, taste like dumped. It tastes like dumped. So, I don't know, I got my wish for salt

chat. I'm not 100% sure. It's gone the way I was hoping. Oh, Canada, I love you. But you know what? I am going to take both Andrew and Tristan up on their offers. and send some samples off to get analyzed and see what we go back. Buy, take them up on their offers, you mean?

Post them, post them some salt. You're going to post some salt to the States? I'm going to salt mule it there myself, and then I'm going to post it to them. All right. And who's going to remind you that you said that you would do this? I think that's a producer Laura problem. She's just going to keep an eye on your diary. Yeah, yeah, yeah.

Well, thank you so much for listening to this episode. We very much appreciate everyone who does this. the podcast of grovelment of tuning in and of course shares this with their friends and family. However, special thanks has to go out to the fine people who make this possible. Our Patreon supporters who put their money where their podcast is and grease the wheels. I'm not joking. I did my tax the other night. And if it weren't for this podcast, I'd be in severe financial trouble.

You're still a little shell-shocked from doing your own. attacks. Yeah, yeah. It was a real like, oh no. Oh, that's not. Sorry, everyone. Thank you for keeping back solvent. Yeah.

Like, yeah, really thank you so much. And if more people want to get involved, head on over to Patreon.com slash Problem Squared. It's been a rough two years, Matt. Yeah, you've had a lull between books and TV shows, right? Yeah. since the channel that my show was on shut down. I should do stand-up again.

Yeah. And then you remember what's stand-up pace. He doesn't pay anything. Yeah. Yep. Anyway, right, rant over. Rant over. If you do support us on patreon.com slash a problem squared,

there is a probability. Who knows what it is, one in an end, that we will read your name out randomly at the end of an episode because we pick three names every time and we give them the special perk of mispronouncing their names,

which this episode shall include To New York B. C. D. Rickrow. Jackers. A nasal, a knack. Well, there's the three for this time. Thank you so much, everyone for supporting.

Thank you for listening. You've been listening to myself, Matt Parker. You've been listening to Beck, Hell. And occasional facts and interruptions. and comments from our producer. Oh, after doing the whole six, seven word thing, imagine this is seven words long, where I thank producer Laura Grimshaw.

I would say Laura does not interrupt. She helpfully aids. Okay. Potato, potato. Back, we got some feedback on our Gema Connect four. In fact, I think we've had two complaints so far. Yeah, the last complaint was, because I had originally done it,

I think letter, And the number. You did numbers across letters up and down. Yeah. And people did not like that. They didn't like that at all. So we changed it. We did.

And I said people are going to complain about this. They did. And I was aware of you. Specifically, on Reddit, as the person who has been doing the Reddit visualization of the games, since the start of battleships, I would like to offer the feedback that swapping the core system in the middle of the game is a right pain in the ass. On the podcast, can you please describe the coordinate system you'll be using? If you do the numbers like the floors of a building in either the UK or Australia, the movie is floating in midair.

No, we didn't do a ground. Didn't do a ground row. We didn't zero index the roads. That's what we're trying to say here. And I think we also caused confusion for producer Laura, who was trying to explain it. I was trying to translate your previous. move into the new coordinates. Got it.

And then I realized I didn't understand the system. There you go. But now I've got it in front of me. Now I'm here again. Is it our current game? I understand it. This is where we are, yes. Are we only three moves in?

Yes, this has been going for three episodes and we've had two complaints. And we're doing one move and episode. I forgot. Now, it's seven columns and six rows. So I think we should do days of the week I love it From left to right Yeah yeah yeah

I would like to do Column V You're doing Roman numerals Yeah Yep so column V Column V Yeah Thank you

Yep I'll answer no further questions at this time You don't need to know the row because it's just going to fall to the lowest empty spot in that column Yes. No, that makes sense. We can just say columns. And I'll do it around in numerals. You do days of the week.

I do it from one side. You do it on the other side. It's as easy as that. A piece of cake.