A Problem Squared - 144 = Numbering Tomfoolery and Number-Based Jewellery

Episode Date: September 28, 2026

#️⃣ How wrong can a sequence of numbers be?👂 What maths-related diagrams that would look good as a pair of earrings?☕ And we have some Any Other Baristaness Here is our dual-purpose Google Form - please answer our questions about number and clothing ordering! https://docs.google.com/forms/d/1tTb398TTacxoqlqJHGonkldwDsqnnMN6V4fRagfPOEI/Behold the weird balls! Here is Thomas Fernique’s Instagram:https://www.instagram.com/fernik_art/p/DcVerFCDiwr/ And head to our Instagram to see Matt looking really happy with a weird football and Bec looking really sad with a weird football.Some visuals to inspire designs for duallery - Brown University: Dual Shapes: https://www.math.brown.edu/tbanchof/Beyond3d/chapter5/section03.htmlSome pre-made mathematical earrings from Maths Gear: https://mathsgear.co.uk/collections/jewellery-etc  Vanessa Schattman on the maths of cat’s cradle:https://archive.bridgesmathart.org/2026/bridges2026-669.html#gsc.tab=0Do you have a problem for Bec and Matt to solve? Tell us about it: https://www.aproblemsquared.com/ Matt has extended his tour - and he’s filming the show in London in October - 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.

And welcome to a problem squared, the problem solving podcast, which is a lot like your local cafe. It's a warm and familiar respite from the world. However, we will never get your name right and we will cease to operate if we run out of coffee. Your host consists of the YouTuber mathematician Matt Parker. That's me. Who is the human equivalent of a large caramel latte. Oh, you see that coming. Tall?

Okay. White? Yep. And sweeter than you'd expect. Aw. B. Wow. I don't even know if you're legally allowed to say those words. I don't think so. I take it back. More like an espresso, bitter.

And me, Beck Hill, a comedian and presenter who is a human equivalent of a cappuccino, short, bubbly, and sometimes dusted with chocolate. That is true. On this episode, I've calculated how wrong numbers can be. I'm going to see if I can get an earring a ding ding ding. And we have any other bussingness. That's where you like clean the tables up. How are you?

I'm good. I know it's been a theme recently that we've both been doing a lot of travel. Yes. But my travels took me to Galway. Oh, Ireland. An island, yeah. The Bridges Math Art Conference was on. It's very much math-first art.

Mark as well. Yeah. You know. And we've talked about this before. We had those mittens. Oh, yeah. They came out of bridges. There you go.

And it's on every year. It moves around the world. I often can't make it. But if it's somewhere I can get to and I'm free, I do like to go along and I was able to go this year. Well, I didn't know until quite late in the day I could definitely get over there. And so I didn't want to commit to doing anything. But I just love being there and hanging out. So I just went there, hung out.

Thank you. Many listeners came up. and said blah, blah, blah, as I was haunting around. A particular shout out to Vanessa, who said hello. Vanessa was doing a presentation about the mathematics of Cat's Cradle, the string between the fingers thing. Yeah, and you know, I couldn't even see Vanessa's talk. There were so many things happening at once, although I've since looked up and found the PDF description of the presentation. So we can link to that.

And this time, well, I did not bring back mittens. I did bring back one thing. I brought back a football. We'd like to see the new football. I never thought, I'd say this, but yes. I would like to see. Oh, no, I don't want to touch it. Take it.

I don't like it. Touch it, take it. Oh, oh, oh no. What have you done? It's horrible. Can you describe why you're so upset at a perfectly normal football made from 12 pentagons and 20 hexagons. Because the hexagons are in the wrong places.

It's a weird shape where if you tried to kick this... It's not a sphere. It's like a triangle-y shape. It's like a triangle egg. It's so good. It's like it's a little football who tried. Like it's trying so hard and failing. Yes.

Look, maybe I should, when I put it that way, kind of feel for it now. Yeah, look at it. Yeah. So I'm also holding, I went and grabbed like a normal football. This is the one I've used in a bunch of videos. And I've got this ongoing campaign to get street signs fixed, blah, blah, blah. The traditional football is made from 12 pentagons and 20 hexagons. And I get very upset when I see depictions, they get that wrong. What you're holding still has all 12 hexagons and all 20 pentagons. But instead of the the pentagons being evenly arranged, they're clumped. There's three of them that are clumped together. There's a couple off by themselves. There's like two in a row somewhere else. It's so good.

Is this the same person who made your... It's not. I have a new ball person. So John Paul... What happened to the old one? Love John Paul. John Paul's balls still out there. John Paul makes amazing geometric footballs. This is a new person. This is Thomas Fernick. Can't believe there's more than one weird football maker. I now have got a second weird football person. Thomas's project is to make every possible different arrangement of pentagons and hexagons. Thomas worked out that there are 1,812 ways to arrange the 12 pentagons and 20 hexagons of a classic football. And this is arrangement number 200. And they're numbered, I hate it. They're numbered in decreasing amount of ballness.

So this is the 200th best ball of all the ways you can arrange. Oh, no. Twelve hexagons and twenty bending. They get worse. Not by a lot. They're all pretty similar. Bullness. And so.

So our producer is laughing. I was just giggling away over there. I think just at the way I'm looking at this ball. You look so upset. You're holding it. It's like an arm's length. Like it's about to hatch. Like a last poor yorre.

It's like the beginning of alien. Oh no. Oh no. Why is this happened? I just hate the idea that there's like more than 800 worse than this. Yeah, yeah. There's 1,612 worse than that. Oh my goodness.

That's not okay. Has he made them all? No, no. What's he up to? He's not doing them in order. What? Even, okay, I don't, everything in my core being. Well, the problem is they're very difficult to make.

Yeah, you don't say. They're even harder to look at. Thomas is deaf. Thomas says you have to find a way to get them all made. Thomas says you have to find a way to get them all made. And this took a lot of effort. They had to make the patches themselves. They had a couple different manufacturers flake out on them.

They ended up flying the patches. Yeah, because the manufacturers were like, oh. Yeah. They just kept burning them as soon as they made them. They would drown them in the nearest river. So they found the factory in Pakistan that manufactures a lot of the footballs that are sold in shops. Okay. And they took a store.

suitcase of patches and instructions out and got them to make a bunch for them by hand. So I really hope that they were responding the same. Like they made it and they're like just laughing at it and then being like. Pretty much. Pretty much. So I don't know what Thomas's long term plan is. They brought a bunch of them to display at Bridges and they have no idea who I am. But they were at a maths art conference and they set up these unusually shaped balls.

And they're like, everyone's going to come along and marvel at my incredible mathematical project. And like, everyone just walked up and went, as Matt Parker seen these? And they're like, who the heck is this Matt Parker? And I show up and they're like, you. And I'm like, I'm sorry. These are incredible. I'll buy all of them. And so what they were doing, they were selling some of them just to try and recoup some of their costs.

Yeah. And so I felt some obligation. What? You're saying these aren't commercially viable? So I don't know if Thomas is something more online or they were just trying to sell a couple at the conference to cover their costs. But I bought one. I love it so much. It's so great. The certificate that Thomas gave me to confirm this is an authentic one of one.

I'm assuming it's an adoption certificate. Yeah, I've got to. Which says you are now the owner of this cursed football. You can never get rid of this cursed ball. Yeah. In the background, now, Thomas has prioritized attention to detail and completeness over graphic design. Because in the background are all 1,812 footballs. Oh, no.

Do you know what? This absolutely, I take it back. I think Thomas is a genius. Yeah. See? Yeah, this is great. Telstar balls gone wild. For Telstar is the name in the 70s when they brought out the original Adidas arrangement.

It was called the Telstar because it has a passing resemblance. to a satellite called the Telstar that had been launched recently. Huh. Recently at the time, obviously. Oh, I, yeah, I hated so much. I love it. Hooray! Yeah.

Isn't that the best art? I think the certificate really helped. The certificate's doing a lot of heavy lifting. The ball is so good. Yeah. Now, how are you doing up to and just before I gave you that football? I'm good. Good.

So, again, traveling a lot. While I was away, I was a little bit nervous because I've been trying to not kill all of my pot plants. Oh, yeah, valid. But I have a little porch, and I asked the neighbours if they could water the plants. Water the little porch. The little porch. I got back, and not only did they water my plants, but check out this little yield. Oh, dang a whole!

There's at least 20 cherry tomatoes. Yes. You're handing them over to me. I'm getting 35 in here. Nice. I've not tried one yet. Yeah, we should try 100%. Yeah?

Yeah. Okay, I'm eating. I'm eating a tomato. Oh, yes. We won't get the sound of the eating. They're flavourful. Oh, they are. Concentrated tomato-y flavour.

I'm going to have another one. This is the healthiest snack we've had in this podcast. It is. Yeah, you're right. There we go. I'm proud. It should be. Good tomatoes.

Thank you. The end. The end. End of story. Great work. Our first problem for this episode comes from Morgan, who went to the problem posing page at a problemsquare.com. They selected problem in the drop down and they said,

Wassa! Back in Matt. A bit of background to my problem. On my street, there is a block of four units which I pass every day on my way to work. The letter boxes for the units are arranged in the following order and it drives me insane. 13, four, two. I'm guessing they're just all in a row. Yes.

They're not like in a sort of... A grid. Yeah. That was my reading as well. And I think they say, like they passed. them in that order. However, it occurred to me that while the sequence is in the wrong order, it could be more wrong. For instance, one is in the correct position and three and four while being in the wrong position are in the right order. A more wrong version of this might be 3142. However,

is there an arrangement that is even more wrong than that? Thus, my question is, what is the most wrong way to arrange a set of consecutive integers? Is the most wrong way, and I must stress that Morgan is capitalizing most and wrong. Is the most wrong way defined by an algorithm which can be scaled up to any number of integers, or is the most wrong way unique to each set of integers? Thank you for your consideration, blah, blah, blah. Matt, before I hand this over to you to answer. Yes, and I got some bad news about how much handing over you're going to do, but carry on.

Oh, interesting. Okay, I understand that this quality is not limited to this number. but I am aware that Pi does not have any recurring patterns. So I feel technically that is the wrong order. Oh, that's interesting. Yes, but is it the most wrong? I mean, yeah, because it's got loads of the same numbers. Every now and then there'll be like one, two, three, four in a row or something.

Yeah, but then how often do you get more than one if you're counting? There's a famous point where there's like six nines in a row. And you're like, ah, that bit satisfying. So you're right, is wrongness just random? I would argue probably not. The problem is with random, randomness clumps and all things are equally likely. So if you randomly picked an ordering of one, two, three, four, you might get one, two, three, four. Yeah.

And that would be pleasing. So not all ones picked at random, but displeasing, is what I'm trying to say. So what we're trying to go for here, and this, I think, is quite a human question. It's a bit like the football. which sequence do we find the most displeasing? Disgusting. Yes. What is the most upsetting sequence?

That kind of comes down to what people find upsetting. Yeah. So Morgan has got some examples here. Oh, so they've pointed out that one is in the correct position. Yes. And that's kind of pleasing. So maybe one of the metrics of upsettingness is making sure none of the numbers are in their correct position. and a mass that's called a derangement.

Yeah, we talked about that. We talked about derangements before when we were looking at calculating E, which is a lot of fun. But then they're also talking about the fact that three and four are in the right order. So even though they're not in the right place, they're in the right order. So maybe subsets that are in the right order we find pleasing. So what we kind of need to do is come up with a bunch of measurements of displeasingness and work out which ones match. what we actually find upsetting.

So I think that I need there to be more numbers to work this out because with four, my brain can very quickly start going, I can see a pattern here. Yeah. And as soon as I see a pattern, that feels satisfying. Yes. Like the more pattern-eous that I see, the more I'm like, okay. But if it's, that's why the ball upset me.

Because there's no real sort of clear. pattern to it. Well, here's one of the problems we're going to hit real quick. With four numbers, there's 24 ways you can arrange them. Once you go to five numbers, there's 120. So the combinations go up real quick. Yeah. And I was like, well, one thing we could do is just try and write down the most upsetting order.

Okay. But I was like, yeah, I don't know if that. That would really give an insight into what we're finding upsetting. What would give us an insight into what we're finding upsetting is if we were to take all 24 different ways of arranging four numbers and rank them from most upsetting to least upsetting. All right. And then we could compare that to the different possible metrics to see which ones best explain it. Okay. And there's a factor of one, two, three, four.

is obviously very pleasing, but so is 4-3-2-1. But not as pleasing. There's a ratio of like a scaling for the same patterns but in reverse. And I'm like it's obviously not one because the reverse patterns aren't quite

as pleasing as the forward patterns. So have you created a game where I can choose which of the two I find better or worse? Oh, even better. For some definition of better, I have created a game with all the permutations in a random order.

Uh-huh. And I would like you to put them in the order from most upsetting to... No, there's too many for me to compare. Then here's the version for just three. Okay. Of which there are six. Okay. Do you want to come and have a go?

All right. Okay. You're going to shuffle them up? All right, sure. There you go, right? So you can grab them and drag them. You want the most unusual, annoying at the top and the most satisfying at the bottom. All right.

So I'm putting one, two, three at the bottom. Yeah. And currently followed by 3-2-1 at the penultimate. Gosh, this is really hard because my brain is immediately trying to make sense of them and be like, did you ever ride a bus with that number? I mean, that, you know, that counts. Like individually, your history with the numbers. So weirdly, 132.

Oh, okay. Because that feels like a bus number. And then this is how I feel. So Beck currently has 312 is the most upsetting. I don't know if I agree with that. Okay. Followed by 213. Yeah, actually.

So 231 is now the most upsetting. 231 is pretty upsetting. Nothing's in its right place. Two and three are in order, but you can't avoid that. Okay, you happy with that ranking? Yeah, because also when there's, I know that Morgan was saying like, oh, three and four in the right order, but they're in the right order in the wrong place. And that, to me, is more upsetting than having them all in the wrong place.

So I come up with some other metrics. Okay. So I had non-fixed points, which is nothing is where it's meant to be. Then you've got inversions, like you don't want numbers next to each other in order. Yep. You've also got foot rule, which is just how far away. And you can have weighted foot rule for how far away each one is from where it should be. Okay.

Now, for three, that doesn't really make a big difference. No. In fact, three kind of limits a lot of this. I also had one for looking at sequences that are all increasing. Okay. Which again, for three is not really a factor. There's too few. And then I did, this is a known thing called the Cayley distance,

which is how many swaps you have to make to get it back in order. Like with the dance? Like the dance. Yes. You swing your partner and then you end up back at the same partner. There you are. That's the one. Exactly that.

Yes. And so that's like not something I think is human. Like when you look at it. sequence you don't work out the Kaley distance, but I thought maybe that would correlate. Now, here's the problem with three. There's not enough data to kind of rank all those different metrics, but what I can do is if I analyze, you have a 0.45% coefficient for backwards compared to forwards patterns. Okay.

You find a backwards pattern about half as pleasing as if it was forwards. Okay. So you're more tolerant to backwards patterns happening in an upsetting sequence is the way to put it. If we're talking about three numbers. Yes. But yes. And three is not really enough to draw any. Big things. Of a very small sample size here, you prioritize non-fixed points. And that checks out because you're most upsetting one, nothing's in its correct place. And there's not much else we can say about anything.

I think what I would find the easiest way to rank these is if it was in a like knockout situation. Yes. Yes. So you can do a bunch of pairwise comparisons. We show two at a time over and over and over again. And for each one, you just click which one's more upsetting. Yeah. Which is beyond my coding ability. Oh, Claude. Well, what I've done here, this is all in JavaScript, JSX, XML. And so I come up with some algorithms and good old Claude here, clipped them together for me into a interface. Yes.

So you can drag things around. What I would like to try is doing what you were saying, a pairwise comparison on four. Okay. But starting with all the ones that are four. and then moving them around until each pair you're happy the more upsetting one is on top. Okay. If you're happy to do that.

Yeah. Then we'll have enough information to know which of the metrics you're actually using. Okay. And then we can use that to scale up to more and more numbers. Deal. By applying them over a bigger and bigger dataset. Okay. If you're happy to do that.

So here, let me just give me a little shuffle. So Beck is looking at a list of 24 permutations. You've watched severance, haven't you? Yes, yes. I see what you're doing there. It's got a real... Viseolate and remove the upsetting numbers. Yeah, yeah.

This number is bad. I don't know why. It just scares me. I do for bad making you look at a list of 24 arrangements and rank them. I mean, I don't know if I can stand by these choices because the more I look at them, the more familiar they look. Well, I'm kind of hoping, as long as you do enough that you kind of think they're annoying ones at the top.

and the pleasing ones are at the bottom. The other thing is because they're four numbers, so things that make sense to me are like any of the numbers starting with one, not because it's ones in the right place, but because they read like years. Ah, okay. And years that have happened in the last millennium. Yeah. Yeah. Yeah. Real recent history.

My brain just looks at like one, three, four, two and is like, oh, the year 13, 42. Yeah. Yeah. So like all of the. those aren't that displeasing, but because we're looking at four number sequences. Yeah, but I think it's valid to say numbers that start with one. It's almost a Benford's law thing, which is saying that it's more likely numbers in use for some definitions of in use and distribution. Start with one about a third of the time.

And so they're more familiar. And you've just linked them because they're four digits to years. Yeah. Wait, is this one pi? Oh, there is pie. 3, 1, 4, 2. Yeah, that's moving down to familiar. Yeah, that's a pretty good number.

I didn't factor in resembles famous constants. But that's a factor. Interesting. Well, you put it down there. The more I see that one, the more I hate it. And it's just the reverse number. You've definitely put 1, 2, 3, 4 right at the bottom. Yeah.

4321 is higher than that. Yeah, it doesn't look right to me. Okay, well, you find 4. one, two, three more pleasing. Yeah, yeah, that makes sense. The one, two, three is appealing, isn't it? So I think once you get to more numbers, the sub sequences start to get important. Yeah, I think you're right.

I'm going to leave it at that because otherwise I'm just... You'll be here or day. I'm overthinking everything. Okay, no, great, great. Okay. So I'm using a thing called the Spearmann rank coefficient, which is a way of comparing two rankings to say how similar they are. Spearmann is just a way of quantifying how close your ranking is to a different potential ranking based on other metrics we could have used.

Okay. And what we do is we weight all the different possible rankings for which ones are more important and work out what weighting of the other metrics we've got has the best Spearmann rank coefficient with what you've done. Okay. So I'm just going to analyze that. Okay, so now we've got weightings for the different possible metrics based on what you did. And you don't care about the Cayley distance at all, it turns out. And now we can generate new sequences based on your metric weightings for any number of symbols. Oh, goody.

So would you like to see your top 10 least favorite arrangements of seven symbols? sure here you go let's see if it's right that is your in theory your least favorite arrangement of

seven symbols 231-6745 I have no feeling I feel nothing I feel no feelings against any of these numbers something I found interesting as I was doing this

and testing it on bigger sets after a certain point it's just random noise it's not enough to be pleasing or displeasing? All of those start with two. So my brain instantly is going, oh, well, that's a pattern.

They all start with two. Yeah, they're big on two. I also think that part of this problem is that with pattern recognition, it's not just limited to whether we see patterns a standalone, but the context. So, for instance, phone numbers,

something might technically fall under, oh, that's not a pleasing arrangement. Yep. But if it is similar to a number, I already know, because it's close to a phone number, or like if it was a big number and it was similar to a credit card number, then I'm not going to hate it as much because I've seen that number enough that it feels familiar and therefore correct. Okay, so if you saw 16 groups of four. Yeah.

You're like, ah, that's a credit card number. Yeah. That's interesting. I think, yeah. So all my metrics are just like jumbled up in the wrong order. But you have such a personal attachment to arrangements of numbers. And maybe that's because the only times I look at numbers is when it's to do with a specific thing. Like I'm not looking at numbers all day long or I'm not calculating numbers.

It's not something that shows up as often. They show up more as words. as such. Yeah, yeah. They already have a meaning connected to them. They already exist as a team. Yes, yeah, yeah. So your apparently least favorite on five should be 21, 453.

But I think there are so many on five. There's 120, probably any, these all just look pretty random to me, to be honest. One's quite close to pie again, but you know, that'll happen. I would like to know in the world. Yep. What street has the most wrong house numbers? By what definition of wrong? Absolutely not in any order that you would expect.

Well, we've just determined there's no quantifiable way to work out what... Well, I would argue there's probably very few streets in the world where the numbers of the buildings are out. Defined out. As in not going up. Definitely in Australia, you tend to get the even numbers on one side, the odd numbers on another, and it climbed numerically upwards. Whereas I know that people get confused on the street that I live because of the way the flats are arranged.

Because each flat has its own number. It's not a flat number. It's as if it was an individual home. Right. So street numbering but across flats. Yeah. But you get different sets of steps to those flats. It still climbs, but it's not entirely clear which set of steps you want.

You're looking. You are surprisingly tolerant of. that not being the case when you were ranking these. You didn't find it upsetting if there wasn't a consistent direction the numbers were going in as you read along each number. But again, we're applying a personal touch to this.

Yep. Because we were looking at trying to look at numbers as much as we could out of context. Yep. But in terms of the way homes are numbered, they're supposed to go up. I argue you're right back where we were. The saying out of order or wrong has no meaning. Yeah, yeah, yeah.

But in the context of trying to find a house, you could argue that then maybe there'll be the most confusing way to locate a house. The reason that this order is so infuriating isn't just because it doesn't go one, two, three, four. Yep. One of the reasons I would argue that this is an infuriating number because it doesn't seem to make any logical sense as to where you would put the letters based on the homes that they're connected to. Yes. It's particularly shocking that you'd expect houses to be in the correct order. Yeah.

But our poor friend Morgan. And I can only assume you go down a driveway and a driveway acts like a street. So on one side of the street, you've got odd numbered homes. And on the other side of the street, you've got even numbered homes. Yep. So then it would, hypothetically, actually, no, it wouldn't go 13, 4, 2. That is infuriating. Yeah, yeah.

That's wild. 13442 is pretty nuts. Yeah. The two has just been bumped to the end. I can only imagine the way that would work. is if it was like a cul-de-sac. So house number one and three, because you're on one side,

are uneven, and then as you turn around, and then you come back down the other side. Yes. Which is wrong. Yeah. That's what I find infuriating about this. Because I don't know how it connects with the homes.

Yep. That's how I would state whether the numbers are wrong or not. Yep. I mean, Morgan's question is just detached from the house situation, what's the most wrong ordering? Yeah. But I think what we've discovered is because my approach is what's the most wrong is what's hardest to assign a pattern to where it's small enough you expect a pattern. Yeah.

Because I found above a certain number of numbers, I didn't care anymore because it just looked like random noise. But when it looked like there should be some kind of pattern and there wasn't, that's what bugged me. Yeah, yeah, yeah. Likewise, I think you've got a similar thing, but for you, if it looks like a year, that's more pleasing because it's a number you're familiar with as opposed to one you're unfamiliar with. I have a family member in Australia who they live at, let's say, so I'm not giving away too much personal information. Let's say they live at number nine.

Yep. There is a house that is already number nine. Yep. And then they are 9A. Nine and 9A. Yeah. Kind of okay with that. Like it bugs me because whenever I've gone to visit,

I'm like, technically this should be 9b because the first one should be 9A. I made a reference about that the other day and some people with me were into Star Trek and they got up on my grill because there's a Star Trek thing about how ship E instead of being the fifth one is the sixth one because just the first one has no letter and the second one has A. See, that should only work if all of the subsequent ships are little ones that live on the first one. Oh, okay, they're sub. Like if it was a subheading. Yeah, I'm with you.

You know, I'm kind of okay with a number and a number A because I like the fact that's ridiculous. But I agree the first one should be A. Yeah. I'm a spreadsheet column system kind of guy. You start A. Yeah. Go up to Z and then you've got AA. Yes.

And carry, no zeros. carry on up. When you're adjusting the volume on a TV, do you preferentially leave it on even or odd numbers or do you not care? My current one does not have numbers. It just has a bar. And so you go by, but volume these days I think I just base it on whether my ears can handle it. But in general, I have a preference for even numbers. I have no preference for even numbers. I have no preference for even raw numbers. I just do the volume I want. Because I know some people are very passionate about leaving it on an even number.

Well, in general, I like even numbers. It feels like it. I like the symmetry. So I feel like the answer is there's no answer here. What's the most wrong? Very context dependent, very person dependent. Yes. We could just find one metric like every digits the greatest distance from where it should be.

But then you'd shunt it all along. And there'd still be an order. You'd have rolled them around. It would be a bit like this, but like on 10, it would be 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, where we just rolled everything along 5. Yeah. So I think it depends on the context of the number of what people would find annoying. Yeah.

If I was looking for a home or a letterbox. Yeah. Then I think certainly just none of the numbers being where you expect them to be or being in any particular. Because as soon as you start getting a consequential order. Yeah. then you're like, oh, well, at least I know that four is following five or something. But if there's nothing...

Yeah. I think the most annoying order would be one, two, three, five, six, seven. You're like, oh, okay. Then four. Yeah. And then 13. Yeah, oh, God. And then two and a half.

That hurts my teeth. Yeah, yeah, yeah. Jumping up to 13, water gal. Yeah, there's certainly a version of Missaponia, which is just aversion to numbers. And I think we're going to get a bunch of hate mail from Bill. You need a trigger warning. So Morgan, my answer is whatever annoys you the most. This was the most wrong way to ask a question.

The question's valid. Just that these are all valid numbering orders. Yeah, yeah. The reason this is the most wrong way to ask the question is I feel like Morgan hasn't provided enough information. Oh, okay. Because yes, I can see why this drives you insane. Morgan, but I'd like to see if there's any type of pattern. Now, obviously, again, no doxing or anything.

You don't have to take photos of homes. But if you could just tell us how the units are laid out, whether in a building or in a little allotment, whatever, and if you have a theory, Morgan, as to why the letterboxes, are the letter boxes going like from left to right? Or are they in a grid or? They're in a grid what's going on that. Okay, yeah, yeah, we need more information, Morgan. I'd like more information.

I'll tell you what, yeah. I'll whip up a Google form. I just want you to type in what everyone thinks the most wrong ordering of, should we do one to five? Yeah. It's a tough question because I don't know what I would say. Yeah, okay. Everyone, what is the most wrong ordering of one to five?

And we'll do it by vote. Next problem was sent in by Hester, who on the problem posting page at a problemsquare.com say long time listener, first time poser. I've got tickets to Matt's getting triggy show in a. October. Yeah. Hoorahe, Hester. See you there.

There's only six, five or six shows, so everyone get involved. Last time I'm doing it. And Hester says they don't have any mass-related accessories to wear a lot of people do show up wearing nerdy t-shirts and various nerdy accessories. You've got your face of I'm not surprised on. And Hester is thinking of making some earrings out of shrink plastic, like a shrinky-dink kind of thing. Yeah. Hester's question is, what are some good trig?

math's related diagrams that would look good on an approximately 1.5 centimetre earring and still be both recognisable and look cool. Now, I decided I was going to try and answer this. But mostly from a creative point, as someone who has used shrink plastic to make various jewelry. You're familiar with the medium. I'm familiar with the medium. I also wanted to give a shout out to one of our listeners, Hazel,

who saw your show last year and made us little Oh, little name things. Yeah, they're lovely. And I believe they used the same type. It might not, but I think it's a similar medium. So basically it's like a piece of clear plastic and then you can draw on it and then you stick it in the oven.

And it shrinks right down. And Hazel's parental guardian gave me this bracelet. Oh, you got like a bracelet. Oh, that's cool. It says back hell and then like a round. rainbow of beads. And that says be chill. Ah, that's really nice. Another rainbow of beads.

That's very sweet. The big chill back hill. I've been enjoying. It's been a good fidget thing as well for me to have. I just wanted to give a heads up to fellow jewelry makers. Yes. Who are listening. So I thought I would basically bring this question to you.

Because obviously, I'm not the specialist in cool maths trig-related diagrams. Right. But I'm aware of the medium. Yes. And so I think with our brains combined. We can make this happen. Yeah. Okay.

So what are the constraints on the medium? Like if I want to shrinky-dink something, I imagine I can start with a big shape and it becomes a smaller shape. Yes. And could I do something that's like, the detail is the wrong word, but like a triangle with pointy corners that would survive? As in can you get like tight corners? Yes. Yeah, yeah, you can. Okay, great.

I would say that the only main issues, sometimes the shrinking isn't super consistent. Yeah, so I was wondering, yep. But generally. Generally, pretty good. Yeah, generally, like, leave it in long enough. It's not going to get any smaller. And sometimes they can get a bit wavy in the center,

depending on how big they were to start with. There are ways around it. You can, while it's still hot at the end, you quickly, like, put it under something flat. Right. That'll make sure it's cool. So it's flat. Yeah, got it. Okay.

And if you have holes in them. I've done that to sort of add clasps or chains or things. You just want to make sure it's a big enough hole that it'll fit. Yeah, because I was imagining you could do, I mean, not this, but if you're like a pentagram or a septagram or something, that's like the star arrangement. That's a whole bunch of hole. and things you'd have to cut out. How big can you start? Like, what's the shrink factor?

How big are you working with in the making phase? Ooh, mine came in like A4 sheets. Yep. And I found that if I worked with a quarter of an A4 sheet, which I merged as an A6. Correct. Thank you. Then, you know, I leave plenty of space around the edge

to cut around my design. and then that's usually a nice sort of smallish kearing size. Okay, okay, okay, so you can work in some detail and then shrink it down to get fined it. Okay. So I find if I use a hole punch on it, that's quite a small. A small hole once it's done. But it's just enough for like a very small like chain link or, yeah. Do you know what would happen if you made like an origami cube or something?

I suspect because you get a wavy. center if you're not careful. It's because it gets a bit gooey. And I think if you try to do it in 3D, gravity will play a role. Okay. Okay. Right. So what I would do if I was trying to make a three dimensional shape is make the separate sides. And glue them together. And yeah, and probably use like nail glue or something as in like acrylic nail glue. Right. Because that's made for sticking plastic. Yeah, kind of fuses the plastic together. I think what you'd want to do is two earrings that are different but related shapes. That would be my go-to move.

And I'm not trying to sell stuff here, but I know on mask gear we have some earrings. And we have a pair of earrings where one's a coffee mug and one's a donut because they're topologically the same shape, which mathematically is hilarious. Hang on. Wait, what? It's a hilarious math's famous cliche joke that a topologist can't. tell a coffee mug from a donut because they're both topologically only got one hole. The handle on the coffee mug is the same as the hole on the donut. And the rest of the coffee mug isn't actually a hole or anything.

It's just a stretched out bit of a donut. Yeah. For one of a bit of a direction. Lucy's got a pair of earrings that I got her where one is a Pac-Man and one is a ghost. Yes. And so then you can wear those as hilarious combo earrings. Yes. So I guess my broad, high-level advice is two-shaped.

Actually, here's an actual suggestion. You can get a triangle and cut it up into pieces that rearrange into a square. Oh, yes, yeah. So you could have one of each and draw on the lines that show the rearrangement. In fact, there's a whole bunch of dissections of one shape to another shape. Yeah. So you could draw them on each and then do that. That would be a lot of fun.

Yeah, that's good. Whereas the same thing twice. surely a hexagon on one side and a pentagon and the other yeah yeah a black pentagon and a white hexagon on opposite sides of your head you may turn yourself into a giant wrong football and it will still look better than the one will still look better than yeah yes you want a pair of mathematical things that are kind of funny to have together yeah there might be a way to do that with pythagoras to have a

a squared, B squared on one side and a C squared on the other. There might be a way to do that with triangles. I can't picture it at the moment. The thing is, I don't know if this is really using the medium to its maximum, but I would want to wear a pair of shapes that are jewels of each other. And a jewel in mathematics is where you take one shape, let's say it's a cube, and you put a dot or you mark the middle. middle of all the faces and then you link them together to make another shape inside.

Oh yeah. So there's six faces on a cube. If you put a dot on all of them and join them all up, you get an octahedron. And if you link up all the points of an octahedron, you get a cube. And so they're dual shapes. That's fun. And I know it's very funny when I say jewel shapes for people who are not necessarily fluent Australian English speakers here, Jewel is in.

jewelry, jewel shapes. Oh, nice. So if you want to do jewelry, you should make jewelry out of dual shapes. And if you could draw on them, if you could make, I'd be really tempted to do it with like a Catalan solid and Archimedean solid that are jewels. But I don't know how fiddly that's going to get. But if you did it with, let's say, a cube and an octahedron, you could try and draw the octahedron on the cube and draw the cube on the octahedron.

Yeah. So one's one shape, but you've drawn the other one on it and then vice versa. Oh, that's nice. Can you show me a picture of the most basic jewel shapes? Deal. Okay, I've got a website I found on, oh, it's on the Brown University. I guess a math professor or someone's put this on here. I'll link to it in the show notes.

If you want to check it out. It's got some diagrams. The website does look like it's from the days of GeoCities. It is from the 90s. You can see one here where there's like a wireframe cube. and inside it, if you join the middle of all the faces together, there's your octahedron. Yeah, yeah, I see it. And octahedron's quite jewel-y, as in like precious stone.

Yes. There's a bunch of triangles, eight triangles joined together. Or like the Sims. Like the Sims thing, above the Sims head, yes. And then over here, that's the same octahedron, but now it's the wireframe, eight triangles. Yeah. And the middle of each triangle is joined together, and that forms an internal cube. Yeah.

So often you'll see the diagram's done like this. where there's a smaller one that's not a big one. But I was imagining two equal-sized, like one's a big cube, one's a big otterhedron, their dual shapes, very funny, and you could draw on the faces to show the other one. Yeah, even these, and as Matt said, we'll link to them, but even these drawn out would make for pleasing images. In fact, there's another pair on the page. One looks like a, wait, what's a...

I was waiting to see how you're going to describe it. Three-dimensional hexagon. Three-dimensional hexagon. You're a hexagon. No, not hexagon. That's a pentagon. Pentagon. Yeah, one's a dodecahedron.

That's made of 12 pentagons. Like our football buddy. Yeah, so dodecahedron. Both side of die. Yeah, D12, correct. Made from pentagons. And the other ones in icosahedron, which is the D20. Yeah.

Well. So it's 20 triangles. I mean, already I'm seeing some particularly nerdy. That's double nerd right there. You've got a D12 and a D20. Yep. There's something quite nice about the way that it's drawn as well because they both do. do kind of look like sort of gemstones.

Like if you had sort of round doings. You should definitely lean into the gemstone angle. Yeah. And if you've got some glitter pens or metallic pens. Are you talking? Yeah, you could do some really nice sort of overlay. You can get sort of shrink plastic in like a mat, opaque. Or you can get translucent.

And if you had a translucent, you could have some fun with that with sort of overlaying. into the gemstone angle. Yeah, yeah. So I really like those. I like that idea. I had an idea. I do think just for the pun alone, I'm already going with,

I'm already going with dual shape. But let's have a backup option. Option B. Option B, again, if it's transparent, you do two circles of different colours that represent two aspects of your personality. Yep. Or two aspects of whatever you want.

And then when you hold them over each other, you create a V diagram. That's really nice. So your third color in the center is whatever. So you could overlay the two discs. Yeah. Okay, so on the mask here, I'm not trying to sell it. Obviously, I am.

We have pendants and earrings that are vendeagrams, but they're each a vendeagram. You're suggesting your entire head becomes the vendeogram. Yeah, technically, yeah. Where you've got a big circle on each ear. Not that, but you could, I'm saying if you were to take the earrings out. Oh, you could hold them over. I got it.

Yeah, yeah, yeah. I didn't mean it's like. Like glasses. Yeah, if you are holding them separately. There's something fun about someone going, what's with your earrings? And then you take them out and you hold them over. Give me a minute. Yeah.

But you could label them because you can write on this shrinky ding, right? Yeah. One is left ear, the other is right ear. And where they intersect is head. Yeah. Perfect. So that would be my suggestion. Although I will say I had a quick look at the jewelry selection.

or math gear. Yep. This next item is both sold out. Yeah. And not available as an earring. Oh. However. Yeah.

The t-shirt slash hat tile. Oh, yeah. If you had one of each, again, you could take them out and then show how they join them together. Or you could have two, you could have like a clump. Two partial clumps that do mesh together. Yes. That could be fun. Either spectre tiling or the hat.

tiling. Yeah. That's really nice. I think we're all in agreeance. And I say all because Laura and I discuss this on the train to the record today. Oh, you guys are in agreement. Well, we were already saying how it's very nice the idea of having something that sort of matches or links up. Yep.

You know, in the same sense that those best friend necklaces or bracelets were like two sides of a heart. We're always very pleasing. there's something pleasing about two mathematical things which combine. And if you were there with someone else, they could wear the same earrings, but on the opposite ears. So you don't have to take them off. You just go stand next to your partner in earring. Yeah.

And then you'll have the match. If you wear two earrings, like one in each ear, you can have pie. And if you're someone with one PSD, you could have tau. Tau, there you go. Yeah. I did it. I did a math thing. You did a math joke.

Yes. One day I'll graduate. So I think there's some suggestions there. Do you have a favorite formula or shape or, well, we know what your favorite shape is, but... It's the horrifying football. Yeah, yeah, now it is. Have you considered getting that's horrifying football? My favorite shape of the rhombic.

Doveragetrogen. Yeah, in general. Just in general. It's great shape. It's fun to say, too. Yeah. It's got everything you need in a shape. Yeah.

Rombi. The decadronness. But if you wanted, you could do something where the, the faces occur, twents. You still trying to make that work? Yeah. Still trying to make quents happen. See, the previous episode. Twockley is happening.

Twockley is happening. I just thought of one more thing. Okay. If you had an A squared square. Yep. And then you had the B squared square. square for their other earring. You could also make a matching necklace pendant,

which is your C squared. And so when you put them together, you get your triangle. Yeah, that's quite nice. Well, Hester, you got some options there. Normally I would say right back in and provide a ding, although that's not what you did. But on this occasion, I think I'll see you at the show.

So do say hello, either before or after the show, whenever I'm around, and show me the earrings you ended up making. Yeah. We'll take a photo. It'll be emotional. And this brings us to any other baristaness.

It was right there. It was right there. It was right there. How embarrassing. You know how annoyed they were at the beginning. Yeah, everyone's yelling that. Yeah, I feel you. I hear you guys.

Okay. So I'm going to start with any other baristaness. Yep. I just wanted to say thanks to, I know I mentioned this in the last podcast, like thanks to people who came along to the show. Yep. But I got a sort of ding from not the. Oh.

the problem poser, but someone who came along to the show and afterwards said, by the way, I just wanted to thank you and Matt for having the conversation about AI. We were talking about people using AI at work in episode 140. Yeah, like four episodes back. Yeah. And because when I was listening to that episode, I thought, oh no, we haven't done a very good job answering that. It's mostly been me complaining. Oh, no, it's the first time we've ever not answered a problem well.

No, but I was like, oh gosh, have I just made it more complicated? Have I just like talked? Have I just used this as an opportunity to vent? But this person just said that it was nice to hear someone else, the other listener actually, talking about their grievances with it because they were finding the same thing was happening at their work. And there was this real feeling of like, I guess we just have to accept this. And actually realizing that other people have an issue with it. and it's being discussed and talked about made them feel just a little less stressed.

Like, you know, oh, it's not. That's our goal. I'm not the only one. Other people are also noticing this, and that means that there is more of an opportunity to discuss it. So I just wanted to thank that audience member, because that was something that I was a bit nervous about, whether it was of any use,

and hope that others found that useful. Oh, good. Thank you, that person. And we heard from Matt, I mean, some Matt. I hear from that. Apparently not you. No, allegedly, who was asking about how to identify if a friend at work is an actual friend or just a work colleague friend. And we chat about that a bunch.

And they just wrote in to say that we definitely identified that they tend to overthink things. and us just saying that, you know, let it be and don't need to overthink it and enjoy the person. Because obviously it was someone like a client. So it was like a slightly asymmetric relationship. And not get stressed about any post work hypotheticals. And they replied to say, obviously it's too soon because they're still working together. So we don't know what happened long term. But they say they feel much better.

And we get a ding or capital letters from me. Thank you, Matt. Who's not me? Yeah. sure. You're welcome. Even though I just said from me. Yeah.

I know you just feel better now knowing that we're all friends. Yeah, it's true. We also heard from Jenny, who posed a problem in episode 142 about how to design a colourful notice board without ruining the walls of a building. Jenny responded on Instagram, which is at a problem squared, and said, we still have Magnolia walls. Early days. And 100% will send photos when we have color and posters on the wall. Ideas are brewing. Right.

I love the discussion and ideas. Thank you both. Other photos, very welcome for inspiration. Okay, so if you have got boards, you've either made already have, send them in. And finally, Mallory Strom is not responding to a previous problem or posing a problem or doing anything, but they did spot a geometrically accurate football sign. Now, I guess it would be called a soccer ball. because this was in West Hollywood over in California.

But Mallory saw a no soccer sign and the stick figure is kicking. What I can confirm is a geometrically accurate football. So Mallory is just rubbing it in. And in California, they can draw a football on a sign. I just love how the person has very straight limbs for someone kicking. That's not good kicking posture. Not a geometrically accurate human. The human's way off.

And we've got one more bit. of any other business. So there was a problem that I was thinking of solving, but actually we need more data. Yep. And who better to get data from than our listeners. Now you've already said that you're going to do a Google poll. Yeah.

My Google form. Yes, a Google form. There's a problem that I'd like to try and solve, which is... Well, you're going to state what it is, and we're not going to get into the details. Oh, no, no, no. It's making that very clear to everyone right now. Otherwise, we'll be doing it now. That would be the problem.

Exactly. Someone has asked, actually, let me double check. producer Laura, do we have the exact wording of the two options? The exact wording of the problem is, do you put your trousers or socks on first? So do you say trousers? Yes. But on the Google form, we're going to say, which do you do first? Trousers or socks, socks or trousers.

And we will have a little option for you to provide more details should you deem necessary. If you wish to elaborate. Yes. And once we've got the results, we will then discuss whether we can solve that problem. So we'll pop a link to that in the show notes. Combination form. You'll ask you for the most upsetting arrangement of the numbers one to five. Yep.

And what you put on first, socks or trousers. Yes. Plus a text box if you wish to explain yourself. Yeah, but please only use that for the socks and trousers. Yeah, don't explain anything else. And if we haven't asked enough of our amazing listeners, if you are in the position, you can support us financially in order to ensure this podcast keeps on going. What do you get? Just more than the satisfaction of...

So much satisfaction. Doing this so much satisfaction. But you also get access to our bonus podcast. I'm a wizard and various other benefits. One of which includes the possibility that we will mispronounce your name at the end of an episode. Yep. We choose our names at random. I don't know how wrong the randomness is.

The randomness is, as wrong as it can be. But on this episode, the Patreon supporters whose names we would like to mispronounce on purpose are... Craig? Oh, gosh, that's probably how they pronounce it. I know, I know. It's probably how they pronounce their name. I'm just heavily implying they pronounce their own name wrong, potentially. Craig.

Andy Arson. K at Y. Of al-law, I, Murrell, son. Thank you very much for supporting us. Thank you, Matt, for supporting me mentally. And emotionally, through these tough times, thank you to me.

Yep, yep. And thank you to the Cafe Manor. who ensures that every cup that we brew is to a satisfactory quality. We strive for satisfactory. Yes. Yeah, we like to have a motto around here. That's right. We strive for satisfactory.

And if she's done her job right, that's been cleared up by producer Laura Grimshaw. Oh, well. Conact four, connect for, connect for. I'm going to continue with my system, which means that this one goes here. That's so unuseful to anyone who is flocking. Checks out.