A Problem Squared - 011 = Massive Halls and Ambassadors' Balls

Episode Date: September 30, 2020

How long is a year of A Problem Squared podcasts? What's the qualification for a room being a room? Is the famous Ferrero Rocher advert mathematically possible? You can visit the Crafts Council campaign here: https://www.craftscouncil.org.uk/support-us/appeals-and-projects/lets-craft-packs-children Delve into luxury with the original Ferrero Rocher ad: https://www.youtube.com/watch?v=4P-nZZkQqTc The best-known packings of equal circles in a circle http://hydra.nat.uni-magdeburg.de/packing/cci/d1.html Correction: Bec's episode of Jonathan Ross's Comedy Club aired on 19th September (Series 1 Episode 2)

Welcome to A Problem Squared, the podcast which is the problem equivalent of bird watching, where we try and find new and exciting problems in the wild, and we document them, we analyze them, and then we solve them with all the calm and efficiency of a bird flying into a school classroom. I'm mathematician Matt Parker. Look, don't laugh. I've put a lot of effort into this introduction. It's okay.

Is that not the response that you're hoping for? I want people to enjoy it, but also I just want to show them we put the effort into the introduction. I'm Matt Parker, mathematician, putting the logical in order for logical, and I'm joined by professional twitcher, Bec Hill. When you say twitcher, are you referring to the fact that I twitch a lot or the platform twitch oh no you know what the platform twitch didn't even cross my mind it was a combination of your excessive amounts of energy and enthusiasm playing off the fact that bird watchers are called twitches i didn't know that yeah there you go well also i should point out that i'm not a professional twitcher in terms of the social media platform. That's a good point.

And I apologize for misrepresenting Beck's career. Were you going to say for getting people's hopes up? Yes. I like to think that our listeners are like, oh, I was so excited to watch Beck play Beat Saber for the hundredth time. I'm very good at it. I have nothing to compare myself to, but I'm pretty sure I'm amazing. Maybe you should twitch.

Maybe I should. Well, on this episode, we will... Work out how we number our episodes. Finally get to the bottom of how many Ferrero Rochers there are. And work out when does a room become more than that. We've also got updates on Beck's 5K t-shirt and our fantastic Patreon supporters. Matt, it's been a month. How have you been?

What have you been up to? I've been all right. I've been making too many YouTube videos. So many. I know. Your face is everywhere. I do apologize. The thing is, YouTube recommends me to me.

So I also have the, that like because i watch youtube under a different account to making youtube yeah it's correctly ascertained that the version of me that watches youtube would like the sorts of videos that actual me is making and so it correctly recommends all of my videos to me and i'm always of two minds because they will recommend it to me just after the videos come out and i've just spent days possibly over a week slaving away finishing the edit i've done nothing but look at this video i'd never want to see it again i'm like that's done i'm gonna go relax on the sofa watch some tv and then there's me again so i'm like it's the last thing I want to watch.

Now you know how Lucy's life is all the time. Well, exactly. We've got a joint YouTube viewing account. Yeah. And so when she's trying to relax or do something else, she'll also be recommended videos of me. There's no escape. But in the back of my head, I know YouTube keeps track of what percentage of people watch the video having seen the thumbnail. So when my face appears on the screen, I know, do I want to add to the percentage of people who did or did not watch the video having seen it? Oh, right.

And I have to admit, i err on not watching it i make my own statistics a little bit worse i i tell the google the almighty youtube algorithm that the video is a little bit not as good as it thought it might have been by not watching my own videos so well i mean if you want i can do that too if that helps that would be really helpful yeah at least one person listening has to watch your video based on the thumbnail and that'll make up for you not doing it well one person who wouldn't have otherwise yeah because i do think you know what i could just hit play and then walk out of the room yeah but i'm like no that's that's not that's a bit disuous. Do you want to have a guess?

I'm just looking up the exact number now. What percentage of people who see a thumbnail on YouTube actually then watch the video? For you or just in general? I've only got numbers for me, but I suspect I'm probably not that totally different. me but I suspect I'm probably not that totally different see I would have thought it was really high because I find that thumbnails that people tend to do for videos now are the thing that will lead you to click more so than the headline yep I've definitely clicked on things based on it looking like it's halfway through the process of something and i want to see where it's going oh interesting but i also know that your thumbnails are perfect

for your channel but they're less clickbaity in the way that the things that i tend to click on yep so i don't yeah i don't know i would think that it's a high percentage. I could make them more clickbaity. Are you saying it's a low percentage? No, well, it's about 8%, depending on the video. I would say 8% of people are like, oh, yeah, I love Holly and Red Dwarf. Look like Norman Lovett. Thanks. More that you're just like, when you wear a black t-shirt against a black background,

you're sort of a floating head. It's a point i'm a floating head yeah i need to buy more colorful t-shirts that's my problem well you know you you're talking to the right person well exactly um yeah and actually i don't know how that compares to other channels but fewer than one in ten people who see the thumbnail will watch the video and so i've i've basically i'm peer pressured into also not watching the video so i won't watch my own videos but my life recently has been cranking out two videos a week because i'm not doing live shows or anything else at the moment but i think i might have to take my foot off the pedal a little bit um because i can't sustain that level

i mean to be fair i've got quite a few videos in progress, so I may keep that going for a while. We'll see. How about yourself? What's been keeping you busy? Oh, I did the Jonathan Ross show, recorded that. Well, the Jonathan Ross Comedy Club. Really? Yep. That's all being filmed. When does that go out? That should, in theory, as people are listening to this, be coming out the Saturday after they listen to this. So it's like the second or third of October, whenever that is. And it's right after Britain's Got Talent. Wow. So obviously I'll tweet about it and stuff if anyone follows me on social media.

But yeah, in theory, it should be in a couple of days. You can watch my face. And for anyone listening internationally, the Jonathan Ross show is a big deal. That's like one of the top prime time TV shows going. Well, this is his new comedy show. So this is all like just stand up rather than a chat show. So it's just you doing a routine?

Yeah, I've got my flip charts, having a bit of fun. That is super exciting. Everyone, you have to watch it this imminent weekend. Yeah. We believe. We believe. We believe. It'll be on catch up. It'll be on catch up. Yeah.

Extra news that I probably should have opened with. I got a shout out on Seth Meyers' late night talk show. What? I know. It was the most surreal moment of my life. So Seth Meyers is one of the late night talk show hosts in the States. People who aren't familiar with their work. Yeah. So, Seth Meyers is one of the late night talk show hosts in the States, people who aren't familiar with their work.

And like all the other talk shows, they had to kind of record from home for a while. And I made a video where I was like, why are late night talk show hosts so bad at filming at home? It's time for a closer look. And I did this thing about how you can do better filming stuff at home. And obviously, I wrote some jokes about um the hosts colbert didn't hear a thing out of them seth myers dropped me a message it's like yeah good advice i'll get a lapel mic what how are you the one giving that advice like how does he not have an entire team who's like we'll give you this stuff well exactly and each time i i was giving advice and i'm like this is super obvious and i would say things like i'm sure your film people have already told you this or suggested this or done that but this is what i

would do but from all i can tell they were pretty much just told to grab an ipad and good luck so i was talking about how to set up lapel mics, what your options are for auto cues if you want to do that for YouTube, how to do lighting, what kind of camera to get, all this stuff. I became his unofficial YouTube consultant. Also, hang on. When you say you became this, since we last spoke or like beginning of lockdown?

Beginning of lockdown. I'm sorry. Why did you not mention this is this because you're like didn't come up in conversation you know i don't what words do i need to say for you to be like oh and by the way i've been assisting seth meyer i didn't occur to i wasn't holding out on you beck it was just happening you know it became my normal life it was just every day oh yeah there's oh yeah no i forgot to mention that during lockdown i became best friends with jackie chan so yeah like i was going to mention it earlier

the weirdest one was because lucy and i watch seth's show and always had previously and one night we were watching it and while we were watching the show i got a message from seth um with another thing about filming stuff and just chatting so So I was like, hey, me and my new BFF. First name basis. I know. But then in his last show, at the very end, after a closer look, he very kindly thanks me by name. He'd previously referred to me anonymously in an article

and he messaged me and said, look, I'm really sorry. You're the person I'm talking about, but we couldn't get a name or anything. And so the whole time I didn't tweet about it. No one knew. I was just happily doing it in the background. Wow. And then out of nowhere, he mentioned me by name in the wrap up of his last episode at home.

And so, yeah, it's been an immense amount of fun. That's so cool. Yeah. YouTube consultant to the stars. Yeah. You've done it, Matt. That's so cool. Yeah. Wow. That's my YouTube consultant to the stars. Yeah. You've done it, Matt. You've finally got my approval. Really?

Wow. This is what it feels like. First up, this wasn't a problem originally, but it's since become a problem. On Twitter, Albert Hickey has said that they were listening to episode 9 of A Problem Squared, and I mentioned in the episode that we were three quarters of the way through the year. And they've written, let me get this exactly what they've said, since episode 1 is when the podcast starts, is this an N out of N plus one thing as 12 months ends at the 13th episode as there is a month between each episode? And that wasn't, that's not a problem per se, but then we started talking about it and it pretty quickly did become a problem.

Yeah, because I think the other reason that that came up is because, and we'll talk about this more at the end of this episode, but we had made a promise that if we could reach 100 Patreons after 12 months of doing this show, that we would continue doing another year. And then the question was, does that mean after 12 episodes, in which case that's technically 11 months, or does that mean after 12 months, which means 13 episodes? Yeah, there's a whole area of mistakes called off by one errors in programming, I guess, and mathematics. And this is a fence post problem, I would say, because the fence post problem is that if you've got five meters of fence and there's a post every meter, how many posts do you need?

And the intuition answer is we need five posts because there's five meters and one post per meter. But then you forget you need one at the beginning and at the end. There's a zeroth post and then one, two, three, four, five. And so people will often forget when you've got a range of things divided up, it's very easy to miscount either how many dividers there are or how many sections there are. So in our case, our first 12 episodes are only 11 months apart because they're like 12 fence posts. And because you need one at the beginning and the

end there's only 11 bits of fence so i guess the question here is when do we stop counting because i said after nine episodes we were three quarters of the way through because i think i count the month leading up to an episode as being the month of that episode. And that's interesting because I think the month after that episode is the month that everyone has to get on board before the next episode comes out. I love the fact that this is classic. I'm thinking about me and you're thinking about the audience. Because in my mind, I was like i was like oh yeah no it still makes

sense because if we were waiting to try and get 100 patreon supporters by the time our 12th episode comes out i know by wording i'm suggesting that's by the time it comes out which already that technically makes the answer but if you were to say like by 12 episodes, then what I would say is if we hadn't reached 100 by the time it went out, I would still give us a month to reach the 100 before deciding whether to continue or not. And I agree. Yeah, yeah. We're done. I would interpret it like if we've got 100 supporters, when we're about to make the 13th episode, we will make the 13th episode. Yeah, yeah. So that's the month after.

But you were saying as well that the month in the lead up to an episode, for you as part of it, because we do our prep, that's when we're finding our problems. That's when we're finding our solutions. That's when we're potentially trying to film epic videos with drones yeah and i very much view these episodes as like a roundup of the month that was and they come out on the last day of the month and they're about whatever happened to us and our adventures with problem solving the month prior, which means as soon as the 12th one is out, then we're immediately working on the next years or season, whatever we want to call this, worth of episodes. Yeah.

If we take both of ours, arguably what that means is we've actually got more months than episodes. We've got 13 months a year. It's the opposite of the fence post problem. Maybe every episode has two months, the month leading up to it and the month afterwards, and just they overlap. Oh, no, no.

Now you're thinking in more than two dimensions, and my brain can't handle that. Yeah, you stack them, and each month is the previous one winding down, the next one winding up, and because they wind down and wind up in a linear fashion there's always the same total amount of episode yeah like spreading out playing cards yeah maybe if we're in the way that a dealer does it really

smoothly where they go and then it's like overlapping but there's but it's the same amount of thickness for the whole i've gone really specific someone listen one person listening will be really impressed by that and thank you person for whoever you are well now i'm thinking is that a consistent amount of card that's a new problem altogether about to say i'm now i've got to get some felt and a pack of cards out and do it properly um anyway the the moral of the story is i think that we will declare the 12 months to be oh what do you reckon i i'm i'm tempted to say no it's when the 12th one goes out no it's after it's a month after it's until there's a month it's until when the 13th would be i understand that that means that if we don't have a hundred by the end of that month, we might

end up prepping for a show that we never record. Yep. Okay. I will begrudgingly accept the run on because I'm sticking in mentally. I'm still imagining that the episode is being fading up in the month before and fading out in the month afterwards. So I think

I'm happy with that. Okay. So I think, I believe Albert, I believe that that's a ding. I think that's a ding. But we'll leave it to you to confirm. So as you know, Matt, I am one of the ambassadors for the UK Crafts Council. Yes, correct. Which means I've been raising alertness about a campaign they have to send out 10,000 craft boxes to kids who need them. Great campaign.

Yep. And people should just go onto the UK Craft Council website. Just Google it. We'll put a link in the show notes. It's a really nice. Look at you. Always ambassadoring. Always ambassadoring.

And one of the things that I was slightly disappointed about was when I realized that being an ambassador doesn't automatically mean that I get a pyramid of Frere Rocher. No. And then we talked about this for a bit and you suggested that the pyramid was square shaped. Yep. I then in a later episode corrected you and pointed out that it is a circular base. Correct. Several eagle-eared is a circular base. Correct. Several eagle-eared listeners pointed that out. Yeah.

And I wanted to know how many Ferrero Rocher are in that pile from the ad in the 90s. It's a classic ad. Can I correct you on one point before you've even started? Which is, in the classic early 1990s commercial for Ferrero Rocher's with the ambassador's reception, it is the ambassador who has organized the reception and therefore has to provide the Ferrero Rocher's to their guests. Oh, you've just blown my mind. So I suspect the reason why you haven't suddenly got it is that's one of your many responsibilities. That's my job. Yeah. You've let yourself down. You've let the craft council down oh no i'm sorry but i guess the good news yes

that i think we can get to the bottom of how many ferrero shares you will require to assemble a platter of the proportions as seen in the commercial. Yes, help me, Matt. Help me be a better ambassador. So we actually had a listener at Setalias, apologies if I'm mispronouncing that, on Twitter. Don't know how to pronounce that. And they sent us at a problem squared. They sent us the way that they would go about working out

how many Fero Rocher are in that pyramid. They've done a really amazing thread, which we'll retweet from the A Problem Squared account when this goes out. But I wanted to know, were their findings the same as yours, Matt? Well, I kind of took their findings as a starting point because they had a fantastic idea to use a website and if you look on their tweets can you see like they've got a they've tweeted a screen grab of the stack of ferrero rocher yeah and i did a similar thing i went through the commercial i got a couple different shots where you can see it clearly screen grab them and had those as my reference points next to it they've tweeted an image which looks like it's got circles made of smaller circles yeah and

then it's got numbers for how many smaller circles are in the bigger circle yeah that's a website that i'm a huge fan of where people try to find the smallest circle you can fit a given number of other circles inside of. Oh, sounds cool. And the small ones are all the same size. And mathematically, it's incredibly difficult. Sounds like a fun Friday night. Sorry, what was that? Nothing.

As long as you weren't, you know, undercutting my excitement. I would never do that. Such an important bit of mathematical research. So the problem is in mathematics, there's a whole area of arranging shapes so they take up the minimum amount of space in different numbers of dimensions. This is an area of maths that we haven't really cracked yet. And our current understanding of mathematics is woefully inadequate to work out how to arrange things in an efficient way. And the website, which I talk about in my book, Things to Make and Do in the Fourth Dimension, because I love this stuff. which I talk about in my book,

Things to Make and Do in the Fourth Dimension, because I love this stuff. It's all the best known solutions for arranging smaller circles inside a big circle. Every time I say that, I do appreciate how ridiculous it is. And so the Sedalius, or however they pronounce their name, I'm very sorry.

They had the idea that if you look at the pyramid, so I was wrong. It's not square based, it looks circular based. And so each layer is circles arranged in a bigger circle. And they went to this website to try and find the optimal way to arrange that many circles inside a circle. And that's a genius idea. So that's what I did. I was like, okay, I will try that. But unlike what they did, where they're just trying to work it out theoretically they've just tried to count how many they can see work out which one

it might be and then work their way up the stack i thought i there's going to be complications once you physically do this with tiny chocolate spheres so i went and ordered 192 ferrero rochers i found a bulk confectionery place. And so I thought I'd give it a go. I'd do it properly. And as you know, I messaged you when they arrived. Yeah.

That I have literally hundreds, hundreds of Ferrero Rochers that I can try and balance in a stack. Well, almost hundreds. Hundreds and a bit. Almost hundreds. Well, here's a spoiler. I did not have enough.

I mean, I shouldn't sound so excited by that, but I am fully aware. Here's a little insider knowledge for the listeners. Yep. Matt does not have a sweet tooth at all. No. I mean, this is probably safest because if they'd been sent to me to try and do this problem, I definitely would have eaten them before I'd solved the problem. I spent two days balancing Ferrero Rocher's on top of each other. They'd been sent to me to try and do this problem. I definitely would have eaten them before I'd solved the problem.

I spent two days balancing Ferrero Rochers on top of each other. Do you know how many of them I ate during those two days? None. Zero. Zero. Absolutely none. I did not eat a single Ferrero Rocher the entire time. Although I would have laughed if the reason that you don't have enough is because you'd been eating them. Because I'd eaten up.

No, no, no. I accidentally squashed two of them during the construction process. But I was still short. I was short more than two. So today, this morning when I was finishing this up, I had to run down to the shops and buy non-bulk discount. Oh my gosh. Additional Ferrero Rocher's i was wanted to complete this and do it properly seth meyer's consultancy money

but you know how many how many consultancy monies i got also zero big fan great number so i started off by doing what we saw in the tweets where I eyeballed how big the circle would be and then how to arrange them within that. The problem with these arrangements is they're not very regular because there's no good way to arrange circles in a bigger circle. Which is why originally I thought this is not how they will have done it in the commercial because it's a terrible way to do it. And I managed to verify through several hours of trying to do commercial because it's a terrible way to do it. And I managed to verify through several hours of trying to do it, it's a terrible way to do it. I tried different sized circles as the base, different arrangements. As soon as you start building up a couple layers,

it's incredibly unstable and uneven. Is it because it gets bigger in the center, but it leans to the side so they start toppling off each other like sand dunes yes yes you get the sand dune effect where they just kind of the whole pile wants to slump yeah out like when you when you look at a like a timer with this with sand in it one of those timers with sand what call hourglass. And then I remember staring at them, not like I was surrounded by them as a child, but like, you know, when you look at one

and you really want it to tower up and reach the top, but it keeps falling before it gets to that height that you want it to get to. Growing up in Adelaide, you spent your youth watching the sands of time. Matt, you're from Perth. You can't like... Hey, I would argue A rung up, but let's not get into that.

At least I'm like only an eight hour bus ride from the next major city. So true. So true. Yeah. So I did. I will admit, because in the commercial they're on platters, which hold the base together, I did blue tack the bottom layer of Ferrero Rochers to the table so they couldn't move out. But then all the other ones on top of that were freestanding.

And if you look at the commercial, they haven't got their little cups, little paper cupcake wrappers. So I had to remove hundreds of those. Yeah. Which they're stuck into. Also, I watched the commercial. At no point does anyone unwrap any of the chocolates. What do they do with their wrappers? Just drop them. I think they just, it seems to imply they eat them whole.

Like. How the other half live. Like how the other half live. Well, all I could assume is that there's another tier of Fure Rocher for the one percenters, which is in edible gold leaf or something. We have to point out, let's check our privilege for a second, Matt. Fure Rocher is not like the every man's chocolate. Like this is a, you know, when you say for the 1%, most could argue that Ferrero Rocher is probably nearing a 1%. Like it's not a chocolate that you just pick up as you're getting your milk.

It's a chocolate for your Christmas stocking. That's the advertising working for you. You know, that's the image they want to project with these gold wraps. Also the price, Matt. That's a good point. I don't know how they, because. Oh, because you don't buy sweet things, so you don't realize. I don't buy chocolate, so I have no idea.

20 pounds for a box is very reasonable, I imagine. Okay, so to put it in perspective, I think these days you can get a Mars bar for just under a quid. Like under, I think they're like 80p for a Mars bar. Okay. Not a king size. And if you bulk purchase Ferrero Rocher, I can tell you, you'd get two and a half for the same money. Oh, see? Now, this is the thing.

We've all been buying our Ferrero Rocher wrong. No, you've got to go straight to the distributor. That's also not to say that that's still not an amount more than some can afford i understand that but you and i are rolling in youtube ko-fi donations oh yeah we got that podcast money now so in conclusion i don't know if they've got some magical edible wrapping better stacking ferrero Rocher out there. But the ones that I was able to purchase and I left the foil on, I could not get to stack in a perfectly circular arrangement. What I ended up doing was finding the circular arrangement that had the most regular ones in the middle.

And that was basically a hexagonal grid of Ferrero Rochers slightly distorted around the edge to make the outer bit a bit more circular but it meant that inside it I had a much more regular arrangement of Ferrero Rochers and then I did a bunch of calculations I did a lot of trial and error because in the commercial, if you watch them take them off the platter, there's one by itself at the top, but the next layer has four and that's just a terrible number to have next.

Balancing one sphere on four other spheres is not a logical mathematical decision. So I don't know what the chef whoever prepares this was doing chef can you imagine stacking for a rush and being like i've done my job as the chef hey having done it it's a skilled job yeah but it doesn't make you a chef i don't know what the requirements are to be a chef. Mathematician. Obviously, they have a mathematician. Delicately.

Well, also, it's a bit too hands-on for a mathematician. See, this is the thing, and I don't know if anyone listening feels the same right now, is that this entire time, I'm visualizing you stacking these Ferrero Rocher and struggling. Yep. And yet, in my head, I'm like, you just stack them. Like, in my head, I'm like, you just stack them. Like in my head, I'm like, it's obvious. It's so obviously easy. And I understand that that's because I don't have it in front of me

and I'm not trying to do it. But it's very frustrating not being in a position to show that I can do it very easily, which I believe I could. Bec? What? Would you like to borrow just over 200 Ferrero Rochers? I mean... And you can have a go.

Is this... We might need more. Well, yeah, there's going to be substantial losses. However, one of the issues is if they're not super regular, if they're a bit here and there, when you put the next layer on, each new Ferrero Rocher you're putting on, you want it to sit in like a dimple, a dip, like a little depression nestled between the ones underneath.

But if the ones underneath aren't super regular, how big the dips are varies, which means the next layer up is a little bit uneven and the next layer up is even more uneven and by the time you get a few layers up it's hard it's hard to say where one layer stops and one begins it becomes a mess and then like you're saying it starts all slumping out and collapsing it's an absolute mess but the the outside of it is the only thing that looks like it's sort of solid layers in terms of like a clear difference between the first layer the second layer and that sense but the but the filling of those layers isn't visible so that could be that could be all over the shop surely yeah but the the outer layers are a manifestation of what's going on inside

because they're resting on the ones behind. Oh, that was deep. Thank you. Matt, get that on a T-shirt. The outer layers are a manifestation of what's going on inside. Matt Parker, a problem squared 2020. I'm pretty sure that might be fridge magnet worthy. My problem squared 2020.

I'm pretty sure that might be fridge magnet worthy. So you won't get neat regular outer layers unless inside has also been taken care of and aligned and at one with itself. So what I ended up doing was having a very regular, it was a compact hexagonal arrangement of these layers of spheres. Because we know mathematically the best way to arrange spheres, but it's just not circular on the outside. So I went for a compromise. I made it look as circular as possible on the outside while being very regular and neatly arranged on the inside. And okay, Beck, are you ready for what I ended up making? Took me two days. Yes, I'm waiting with bated breath.

Sending it now. And we will put these on Twitter and on Instagram. Way! Yeah. Check that out. That looks amazing. Is that solid Ferrero Rocher? Solid.

Yep. That's chocolate all the way down. You've basically done. I see what you mean. It looks more hexagonal. It looks hexagonal. Yeah. Because I made one which was a bit more circular, but it was still too small. When I built it up, it stopped one layer short of what you see in the commercial. I think the angle, the steepness in the commercial is not physically possible stacking Ferrero Rocher's.

the commercial is not physically possible stacking Ferrero Rocher's. And so I had to widen out the base a little and that made it a bit more hexagonally. So it doesn't look quite as round, but I convinced myself from the right angle, it looks enough like the ones in the ad. It's not perfect, but I think that's as close as you're going to get in physical reality. Yeah, I think you're right. That's amazing. I do still want to have a go at it though. I still think you should send these to me and not because I want to put them into my belly. Well, I will count them and send you a known number of them and you can have a go at stacking to see if you can improve on that arrangement. Yes. Follow on problem. Uh oh. Possibly two.

Here we go. When we got into this, then I was like, well, hang on. In the commercial, the famous line is, ambassador, you're spoiling us or some variation on that thing. Yes. And I was wondering, is 216 chocolates spoiling the guests? 38 pence each. 16 chocolates spoiling the guests, 38 pence each. So, Bec, I believe you've tried to work out how many people were at the ambassador's reception.

Yes, I used my ambassadorial skills to guess how many people were at the bowl based on the ad. Because you asked me to work it out and I started counting and then realized that, first of all, they're moving. They're walking in the ad. They're all moving around. It's very hard to count things that are moving. And secondly, at least half of them are in black tuxes with their backs to camera. So I couldn't tell if it was the same person between shots or not. Like I could tell you there's like five ladies that are definitely different,

but all the people in tuxes, I couldn't tell you how many other people are there. So what I did is I guessed how many people are there because they're not socially distancing. Well, you're an ambassador. I have to know these things now. It's a gift. I assume you go to a lot of ambassador receptions and the like.

Well, not yet, no, but I'll have to hold them, as you pointed out. Oh, exactly. Yeah. So I think it seemed to be a very big place because they had statues and stuff and columns and everything. But all the people inside seemed to be quite squished up. This is the ambassadorial insight that we need. I guess that there was about 200. Oh.

But I'm happy to guess that there's 216, if that helps. 200 plus potentially 16 dropped for Oroche. Because I was about to say, oh, well, that works out to about one each, which is not necessarily spoiling the guests. Hey, it is if normally you get a mars bar well exactly for the similar price point but then i'm like well hang on maybe the ambassador is spoiling them by deliberately finding an arrangement to have precisely the same number of ferrero rochers as people because if there's anything an ambassador does it's you know stop uh arguments and people

getting upset so having the exact number of confectionery items as guests i mean that's some top tier ambassadoring surely unless they meant that you're spoiling us in terms of that they're spoiling their enjoyment of the evening by only giving them one fraiche and wanting them to have more. You're spoiling all our fun. Your onerous dessert rules. They cut the line too quick. It's, you're spoiling us, Ambassador. This whole evening, you've ruined it.

They actually keep, they go any further. Right, right. Yeah, because originally when I was when i was counting them i was like oh there's only about 50 but i think just given the size of the place and how tightly packed they seem to be in there i'm going to assume that off camera there's at least another 150 that feels totally reasonable yeah now when you're planning your first ambassador's reception, you probably do want to actually spoil your guests. Yes. So I thought I would calculate the maximum number of Ferrero Rocher's you could have in a pile.

Oh. And by maximum, I mean the point at which it will collapse under its own weight. Ooh. So I had to do a couple of things. First of all, I had to work out how heavy a Ferrero Rocher is. And I did it a bit like macadamia nuts It was chocolate in shell So I worked out the mass

When it's still got the foil wrapping But not the little cup thing that it sits in So I weighed a whole bunch And averaged it out They're 12.9 grams each With the wrapping I then worked out how much force the chocolate can withstand before it collapses. My wife, Lucy, actually walked into the kitchen and there was like a countertop full of squashed Ferrero Rochers

because I'd been pushing them into the kitchen scales to see what mass it would register before they would crush. And some of them, they're variable they're not a consistent building material i would not want to use this i know they vary quite a bit and i don't know if you could go through and pick out all the hardiest ones about one in ten would easily get well over three kilos of force before it would go. Or three kilos of mass equivalent under gravity. It's like that Bible saying, isn't it? The man who builds his house on sand is a fool.

The man who builds his house on ferrochete will, it will last slightly longer upon this chocolate build my ambassador reception and so um this on average your standard issue for a share you can put a total of 2.8 kilograms on it before it crushes underneath the weight that's my average that I worked out roughly. And so I then calculated, because now I know the mathematical optimal arrangement, having done it myself, and then run the numbers on what you end up getting, you can have 650 layers of Ferrero shares in a pyramid before the bottom layer will be crushed by the weight of all the ones above it. You're not counting the weight that I'll add by climbing up it. No, no.

It's going to be pretty big. It's a total of 68,814,850 Ferrero Rochers. Wow. Which will cost you just over 26.25 quarter million pounds to buy wow that would be spoiling us exactly well i'm just saying that's the bar that's the upper bound on how spoiled you can make your guests thank you and actually if we assume that an ambassador's reception does have 216 people at it, they would have 318,000 each. So there you go. That's pretty spoiled.

Yeah, that's very spoiled. Before we push on with the rest of the episode, I just want to make a point that we have not been sponsored by Ferrero Rocher. Oh, no, absolutely not. Quite the opposite. Yes, the opposite. If anything, Matt has given them money. Quite the opposite.

Yes, the opposite. If anything, Matt has given them money. So if you are from Ferrero Rocher and you think that that was worth sponsoring us for, do get in touch. Add a problem square. What? You're shaking your head, Matt. I do not authorise this Orchid Donut at all. I've got enough Ferrero Rochers in my life right now.

I do not want to be sent any more. I meant with money. Oh, money oh money oh that's fine yeah we have a problem in from simon on patreon who says it's a question no one has managed to answer wow apparently they use this as an icebreaker sometimes when they meet new folks at a party. They want to know, how do we determine when an area changes name based on volume? I mean, that's a good, messy question so far. So they, oh, they're talking about rooms in a house. So they say, at what point does a room become a great room? At what point does a great room become a ballroom? When does a ballroom become a great hall? And the other direction, what about a hallway? At what volume does a great room become a ballroom? When does a ballroom become a great hall? And in

the other direction, what about a hallway? At what volume does a hallway become a room? And when does a closet become a room? Is it number of doors? Okay, so the problem here is, Bec, how do we classify what a room is? Yeah, I've got a few simple things that I think absolutely cover everything here. Bold of you. Number one. Yep. What makes a room a room is whether it can fit the thing that the room is named after. Got it. So a closet can't be a bedroom because it's not got a bed in it. If you fit a bed in it, then it's a bedroom. A lounge room can fit a lounge in it, meaning like a lounge chair. A lounge room can fit a lounge in it, meaning like a lounge chair. A ballroom, you can hold a ball in it.

Like it's very simple. However, I reckon I could fit a bed in my lounge. Sure. And then it's a bedroom. Oh, okay. It's a bedroom or a lounge room. If you've got a bed or a lounge in there, it's a bed or a lounge room. It's named after what's in it.

So I think that's the really simple answer there. The second thing is a hallway. This is going to blow your mind. The word hallway comes from the word hole, which originally is basically referring to a large building. Like a town hall. Exactly. So the hallway isn't defined by the fact that it's like now you could say a hallway means a passageway or whatever, but essentially it comes from the fact that it's a room that does have many doors coming off of it. So a hallway technically is a room. It's not

like in the same way that a hall is a room. So let me just try and make sure I got this right. So let me just try and make sure I got this right. Back in the day, a house was just one room, a hall. And then we gradually had more and more rooms attached to the outside. And the hall bit got smaller and smaller and smaller. So now it's not vestigial, but there's still just this little hall in the middle of the house that used to be the whole house. But now it's just that little bit. Whereas the town hall, it's still just one one big room it's still a big hall and the defining feature is the number of doorways essentially originally the term hole comes from just meaning building which is why

you're thinking of town hall and stuff because it was just like it the etymology of it is it means like safe and cover like that's kind of where it it comes from a lot of other languages so it's it's sort of a mix but um more i think it was around this i could be very wrong here but i was i believe it was around the 17th century where um in use it meant it came to refer to the main central room in a building that had other rooms attached to it got it and as and then we get on to the point that you were saying that as it comes down and the houses get smaller and smaller, the hall would get smaller and smaller.

And now we come to acknowledge a hall as being a very small thing, but actually a hall is relative to the size of the building. So its name doesn't change based on its volume. Its name remains regardless of volume. So it's always a hall is what you're saying? Yeah. So a room is what it is as long as it can fit the thing it's named in after it, inside it.

But if it's got an above average number of doors, it's a hall. Yeah. If it has other rooms coming off it, not above average number of doors because then that could be, you know, like you could count a like an actual cupboard, which isn't a room. OK, I keep thinking I want I want something like it's the volume of the room in cubic meters divided by the square of the number of doors. I know that's what you want. That's not what it is. It's much simpler than that.

Okay, fine. And that's why I think this person on Patreon, I think they're too smart for their own good. And their friends are too smart for their own good. They're overthinking this. It's very, very simple. The name of a room is based on what you can fit in it. A hall is based on the fact that it's a space with loads of other rooms attached to it. Hall slash hallway, interchangeable words.

Got it. And to answer the final question, when does a room become a great room? Another very simple answer. It's when Bear Kill's in there. Oh, yeah, baby. That's what makes a room a great room. Put me in there. Oh, yeah.

Party time. Excellent. So, yeah. Problem solved. Ding. Bye. I have no additional concerns or query. That is a problem solved right there. Simon, let us know if you're as convinced as Beck is by her answer.

Finally, we have time for any other AOB business. And Beck, we need to know, how is the 5K t-shirt doing? It's finished. It's done? It's finished. We've filled up the 500 squares. Oh my goodness. Yeah. So we've got 5,000 pounds.

We'll be getting that across. By the time this comes out, there should be some info on my socials about the money going to WaterAid. Amazing. Yeah. So also, this is a fun thing i wore the t-shirt on the jonathan ross comedy club no way that's amazing so anyone who's listened to that episode where you and my brother helped me divide the shirt up you can now see the finished product on the jonathan ross comedy club uh where i'll be wearing it. So your t-shirt's going to be on Prime

UK television. It should be. It's £5,000. You've delivered everything that you promised on that t-shirt. Yeah. That's amazing. There will be some more news in the future. It'll, it's still, I'm still planning to put it into an art exhibition and go further, but we can

talk about that further down the road. Excellent. and we will put a screen grab of you wearing it on uk primetime television on jonathan ross's new show we'll put that on all our social medias which are almost without exception our problem squared yeah our problem squared instagram twitter i think that's it final update is thank you so much our new patreon supporters this is episode number 11 of 12. We've been going for, I would say, approximately 11 and a half months officially. And that brings us up to 97 Patreon supporters at the time of recording.

So it feels overwhelmingly likely, regardless of where we decide to draw the line on when the first 12 months is up, that we will hit 100 people and we will be obliged, according to our own rules, to do another year of a problem squared. Imagine if, after listening to this episode, loads of people stopped supporting us so that we don't do another year. They're like, whoa, whoa, whoa. I don't think I can commit to this. We can't have that on our conscious.

We're all at back. So obviously a massive thank you to all those new Patreons as well as the ones that have been with us right from the start. But most of all, just thanks to all of our listeners. I mean, this is the reason that we do it. It's mainly so that we can have fun and, you know, share it with you. So thank you. Tell your friends.

That's just as important to us as any type of financial support. Bye.