A Problem Squared - 145 = Trousers & Socks and Heaviest Blocks

Episode Date: October 12, 2026

🧦 Do you put your trousers or socks on first ?👖🎲 How much would a standard pair of dice weigh if they were made up of just protons and neutrons? 🎲🏉 And we have some Australian Ozzie Ballness that may or may not be in the right order.Thank you to everyone who responded to our questionnaire about number and clothing ordering! All the results are in this episode.What would happen if a tablespoonful of a neutron star was brought to Earth? https://www.astronomy.com/science/what-would-happen-if-tablespoonful-neutron-star-was-brought-to-earth/ Take a trip back in time to see Matt putting both his socks on simultaneously: https://www.youtube.com/watch?v=hs7fg27Iiq8 Do you have a problem for Bec and Matt to solve? Tell us about it: https://www.aproblemsquared.com/ 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.

Hello and welcome to a problem square, the problem solving podcast, which is a lot like the AFL grand final. As in Australian rules football? No. Yes. Australian Football League. Yeah, Aussie rules. I was trying to remember what AFL stood for.

It must be Australian Football League. We may have already blown our sport expert cover at this point. The point is it's a lot of excitement and entertainment generated by Australians under their own rules and looked on with bemusement by the rest of the world. I'm Matt Parker. I'm a lot like the rules for marking the ball in AFL, in that it requires a lot of attention to detail and calculating distances to the nearest meter.

I'm joined by Beck Hill. Now, you might think comparing the podcast to the AFL grand final, Beck would be an iconic Australian performer, Kylie, who did the pre-show show entertainment this year. But she's not, she's the ball. Wait, Kylie Minogue was the ball.

No, you're the ball because you really make the podcast what it is because you never know what direction you're going to bounce in. This is true. Yep, I'll take it. And on this episode, I'll finally solve the problem of socks or trousers first. We've all been waiting. I've worked out what happens if you roll some really weighted dice.

I've waited this long to find out. We're still waiting, waiting for the weighted dice. And there'll be some Australian Aussie, spelt with an O. That is how Aussie is spelled. Ballness. Ballness. Yeah. Australian Aussie baldness.

So, Beck, have you been? I have been well. Since I last saw you, I attended the wedding of listeners and fans and friends, which were the wonderful Tom Crosby, who was a performer who I would say is maths adjacent. There is some crossover. Tom's done an evening of a necessary detail. Yes. Does a lot of Rubik's Cube.

Rubik's stuff. And has been on Manish a trick. No, full. That's the word. Full pen and teller. Yep. And Tom's now wife, Charlotte. And so I got to attend.

I was DJing their wedding. I DJed the wedding. I had a great time. It was lovely. There's nothing better than attending a brilliant wedding and then getting full control of the playlist afterwards. I cannot recommend it enough. And I wore a white shirt that I've been meaning to give to charity for years because I don't tend to wear it.

And then I thought, I'll wear this with a suit. That will look nice. And so I ironed it. And it turns out all I had to do was iron it. And then people go, wow, what a nice shirt. And I was like, oh, I've unlocked the secret. Discover ironing. Yeah, I discovered ironing.

And I was so proud. And you'll be happy to know that I made it all the way to just before I've been. I was about to start DJing before I dripped an entire rolls worth of ketchup down the front of it. Good work. I'm learning. I had packed two spare shirts just in case I ruined, yeah, ruined them. So the wedding was brilliant. I wasn't going to mention this, but I also DJed a wedding.

What? I'm not going to name anyone here because this was a private friends having a wedding. But they asked if I could bring robo DJ with me. Amazing. Which I did. Yes. So the robot who DJs in my current tour show came and DJed the kind of having something to eat, people coming into the marquee space part of the wedding. That's awesome.

There's a lot of fun. That is great. What I'm saying is we're both equally skilled. Look, I stopped the music twice because I was dancing so hard. I knocked my laptop. So I'm not going to pretend that. No, Robo DJ didn't do that. Robo DJ was pretty good.

Fortunately, no one said you've ruined my wedding. Yeah, but it was wonderful. Everyone was amazing. I got very emotional. Yeah, it was beautiful, really nice. And they did Terry Pratchett readings. It was like a very on-brand wedding. Wow.

Yeah, yeah. Highly recommend five stars would go again. Can't we be out nerd at the wedding I took a robot to? I know. Well, you know what else I did? Putting on a hat. Okay. So you're wearing Fremantle Dock's cap.

Is that the Fremantle Dock's cap? The Fremantle Dockers cap. This is the hat we've discussed previously. Quick recap. Well, yes, you did. You put it back on your head. Back on again. Recap, recap. Recap and the cap.

It's a cap on a cap. Recap cap. Yeah. So I bought the hat when I went to see a docker's game. Yeah. And my mate Trent was watching remotely because he's in the UK. I happened to be in Perth. They'd been doing really well this season.

Suddenly they were losing. He's like, go buy a hat or something. I went and bought the hat. Massive comeback. They won the game. Since then, lucky hat. Yeah. Every now and then, since then, I get a message from Trent saying, put the hat on.

Yes. Does that be doing badly? Now, Trent follows the docker's very passionately and has since the 90s when they started. I followed them very casually since 1996. So he watches all the games. He's like, quick, put the hat on. I put the hat on. And they made it to the semi-final.

So this is the game before the grand final, before the Grammy. And they wanted to make it into the Grammy. And so in the semifinal, they were way down. And I was wearing the hat. And I was watching the game as well. And so I put the hat on backwards. Oh no. And they had a massive comeback and they won the game.

Oh. It was incredible. So it was even more lucky when you wore it backwards. So it turns out if you need to up the power of the hat, the correlation hat. You have to adjust it. Yeah, you pop it on. The dockers haven't made it into the grand final since 2013. Okay.

And Trent and I went and watched. We went into London because the game starts at like 5.30 a.m. over here. So we go in to Bloomsbury Lanes. in London where they'd kidded it out for the grand final. So I'm there at like five in the morning in a basement bowling alley, holding a pie and a beer. And I'm like, how did this happen? Yeah. Yeah.

But it was like Aussie run. And now it's been 13 years. They're back in the grand final. Yeah. So Trent and I found a different place that was showing the game. So I was there at four in the morning in London, Vauxhall. Yeah. To watch the Australian grandfinal, the granny.

Uh-huh. It's been a long time since I was kind of part of the working holiday visa temporary Aussies in London and community. But these things are very much put on here for a couple years. Yeah, yeah, yeah. And there's a bunch of us old people who have assimilated. And so I was like, I've been so young and excited. But everyone rammed in. There's like maybe, you know, several hundred people cramming in the thing to watch the game.

And it was neck and neck the whole game. and I even put the hat on backwards. And they would have been like, and I put that, hello, fellow kids. Yeah, exactly.

What's up fellow kids? And I had to skateboard over my shoulder. Someone did walk by and they're like, oh, I love the mass videos. And then they get one. And I'm like, not now. They're like, oh, I didn't,

not like this. They're like, I didn't realize that YouTube was having a midlife crisis. Oh, wow. That's having a breakdown This is like your version of like when male comedians end up going on Streetly come down Yeah exactly yeah

I'm getting caught with their dance partner It was like oh do you know stand up masses that are going to chuck backwards And drinking with young people at 5am No good luck I got an email from someone after saying Oh I spotted you there but I thought I wouldn't come and say hi Thanks pal And now put the hand backwards

And the dockers searched ahead and with like four minutes to go they were like three goals up which is basically game in the bag yeah we were so excited this would be the first ever grand final win for the dockers yeah and somehow what the Brisbane Lions scored three goals did they not know about the hat no one told them I was wearing that it was phenomenal so they do the they don't bounce it anymore They threw the ball up in the middle. It's a massive field. And they honestly, they just grabbed it and just kicked it once or twice down the field and goal.

And then they did it again. They should just do that for the whole game normally. I know. Way to the end. The team could have done that the whole game. Honestly, they're like objectively an incredible game. But to basically feel like the game was one and everyone's pre-celebrating and then the other team just took it. It was incredible.

Wow. I was so angry. But I was like, that's allowed. Like, that's the game. So the hat, the hat has failed me when it mattered the most. I'm going to have to retire it now. Yeah. Yeah.

That's a shame. Yeah. You should have put it on Inside Out? Now I know. Next season. You've got to do it something different every time. Next season, Inside Out. Yeah, used all the magic early.

Yeah, I know. Also, I appreciate the fact that there'll be some listeners who already knew the result of the match. Oh, yeah. All right. But I was on the edge of my seat. I said, I don't know what happened. I don't know everyone.

Yeah, that's great. That was so much better than your story about trying to watch the World Cup. Aw. Our first problem today was sent in by Nathan, who went to the problem posing page and said, do you put your trousers or socks on first? what is the general consensus of clothes putting on order blah blah blah nathan now beck we've had some foreshadowing that you're looking into this yes because on a previous episode you asked listeners to complete a survey explaining or least saying and then justifying the order in which they put on their socks and their trousers yeah

despite the fact it's obviously clear you put your trousers on first I can't always All right. Wow. So, I believe you've got, you've looked into this and you've got the data to back it up. Yes. So, what's the deal? Okay, well, firstly, let's address the fact that you put your trousers on first, apparently. Explain, explain yourself, Matthew. Well, I don't put the socks on until I leave the house.

Oh, you're a bare foot person. Yeah, a bare foot person. Yeah. So I'm not going to walk around trousers. Well, I'll do sometimes, but my house, my rules. We need the poet. Yeah, exactly. So I'll pop my trousers on, do stuff around the house,

and then chuck on the socks as required to leave the house. Have you always been a no socks to the last minute guy? I think so. I think there are barefoot people and there's socks people. I'm a barefoot person. I do put socks on when guests are coming around. In addition to my trousers. Yeah.

You don't want to subject your guests to those days. disgusting. Oh yeah, keep these dogs under wraps. At least not for free. Yeah, not for free. You never know. You can't trust your friends. They might take sneaky picks and put them on wiki feet. Yeah. Yeah, I think there's barefoot people and sock people. See, I'm a socks like as soon as I get out of bed. Oh, wow. I'm not only a socks person. I'm a socks and slippers person. Oh yeah. I get cold feet. Like literally, my feet get really cold really easily and I hate it. I could never understand how people could just be okay with their feet being cold and then I later realize that people just have actual circulation yeah yeah and probably neurodivergent thing as well I that's your answer to everything

I assume this question is less about do you live your wider life such that you would sock or trouser earlier in the day than the other and more if you are getting dressed from scratch and in front of you a pair of socks and a pair of trousers which would you put you put on first? Always socks. It's the first because my feet get colder than the rest. I have swimming socks. My feet get so cold. It is the first thing I do when I get out of bed like underpants and socks. So I do undies first because I'm not a monster. We live in a civilisation. We live in a society. And so I do undies and socks and because undies and socks are kept in the same place, they're both out at the same time. I always have my undies and socks in two drawers.

and it's always undy draw on top and then sock underneath because that's that's the order that's the vertical height they exist in when I'm wearing them do you keep one of your clothes at the height that they are on your body I find the very because you hang shirts up and I put trousers in the drawer under that and then underwear and then so see I hang everything

like as my if I can it's hung Like, so shirts, jumpers, trousers, everything. I need more hang in space. That's what I'm going to wrong. I mean, they're rammed in, but I have to be able to see them in their sort of natural. Right. Yeah, yeah, natural hand. If they're folded, it's, it's when someone was helping me sort through my clothes and things to, like, get rid of some of my clutter.

And she suggested that my tracksuits, she said, well, your tracksuits, we could put in a draw. draw and I had an emotional reaction which surprised me like I felt like crying at the idea of like no they need to be with the other clothes. That'll be, but they'll be lonely. Well, no, it was more like I will forget that I own them. Yeah. Wow. Yeah, I'm very much everything has to be uphanging, including, you know, those shoe storing

things that you hang on the inside of your water. They're like plastic pockets, yes. Clear pockets and you're meant to put your little. They sell like these things. They hang and you slot them in. And they don't really fit big shoes, but you might put like flip flops or things. I use those to store my socks and undies and things. So I can see all of my...

I can see them all. That's very funny. Yeah. I give socks so little respect. I only own the one sock. I know. You've talked about this. Yes, exactly.

You have a draw of loose... Socks are just functional... Yeah. Yeah. Whereas I have to pair my socks with the amount of... If there's some heel wearage when I'm hanging them to dry. Yeah. I check to make sure that they have their same amount of...

They're wearing evenly. So they'll wear out at the same time. So I'm not getting rid of one sock. What experiences in life do you think you no longer have time for because you're dedicating this much to sock? Curation and management. Is it probably looking at a rainbow going for a walk? Cripping for the podcast.

I love that, obviously. So I do like putting on my socks first thing. That is the first thing I will do. And it's to the point there. even if I'm just getting up with a dressing gown and I'm making breakfast or something. On go the socks. On go the socks. Wow.

Yeah. So socks and undies are always like first thing. Well, I feel like Beck, we've kind of, we're deadlocked here. Is there a way to break this tie? Well, I need to give credit to producer Laura Grimshaw. Yeah. Because when you said, Beck, you've done the research. By research, I mean, I mentioned the problem in the last episode.

Someone made a form. Yeah, you made the form. I made the form. Laura went through the answers to the form. Laura went through the data. And the answers are now in front of me. And they've magically appeared in front of you in the Google Doc. And I would have done it myself, but I was too busy trying to pay my socks.

Evenly. There it is. That's where the time's going. Oh my goodness. I've just scrolled through the data. That's a ridiculous summary, Laura. Your socks must be in disarray the amount of time you've put into this. They're very carefully paired.

I care a lot about my socks because I put my socks on first. Okay, you're not here to break the tie. Right. No, yeah, you are, actually. I've decided. All right, Beck, talk us through this. Yeah. So you may have seen, we've had 306 responses.

There's too many. It's too many responses. I love, this is why I love our listeners, because we'll casually be like, oh, does anyone want to create a visualization or sound version that will help us understand the Abababab order? Or we'll throw it. something out there and people will respond. And I love the fact that people are like

Yes, Matt and Beck need to know and we did. We needed to know. 306 of you, thank you so much for taking the time to let us know about socks versus trousers. So I'm going to save the result for the end. Oh, okay. Because that's how narrative suspense works for listeners. First, let's have a look at what people who side with you have said, what their reasons are. Normal people. So, Laura has done a lovely job of summarising some of the reasons people have given.

This is a sample. A representative sample. A representative sample, exactly. So some of the answers are essentially, I live somewhere hot, socks are optional, trousers are not hot. That's my argument completely. Yeah. Even though I no longer live somewhere hot. No.

But you're used to it. Yeah. Yeah, yeah. One of the other answers was dressing from the middle out feels better. A few people said that, which I really like. Yeah, I like the term no isolated islands of clothing. Contiguous clothing only. What I do like is I match the socks to the trousers, not the trousers to the socks.

That's valid. So once you got your trousers on, you know what socks you want to wear. Yes, you don't put the socks on first, then pick trousers that match. Yeah. I mean, I've removed this complication from my life. Yours are all the same black socks, aren't they? Mono socks set up, yeah. I get the same pair of bamboo socks.

Do you believe I'm wearing them right now? Yeah, me too. So I've got black ones and white ones in my little hanging thing. I also have some pockets for novelty socks, which are socks people give me, which I usually wear when the other ones have all worn out. You know, that's the only exception. People will occasionally give me like socks with maths equations on them or something. Yeah, they do.

Yeah. But I'm all about the comfort. I throw them into the nearest hedge. Hedge is such a specific thing. There's no better place to throw things you don't want than a hedge. Bowling balls. So I have these same socks and they're kind of just above the ankle. Right.

They're not like all the way up the calf but they're not below the ankle so they get like they don't get pulled down by way. Yeah, you don't want them going. Because I wear boots a lot. They have a heel town. Yeah, that's right. Yeah, I'm a big fan of the same socks. Once you've got a... Once you've got a sock that works.

You know? I've been locked in since university. So someone else said bigger items get put on before smaller items. Oh. Given the items do not overlap. So they did have to specify they don't put the job before. They're not superman. Yeah, yeah.

When undressing, the order is reversed. Okay. So then you would take your socks off before your trousers. That's interesting. I find that my socks come off with my trousers. Yeah. They just get caught. They just come off with them.

The amount of times I've thought of... Yeah, if I can't find a sock, it's rolled up in a trouser leg. Someone said they put their socks on later before they put on their shoes so their feet have more time to air dry. I'm assuming this is post-shower. And they're not just a very moist person. You feet some time in the air? I like the person here who doesn't like socks to pass through the holes of the trousers.

Feels wrong to be knotting things through toroid. So your trousers, I guess, are a double hole torus at the end of the day. Right. And they're passing... Is that what the term is? Yeah. A genus 2. Okay, explain.

Oh, it's just a number... We count the number of holes in surfaces in maths. And genus... Is the number of holes. So it's not spelled like jeans. No, no, no, gene... Yeah, it wasn't a pun. Yeah, yeah.

Maybe the knotting things, each sock passes through a different hole. they could feel what's the word I'm after here displeasing yeah and I will actually come back to this when I give you the answers from my fellow team team socks first but before I move on to those I want to give a shout out to Nathan from Wollongong in Australia

who said they do the left trouser leg then their left sock followed by the right trouser leg and then their right socks something wrong with that Nathan that's not right mate Like, technically one sock is going on before the trousers. If you class the trousers being on half off, not being fully on. Suck, half.

There's always more sock than trouser on it. There's always more trouser on than sock until you're finished. Oh, yeah, there's always equal to or greater trouser than sock. Yeah. Yes. Yeah, that's right. Although we did have someone said to stop messing around, you could go left to right. So you go, sock, trouser.

and then the other sock. Bracketed, bracket it by socks. A little sock trouser sandwich. So here are the explanations from people who said socks first. My favorite is just socks, then trousers, job done. Which is not an explanation. But I agree. This is stating it again.

Someone has said that if you do the trousers, then the socks, you have to lift the trouser leg up to put on the socks and then pull the trouser leg back down. And that is a fath. Not how I put them on. Go on. Such speed, it blows the trousers out of the way. Then they gently fall back down. There's a josting they just come off like stripper trousers.

Yeah. Whip? Yeah. Now, someone else said it only matters for calf-length socks. They said if the trouser leg is fitted to their calf, it's hard to pull down over the sock without the sock rolling back down. And I think that is the main reason. I think it's the fact that, yeah, so often if you're wearing.

any sort of trousers where you have to put them over the top again. The trousers are now in the way. Yeah. I accept that as an argument. They don't mind for ankle-length socks, but I have the same thing. I like the fact that when I pull on my trousers, they're going to pick up any slack left behind by me not pulling on the socks properly. Like if there's any slouching, the trousers are just supporting, they're going on in the direction.

That's why they come off with the trousers. They're moving in the fail-safe direction of foot movement. And someone else said socks first, less untucking. They said see also shirt first. So they do shirt first, then trousers over the top. Okay, I'd agree with that. Do you know what? I think that I don't really pay attention to whether I do shirt or trousers first.

I think it's just whichever one I grab first. But definitely always socks first. Someone else pointed out that because underwear goes first. And I feel like that, not that we asked. I think we're all in agreement. Most people agree underpants first. And they said sort of the. same thing that I said earlier, which is you're doing pants and your socks are already

usually with your underpants, so they're there. Oh, okay. So they come on at the same time because you're already standing there. I agree. Someone said, I don't know if shorts are included, but let me clarify, long pants, so trousers, go on after socks. When they wear shorts, the order doesn't matter. I would still go.

I will say I do often get my socks out the same time I get my pants out. underwear and socks come out at the same time. I put the underwear on. Then I just yeat the socks downstairs. I think you get them as close to the front door as possible. I think one of the other explanations that are trousers first person said was because you generally tend to, well, they sit down to put on their socks and they don't want to sit in their underpants on something. So they put trousers first so they can sit down and put on their socks.

Stand up like an adult. Yeah, yeah. I place the socks on the ground. And then I jump into. I do do my socks standing up. One of my first ever viral videos was me putting on both socks at the same time. Someone did an interview. Is this a Wallace and Grommet style contraption?

Someone did a ridiculous interview and the kind of takeaway meme was them trying to say people put on their socks one at a time. Oh, yeah, yeah. As a kind of thing they would then insist on sharing on social media. This was like in 2011. Yeah. And I was like, that's ridiculous. I put on both socks simultaneously. And then I just did a hard edit between one of take of me jumping, pulling up the socks,

and then me landing wearing the socks. Yeah. And it was just one of those perfect times where you couldn't really spot the edit. We'll find that. We'll find that video somewhere. Find it, put it in the show notes. Yeah, yeah, yeah. This is what I said I was going to come back to as well.

Someone said, it feels so much nicer slipping your feet through trousers when you have socks on, especially around the toes. producer Laura has added Producer Laura fully agrees with this weird explanation. Now did producer Laura add that or our listeners just adding all caps producer Laura notes? No I add

that's my commentary on the explanation but I really hate being barefoot so I have my slippers like flip flops by my bed. Oh my goodness. I am not barefoot at any point this is why we get along

and I have really small, really sensitive fee. Yeah, because they've never met the outside world. I hate... I've got no immune gist. Exactly. They've been raised in captivity. They can't cope with it. You've got to let them out.

Experience life. So, yeah, so I... Harding them up a little. Immediately into flip-flops. Yep. And then when I'm getting dressed, the socks are basically underwear. Wow. And also because, like, most trousers are, like, tighter.

So rolling them up to pull them back over the sock is annoying. But I also don't like the feeling of my bare feet going through like jeans. Right. I'm the same. Okay, so I'll tell you why. I've got quite large feet for someone of my height. Yep. That's why you're both involved in the podcast.

You average out to normal size feet. I've got big feet. I got big old feet. I trip a lot. I fall very little. I catch myself. Yeah. And so I'm like, you know, those toys with the heavy base where you push it and it comes back up.

Yeah. You get knocked down. But I get up again. I'm the side show Bob That checks out Yeah yeah I'm often hitting rakes It's also true

I'm related But I don't have a backyard I find that my toes get caught When I'm putting It like my toes get caught in clothes Right So like in trousers and stuff On the way through their catch on something

Yeah so like especially if it's something with a You know a cuff down the bottom I honestly I'll get like a little toes sort of scrunched up the corner. I hate that. I hate it. I hate it.

Or you just own ridiculous trousers? I mean. They're like booby trapped. I don't know if you've known this, but society hasn't been kind to women when it comes to trousers. That's a valid point. But it sounds like there's like dead ends and like trick. I think, well, only recently have palazzo pants come back into fashion and only now have I started wearing trousers.

I used to not wear trousers because they were too fitted. They're too tight. Like women's trousers. Yeah, that's a tighter. Yeah, and I don't like the tightness. Weirdly, I will wear tides. Yeah, but they're like not the primary. Tides are the only time where I don't put socks on first because that's madness.

So I'll go undies, tights, then socks over the top. Okay, yeah. Because you need something to catch all that sweat around the feet. That's more than we need to know, but thank you. I'm going to guess that producer Laura agrees. Yeah. Oh yeah, yeah, yeah. Trousers are hard clothes. Trousers are hard clothes. And so I feel like I need more protection. So I need to protect my feet from the hard clothes.

I think there's a whole side conversation about how producer Laura has underdeveloped baby feet. That is need to be hardened up in the real world. I was going to be like, don't be mean. And then I remembered that Laura apologized for having to go. slowly because she struggles to walk in bare feet. With a tiny baby feet, yeah. Yeah.

I've got tiny baby feet. You've got tiny baby feet. I feel like that's a whole separate problem. We haven't got time to unpack. I can buy children's shoes. But this is what's interesting. You have tiny baby feet. I've got big feet and they're actually quite hardened.

They've got like the calloused. I walk a lot so they get calloused anyway, regardless of what shoes or socks I'm wearing. Now, I will walk barefoot on like sand or grass or whatever. I don't hate it. I don't hate it. I hate it. I hate it. I hate it.

It's a temperature thing for me. Speaking of walking, we, I think we've travelled a long way from the original problem now. Okay, so we want to get back to the point. Yeah. So you want to know how many people. Give me the result. 306 responses. Well, first of all, we did give an option.

Well, you gave an option for generic joke response. They could either say socks on first or trousers on first or you could do generic joke response. Literally pick generic. That's what it says. Generic joke response. I know our listeners love a joke response. Yep. So I gave them that just as an option in the dog.

The menu. Yeah, 11 people. Like, yeah. 11 people either made the joke about how we don't use the word trousers in our country. A lot of Americans don't like the word trousers. Yep. And I guess Australians as well, we don't, we don't. No.

We say pants just like Americans. We've been in the UK long enough. We don't say pants for trousers because British people find that hysterical. Yeah. Same with thongs. It's same with thongs. We've both been saying flip-flops and gritting our teeth every time. Yes.

It was either that or the other generic response was, I'd feel stupid if I had socks and nothing else. Oh yeah, about it. 295 people took the brief seriously. Yeah, 295 took it seriously. Yes. Of them. Ooh, boy.

168. That's over half. Yeah. Versus 127. Less than half. 168. Said trousers first. Oh my goodness.

So your team one. Not by much. But not by much. No. You're going to run some maths. I'm going to work it out as a percentage. I don't know that counts as running much maths. It is when you're me.

Oh, not by much. 57%. Yeah. It's bigger than the Brexit vote. That's true. And that was... And that made generation-oldering decisions. Yeah, so I suppose now we all have to win trials first.

57 to 43. Wow. Yeah. So it's interesting. It's close. It's close. It's not a super majority. No.

And also that is of people who listen to our podcast. Could be. And went to the form to fill it in. Okay, if you're listening to this. I hope more than 306 people listen to this podcast. We haven't got evidence of the rest. You know, it's at least 3006. It could be that actually a majority of people put socks on first,

but they are smart enough to not waste their time. Nah, they're spending so much time looking after their sock collection. But they haven't got time in the survey. Yeah, probably. They're listening to the podcast while sorting their socks out. Yeah, that's it. Now, we did hear from Nathan who posed the problem. The original Nathan.

Because Nathan wrote in to say, I'm the original set of the question, here to justify my position. Can I just say it's unusual to already have feedback from the problem poser? Well, we've answered. It's only because we teased it with the survey previously. Yeah. Nathan wanted to get in there with more deeps. Now, Nathan did get on touch. We didn't mention in the previous.

this episode that Nathan was the problem poser. We just said we're going to do a form. It's very presumptuous of Nathan to assume we were referring to, there could have been hundreds of people. There could have been waves of people asking this question. But Nathan did. No, Nathan was correct. Identify themselves.

Yeah. And said, I'm here to justify my position. Primarily to offset my partner who I suspect has also put in a response. Oh. So I think we're starting to see now why the question was posed. I was to say, now we know why it was a problem. Yeah. I love when our show becomes the adjudicator.

Yeah, for arguments and couples. Yeah, yeah. I'm for it. I like it. I don't know. Are we team Nathan or team Nathan's partner? So Nathan says, I put trousers on first. I get out of the shower in the morning while still in the wet room, which,

ooh la la, la. A wet room. This guy is wet room. Any room could be a wet room if you. If you live on my flat With my track record of flooding it I get my underwear I get my underwear

I get my underwear And chosen bottom half for the day Be that more likely shorts Which do not have all the issues My partner has about putting trousers on first Okay we're getting a lot of background information On the relationship here Yeah yeah or indeed trousers

I do not want wet socks Fair I also live with my parents and therefore need to be somewhat presentable by the time I've left the bathroom. Very, very considerate of you. Whereas my partner has lived alone for some time and therefore only needs to worry about the dog and the cat seeing her. Thank you for picking my problem, Nathan. Now, I'm going to throw a spanner in the workshop for explanation there, Nathan, because I also get changed in the bathroom before I leave the bathroom.

Yes. I get dressed in the bathroom. Even though you live alone. Even though I live alone. Primarily because the bathroom is to warm from the steam. And again, temperature. So as soon as I step out of the bathroom, I'm going to move. immediately get cold.

And the rest of the house is equally wet. Yeah. I'm actually very good at keeping the bathroom floor dry. I dry myself off while I'm still in the shower bath area. So that by the time I step out, I'm not leaving drips or anything. Obviously, I've got a bath mat and stuff. Sorry, Bath Beck, you have a bath mat. And so.

And we're not starting the debate if people dry themselves in the shower outside the shower. No, I know. One at a time. I hate a wet floor in the bathroom. It's one of my pet peeves. That's why it's so far. I know. Whenever you soak your entire flat.

I hate a wet floor so much. Yeah. And the reason I hate a wet floor is because I'm always wearing socks and they just soak up. And then my feet are cold and wet. So I understand not wanting wet socks. I also think, you know, just get a shower curtain. Yeah. Stop that stuff spreading everywhere.

I agree. But yeah, I get that. Now, we also received this response. I am the girlfriend of the person who submitted the socks or trousers. Yes. We got to tease more problems before we solve them. Get everyone, flush everyone out of the woodwork. That's great.

I wonder if they listened to the podcast together or they separately realized. Yeah. Or Nathan went, that's it. I'm going to ask this podcast. And girlfriend's like, all right then. Fine, I'm going to answer it as well. Yeah, yeah. This is how we gain listeners.

Right. We've got to ask more questions. One argument at a time. Yeah. So the girlfriend also says, socks first means no scrunching of trousers to put on socks. That's what Laura and I are talking about. Women's trousers tend to be tighter.

That's very true. You can't get the trousers in the socks accidentally, which, yes. Yep. And the only time I have tucked trousers into socks is if I'm, like, about to ride a bike or? Yeah, cycling's the anytime I'd do that. Yeah, yeah. Also, skinny jeans exist and no one wants their socks bunching,

trying to put their trousers back on over their socks. Yes, so I'm with the girlfriend who hasn't provided their name. But this also makes me wonder, because I don't know what the, and just to say, there is, look, gender is not a binary thing. But I don't have the demographics, the gender of people who listen to the show. We've learned that even putting the order you put your, socks and trousers on is a spectrum. Oh, but this is one I'm wondering.

I wonder, and I'm not, look, we, we can't keep going down this rubber hot. No, we're not doing on the survey. But I do wonder. Is there a correlation? Would there be a correlation between the number of people who have said socks on first and what clothing they wear, whether they're more generally pushing towards feminine clothing? I 100% reckon there's a correlation between wearing feminine clothing and sock ordering. due to the complications of tighter fitting clothing.

And not necessarily that we're not saying if you do socks first, you wear feminine clothing. But just I wonder if you were to look at an overlay of those, if that percentage. I think if all you wear a baggy clothes, the world is your sock order oyster. Yeah. Put them on whenever you want, however you want. It's the privilege of baggy clothes. And that's why Madness sang about the. Well, I guess the conclusion is 168 people are wrong.

Nathan is wrong. At least 160. I guess the conclusion to that is... You do you. Yeah, you do you. I mean, Nathan asked us, do you put your trousers or socks on? What is the general consensus? And those were the answers.

The consensus is it's close, but trousers have it just by a nose. Just by a toes, I should have said. That would have been funnier. I don't think Would it? I don't think the order Funny er is relative I didn't say in absolute terms

I didn't say funny I don't think the order that anyone gets dressed impacts anyone else but it's a fun discussion to have Yes So thank you Thank you Nathan

Thank you 306 of you who responded And thank you for everyone else Who's still listening Our next problem comes from Oscar, who says, how much would a standard pair of dice weigh if they were made up of just protons and

neutrons? In other words, if all of their empty space was filled with stuff, what would happen if you tried to roll such dice? Now, as always, Matt, explain the question to me. So, dice, familiar with dice? I am aware of that regular roll dice, play a board game. Cubes, dots, pips. Cubs, dots, pips, etc. And you can get diced made of ridiculous things. Like particularly D&D people, but anyone like... Teeth. A hundred billion.

You can get mammoth ivory dice. What? Because that's... What in the name of privileged millionaire? Surprisingly cheap, relatively. Yeah, Manchester marks. It's like ethical ivory because... They're not alive anymore.

You can't kill a mammoth to get it. Sure. But up in like Siberia or someone... where they keep dropping out of the permafrost as it's melting. So like there's a surprise, which is not good news in general. But there's a surprising amount of mammoth ivory. Like it's still obviously rare and expensive, but it's not like. Matt, do you own a pair?

I do not. I do not. I do not own that. And I wasn't intending to talk about that. I just thought I should add some context that sometimes gamers like dice made of unusual things. Yes. And you can get like metal dice. which I imagine is where this conversation may have come about

because you can get some very heavy dice. Obviously, weighted dice is a whole thing about when they no longer land on a random side. This is just weighty dice. Still fair, very heavy. I don't know if this came up because Oscar was discussing heavy dice at a D&D session, but that's the spirit in which I took it. And Oscars obviously thought what would be the heaviest dice. Like forget tungsten or...

or osmium or these are the heavy metals are. Sure. Just go all out. What is the stuff that's not protons and neutrons normally? Well, electrons. Yep. Is like the particle answer. Empty space.

If you ignore some of the complexities of quantum mechanics is the actual answer. So you've kind of got tiny, tiny nucleus, like comically small nucleus, which is the protons and neutrons. And they're quite big. They're big and chunky. They're actually, this will be useful later, they're called Barryons. They're named after Barry. Yeah, yeah, yeah, yeah.

Keep calm and Barry on. Keep calm and Barry on. Yeah. We should name the protons and neutrons, Barrios. Barion luggage is probably the only luggage you're allowed with Ryanair without having to pay extra. Well, it's very funny. I think Barry is actually like Greek for heavy. That works particularly well.

So they're the big heavy ones. electrons are tiny in light and they exist in a let's say a cloud around the nucleus and I forget the exact analogies but it's something like the nucleus and an atom is like a pea in the middle of a football stadium it's like it's a ridiculously small part of the atom so there's a sense in which reality around us matter seemingly solid things is vast majority empty space Right. Because of the interactions of the electrons. This explains my brain. Exactly. The fact that the electrons interact at a distance, everything stays apart and feels solid. So what Oscar's doing here is saying, well, what if there wasn't empty space?

What if it was just barons crammed in? And could that be a thing in any? Like, nothing doesn't have empty space. You are so close to being correct. Oh. Effectively nothing does. There is one exception. Is it nothing?

There's not nothing. Okay. It's going to get meta. No, exactly. Neutron stars. Yeah. It's when the universe is like, what if a atom nucleus but the size of a star?

It's basically a star-sized atom nucleus, which shouldn't work. And if you ignore black holes, which I think we should, because they're a glitch. Because they're terrified. They're there. Well, black holes are the closest I get to thinking we live in a simulation.

Because black holes feel like whoever was programming the universe messed up. Someone told me that they had a theory that our universe is inside a black hole and that's why it's expanding because it's pulling in from something else. Oh, yeah. Black holes are a blank canvas upon which you can apply any ridiculous theory issues. It's true. Okay, I've just programmed up that universe simulation you wanted. Okay, do, do, do. And I'm coming to you, I'm like, hey, I got that universe simulation.

It's been running for a while. One small problem, I've just realized. Okay. Every now and then, some of the matter disappears. This was terrible Python code, wasn't it? It was terrible Python code. God is, you are God, basically. Who's God?

The person who coded the simulation of the person who commissioned it. Yeah. And I looked at all the physics equations. And I thought the universe is going to work great. And for billions of years, it was great. But it turns out if you get too much matter too close together, the gravity I programmed in causes it to collapse down to nothingness. Sure.

But you don't lose it because even though it no longer has any special size, it's still got the mass gravitational pull and is somehow spinning despite having no size. And I'm like, is that going to cause a problem? I don't think so. They very, very slowly evaporate. Yeah. There's not so many that stuff doesn't function. And actually, you put a couple of big ones in the middle of galaxies.

They're really handy. Okay, yeah. So it's a couple of bugs, but like, I don't think it's going to affect the overall universe experience. Thank you. Okay. Right. So they ignore that. Paid.

Yeah. Thank you. So that's black holes. Okay, thank you. Neutron stars are not far off, but they're just on the inside of plausible. So you have a sun or something, depending on the end of the final life stages of a regular star, it can kind of collapse and collapse and collapse. And you get this runaway gravitational thing where, because protons and neutrons don't want to be that close to each other. But with enough gravity, they can be held in place.

But there's a kind of a critical mass you need in the first place to cause them to get compacted at all. Oh, yeah. It's got how COVID got everyone to feel like they're working together. Exactly. Exactly. Yes. Yes. Without the external COVID pressure or supernova, you don't get the conditions. Or basically, it's an office. They've been forced to work together. They've been forced back into the office. Yes. And occasionally it means that there is interpersonal issues in the office. People bumping off each other. Yeah. Hey, you in the same spin state as me. You know the usual. Yeah. And then it settles again. Yeah. Hashtag Firmioon problems. So. Yeah. You know how everyone's still using hashtags. Thank you.

Oh, my hat. I haven't got my hat. It's so. It's like you being young. Just what the hell on backwards? Hey, hashtag backwards cap day, everyone. Or is it no cap now? I don't know.

I've lost track. Oh, yeah, that's right. So, anyway. That's why they started saying no cap. Because they were speaking to you directly. Exactly. Mate. No cap.

So, so neutron stars are super, super dense. Just neutrons and some protons mixed in one. not. And they're all kind of as close together as they possibly can be. And the reason I thought about neutron stars, other than I love them, they're just incredible. In this context, it's a cliched bit of science communication to talk about how heavy a teaspoon worth of neutron star would be. And what we're talking about with these dice is basically a teaspoon or two. Right. In this case, lumps of sugar, as opposed to a spoonful of sugar, of neutron star. Yeah, a sugar cube. So I was like, great, I'll just quit look into it.

So I, first of all, pulled up an article from astronomy magazine from a little while ago. They were talking about this, saying that your standard issue neutron star is actually not that massive in terms of mass. It's like one to two times the mass of the sun. So a bit heavier than our star, but not outrageously so. Now, they say, and I haven't, despite living with a solar physicist, I didn't fact check this, just reading it now. They're saying if you got a tablespoon of the sun, depending on where you scoom. It will burn your throat. It will ruin your spoon.

They're saying it's about two kilos per teaspoon. Wow. Two kilos. There will be a point in the sun where that is true. Sure. So the sun's pretty dense in the metal, not dense on the outside. I mean, arguably, we're inside the sun's atmosphere right now, but that's not, it's not get old Lucy about this. So there's like, they reckon, who am I to question astronomy magazine, two kilos per teaspoon?

They then say that a, oh, they switch to a tablespoon. Oh, now that you can't throw it the place. Now they're saying a tablespoon of neutron star weighs more than one billion tons. About the mass of Mount Everest. Holy moly. Yeah, it's dense stuff. Interestingly, side chat, I dug around and people have noticed. So I think the first person I can find online,

someone called Jonathan Swinton in like 2003 realized everyone who talked about this cliche how much is a spoon full of neutron star everyone gets wildly different answers including NASA has two estimates that differ by about a billion tons per teaspoon because the volume of a teaspoon or tablespoon or what people use in the examples varies a bunch

and the density of a neutron star varies Right. Depending on where you are in the neutron star. Okay. And so you'll see wildly different figures for this. Can I ask a question about density? Yep. So let's say that neutron star is it an element in the same way that like iron?

That is a really good question. Or like carbon? No, you're right. You could argue that neutron star is itself an element because it is a job. because it is a giant atomic nucleus of some description. Yeah. I'm trying to imagine like, is it solid like diamond? It is solid-ish.

It still has changing density. So it's probably more like a Jupiter setup. In a hypothetical world, could you have a neutron star waiting ring, engagement ring? Yes. Because if diamond is carbon that's like super compacted. Yes, yes. So diamond is carbon that's not necessarily super compacted, but is incredibly well linked between the carbons.

Okay. But it does occur under pressure. It takes pressure and heat for it to do that. Yeah. That's what I'm thinking. Yes, 100%. And I think after that may, it's probably is more dense than, you know, charcoal. Neutron star is like one giant atomic nuclear.

It's an element in the same way that like tomatoes are a fruit. Yeah. You could make an argument for it in one sense, but not in the way we actually categorize things. Yeah, exactly. No one likes that guy, points it out when you're trying to make a sandwich. Yeah, bingo. Oh, you want a fruit sandwich. Yeah.

Did you know that olives are a droople? A droople? Yeah. It's a droople. It's the same family as cherries and stone fruit. I did not know that. Great. That was something I found out recently.

I'm glad you glad you had that it's ready So next time I call someone a droople Yeah Which you do a lot And it's about time you knew what it meant And now I know I'm accusing of being in the same family as cherries Yeah

Anyway I feel like actually You're getting distracted I'm getting distracted I've gone too far in the neutron star direction Because Yeah because we're trying to work out Can you make some dice Yeah cared about dice

Not engagement rates So I did look into it And that argument of a teaspoon of neutron star having about the same mass as Mount Everest. Table spoon. Which is about, or a tablespoon, a spoon, a reasonable size spoon of sufficiently representative neutron star is pretty close to the dice we're talking about. It's pretty close to Mount Everest is roughly a billion tons.

It's heavy. It's heavy. So if we answer Oscar's actual question, and I'm assuming 16mm dice, which means they have a volume of 4.1 cubic centimeters each. So we're talking roughly 8 cubic centimeters of dice, 8.2. And if you put in the density of just not necessarily the middle of a neutron star, but packing in neutrons and some protons as much as you can with no gaps,

they do come out by my calculations to about 1.1 billion tons each. So you've got 2.2 billion tons of dice, which is roughly a Mount Everest each. And that's more than the mammoth ones. That's more than the mammoth ones. Yeah, you would have, you'd struggle to roll those, wouldn't you? Isn't that so happy for such a small thing that you would just make everything, it would pull in stuff around it?

So, so excellent, good point. Now, Oscar does say, what would happen if you tried to roll such dice? And you're absolutely right, you're like, well, hang on, wouldn't it draw things in? Now, if you walk past Mount Everest, you're not drawn into it. But the mass is pretty spread out. So they're basically a Mount Everest each. Yeah. And let's, if we go beat by beat, if you were to, I don't know how you got them or how you pick them up to roll them.

Let's just say they magically appear as you're rolling them. So you're rolling normal dice and they magically become all neutrons. They're now instantly each the mass of Mount Everest, but way more concentrated. And you can't get, the point is you can never get that close to all the mass of Mount Everest at once. Because if you start, if you're outside it, it's actually a long way away. Yeah, yeah. If you tunnel into it, some of it's now behind you, pulling you back. Yeah, yeah.

So it's subtly different. And I think order of magnitude, if you're closer than 10 metres, you'd probably feel more gravity from the dice than from the earth. Give or take, very, very, very rough. Does that mean if you put them on your shoes? If you can walk up or walk you. If you were under them, you would go up towards them. Yeah, right. Yeah.

But slowly, because they're not, like, way more powerful than normal gravity. They just, they'll draw you in. Did you say that a neutron star is, like, towards the end of a star's life? Yes. So our sun could eventually become a... I don't think it's got the mass to do that, but potentially, yes, that kind of stuff. That's the kind of thing that would happen, yeah. So at some point, we're not going to, like, so they float up because the sun's getting old.

But also, if the sun suddenly became a black hole or a neutron star or anything of same mass, it would be, apart from the lack of light coming off it now, it'll be indistinguishable for us because it's still the same amount of mass, the same distance away. So things, it's like, if anything like becomes a black hole, it doesn't suddenly start vacuuming everything into water. Like, it doesn't be like, but it does suck, but not like that. It's like a hole in something. Yeah, no, a black hole would just be like the same thing.

It's still the same mass. So actually, unless you're like inside. it doesn't make a difference. Yeah. And there'd be no light coming from it. So we'd all be dead anyway. The sun became a black hole. There'd be no light.

So we would notice that. We need that. Eight minutes later. Yeah, that'd be pretty nice. Life and stuff. Yep. Yep. But these dice are way smaller than neutron star.

But they are still each and Mount Everest. But now here's the issue. In this hypothetical, we're going to gradually turn it back up towards reality. Because at the moment, we've got these dice appearing and just hovering in the air. What if we let them fall? Well, they're going to hit the ground or the table with phenomenal pressure. Yeah. Because all that mass is going to be on a very small area.

Yeah. And just like if I went outside and I got like a steak or something with a pointy end, I pushed it. I could start to drive it into the ground. Yeah, yeah. Because I've got enough pressure on the small end that it's going through. The dice are so much forced because of gravity on such a small area. They would just penetrate straight down. Yeah.

To the, I reckon, assuming they don't. get destroyed, they would head straight for the center of the earth. I was going to say, because the earth is not a neutron star. No. And so that means, way less dense. Nothing is that dense. Nothing's going to stop. There's always going to be space for stuff to get pushed aside if something's heavy enough. Yeah. I think they would appear and instantly fall, punching a small hole through everything. Yeah. Straight to the center of the earth. I actually didn't work out how long that would take. Not that long. Yeah, 20 something minutes that would be at the center of the earth. And then they'd probably yo-yo backwards and forwards

because that would overshoot and then come back and that's my guess would that make the earth go bleh it's not that much mass compared to the mass of the earth no that's true like it's a lot compared to any density near it so it would punch through but what's another Everest

you know it's not a big change you said that so kind of what's another Everest now we've got three Everest that's all well and good but the bigger issue is protons and neutrons don't want to be right next to each other

and it only works in a neutron star well it works in a nucleus because there's a very small number of them and quantum stuff a neutron star is the incredible gravitational pressure from everything else if you suddenly removed a little couple cubic centimeters of effectively neutron star just neutrons and protons

they're immediately going to want to separate from each other Oh. So what would actually happen is the moment they exist, they would blow apart in comically small fractions of a second. Okay. And I did some, again, some back of the envelope calculations. So you got these barons crammed into what I think is called a Fermion C. It's a bunch of them hanging out together.

A Fermion C. Firmion C. I think that's like on the South Coast, isn't it? Yes, Fermi on sea. And they don't want to be near each other. And there's a bunch of very complicated equations to give you the energy, average energy. Is that Fermi is in like Fermi's paradox? Yeah, it is.

Yeah, same Fermi. It's a type of particle where it follows certain rules that stop there from being multiple particles with the same energy and spend hanging out in the same space. Which is why they can't get too close together. Like a good dungeon master. A good, don't you, Master? Because we've packed our Fermions so close together, they're all going to be different energy states or spin states, and they're all going to want to get apart real fast.

I estimated, and this is a meaningless unit, it's like 75 mega electron volts each, and they're going to want to separate real fast. And then I tried to convert that to be what it would be compared to, like, high-end explosives. Okay. And it's like a billion times more explosive power than all nuclear weapons on the Earth.

Oh, gosh. It's, yeah. So what you're saying is don't. Don't make it. It would be a phenomenal. It would be the biggest explosion that had ever occurred. So we don't have to work out how much a pair of dice would weigh if they're made up of just protons and neutrons. because if you're trying to do that, you would exploit everything.

You'd basically blow a crater. Yeah. Kilometers, if not hundreds of kilometres across. You damn fools. You blew it up. It's not enough to destroy the earth. Okay. Well, that's good.

Back of the envelope. Good to know we don't have enough weapons yet to do that. It's about 0.01% of the energy required to gravitationally separate all of the earth apart. So that's good news. But there would be a heck of a... The effects of which, though. It could be an extinction level event. I would say so, most likely, surely.

Yeah, and you'd have all the nuclear radiation issues of a regular atomic explosion. Also, it's got the nuclear... It's got the nuclear fallout too. Yeah, so we're all like mutants and stuff. Yeah, yeah. We know we're dead first, probably. Yeah, I hope you're happy with yourself, Oscar. I mean, a heck of a nuclear winter.

But it may be almost all life on Earth. I hope it was worth it for your dumb dear. Exactly. And that would happen in like under a second. So, yeah. So we wouldn't have time to... So in conclusion, don't. You wouldn't have to worry about it, I guess.

I mean, in reality, you can't get... That mean, neutrons together and transport them. So don't, don't, don't. Very heavy. One Everest each. They, when you try to roll them, they'll just destroy all life on Earth. Yeah. The end.

I'm going to give that an exploding. Hey, good work. Thank you. Thank you. Sort of makes the mammoth one seem a bit less unethical, doesn't it? It really does. And now it's time for Australian Aussie ballness, where we take care of outstanding bits of business from previous solutions.

And we've already discussed at length, long trousers and short socks. At the same time, double survey, two surveys for the price of one, the same 306 people answered my question of what is the most wrong ordering of the numbers one to five. Yes. This is of a problem sent him by someone named Morgan, who walked past four houses in a horrifically numbered order. Yep. And we went back and forth and trying to work out what's the most wrong order. and we decided just to ask, ask the listeners. And as of the time of recording, we did just double check.

288 valid orderings were put into the survey. And producer Laura has crunched some numbers for us. And we discarded anything that wasn't a valid set of the five digits from one to five. What do we got? So the most wrong ordering of the numbers one to five is 41532. And this is just based on people's vibes, right? Pure vibes. But the whole thing is vibes.

That's what I realise. I try to come up with metrics for it. There's no metrics. It's just vibes. 41532. 41532 was the most wrong according to the most people. That's 23 people voted for that. I'm not going to go through them all,

but the arrangements that got the most votes. Yeah, there are a couple in the top. Yeah. So there's also 31524, which is the most. most wrong according to 19 people. 4-3-1-5-2 was the most wrong according to 16 people. And then we had a tie, 13 people, each voted for 4-1-3-5-2 and 352-1-4. And then 4-2-1-4.

And then 4-2-5-1-3 was the most wrong according to 11 people. Yeah, they're all the kind of close cluster. Yes, everything else received under 10, like single-figure voting. So interestingly, so there's 120 possible combinations of 1, 2, 3, 4, 5 and within this survey, only 74 combinations received votes. Yeah. Yeah, it's only just over fine. Some of them are totally fine. Yeah.

People have no feeling about whatsoever. Apart from the jokers who voted for 1, 2, 3, 4, 5. I think they were there mainly for the sock trousers survey. So I think it's interesting, there's a whole cluster that are all similar-ish, but heads and shoulders above that, digits are. that is 4153.2. I did actually run a quick simulation to work out how significant this finding is. Because if people were picking at random, we had 288 responders and there's only 120 arrangements of the digits 1 through 5. That should be 2.4 votes each. Yeah. And this is way more than that. But you're like, oh, but if it's random, it might clump. So I simulated a million random surveys.

and in none of those surveys did the top scoring combination get more than 16 votes and the probability of getting 23 votes all on the same one at random is like one in a trillion. So it's significant. Like that ordering

it's not just random noise in the survey responses that's a significant clump. So the kind of definitive answer to our question is 4-1-5-3-2. Yeah. I did compare it to what we did last time. Now, you arranged things that were only four digits. Yeah.

And all your top ones started with a two. So something about in four digits, two was the most discombobulating one to start with. Interestingly, on five, 40% of the votes started with a four. Like, way higher than you'd expect. and a surprisingly high number ended in a two. So there's definitely a preference for starting digits. I did run it through my old models. It looks like it's about people care about reverse patterns,

about half as much as they care about forward patterns. But there was such a massive spread. The only thing that's significant is 41532 was agreed to be the worst. Yeah. With a bunch of equivalent runner-roops. And the fact that people manually typed in the number, it's not like they were being led by any, is pretty interesting. 23 out of 288 people all typed in the same five-digit number, which means that probably a lot of us have the same pin code. Almost certainly.

That wasn't just like the natural peak of a distribution. That was a lone spike. So that is a particular. That's the one. That's the one. Thank you, everyone. Yeah. 41532.

In that same episode, I also said that I would like some examples of terrible street numbering. You did? In the real world, like actual streets. Yeah. And we got some brilliant answers. But due to this episode, already running a little. bit long. We're going to save that for any other business next episode. So you'll have to wait till

then. Well, that is it for today's episode. Thank you for listening to the AFL grand final edition A Problem Squared, which happens roughly every 13 years. We like to thank everyone who listens to this podcast. You all are equally meaningful and wonderful to us. But some of you are more meaningful and wonder than others. And those are the people who support us on Patreon. And keep this whole enterprise running. And to thank those fine Patreon supporters, we pick three of their names at random every episode to mispronounce, which this time shall include

Mitch Elf. Klimen Sribay. De Smond. Vandem. Ear. Ere. So to those three people who probably don't even know who they are and we should have really thought this through, have we?

And everyone else who supports the channel either by giving us actual money or just listening and sharing it with your friends and family, thank you very much. This is it for the end of the episode. I've been Matt Parker listening to Beck Hell and our producer, Laura Grimshaw, who is a bit like the 4,100E Series 2 Siren

Well, I looked it up made by Sirens and Horns, the Siren and Industrial Air Horn Solutions people. They make the 4,100E Series 2 siren. Much like that siren, producer Laura, make sure we start, stop and take breaks at all the right times. Thanks for listening, everyone. Thank you. Gosh, I hate sports. Okay, Beck, we're once again in the same room. I'm holding aloft the game of Connect 4.

You cannot go in the middle column again for it is full. I mean, you can. Maybe you don't tell me what to do. I would like to please go. It's just extra pressure because I know all the fans who are going to be. I don't think there are any right moves the way we're playing this game. I'm going to go controversial. Yeah.

No, I'm not. I'm going to go. 7D. 7D. Oh, that is a bold move. Interesting.