A Problem Squared - 005 = Airplane Stacks and Backpack Hacks

Episode Date: April 1, 2020

- What went wrong with the audio of episode 003? - The best place to put a backpack on a crowded train. - How many Boeing 737s will fit? - Making a perfect guest bedroom. - Bonus: Bec has feedback on Matt's rice calculation Support us on Patreon! https://www.patreon.com/aproblemsquared Review us on apple podcasts: https://podcasts.apple.com/gb/podcast/a-problem-squared/id1490290676 Twiiter: https://twitter.com/aproblemsquared Instagram: https://www.instagram.com/aproblemsquared/ Listen to the BROKEN version of episode 003 and see how you hear Bec! https://www.dropbox.com/s/kvdbytyu1jazr15/A%20Problem%20Squared%20Episode%20003%20BROKEN.mp3?dl=0 Wikipedia page on surround sound Matrix Decoding. https://en.wikipedia.org/wiki/Matrix_decoder Watch Bec's flip-chart of "Non Je Ne Regrette Rien" by Edith Piaf. https://www.youtube.com/watch?v=RTH9MKiYvM0 This is the audio file of Non Je Ne Regrette Rien that Bec sometimes has problems with. https://www.dropbox.com/s/zfh910uve85vdvk/Edith%20Piaf%20-%20Non%2C%20Je%20ne%20regrette%20rien.mp3?dl=0 There are only 10,575 Boeing 737s which have been made and delivered. http://active.boeing.com/commercial/orders/displaystandardreport.cfm?cboCurrentModel=737&optReportType=AllModels&cboAllModel=737&ViewReportF=View+Report Check out our instagram for photos of the 'Futuristic Garden' Bec gave Matt for their spare room. https://www.instagram.com/aproblemsquared/

Hello and welcome to A Problem Squared. This is episode 005, following very hot on the heels of 004, which in fact we just recorded this morning and released mere days previously. And that is our all viral episode and this one will be 100% virus free. As always, I am Matt Parker and we also have Beck Hill. Correct. Now, we're going to try and catch up on all the things that we wanted to do last time before Beck got quarantined. Yes. And to bring everyone back up to date, previously on A Problem Squared You've wanted to do that for so long. I've wanted to do that so bad, yeah. That's where voiceover

Beck comes in. Do you want to hear an ad for tea? Yeah, go for it. I'll take out the brand because I don't want to work for free. Iced tea for some burst flavour that really lasts. Anyway, previously on A Problem Squ squared we were talking about the optimal way to brush your teeth yes and uh we answered that in episode 003 and we've now got a response from the person who

asked us about their problem uh someone goes by a manic and they replied to say, I quote, I'm amazed at how thoroughly you answered my problem, especially with Beck going above and beyond in roping in a dentist friend. Yay! There you go.

Officially, someone sent in a problem. We solved it. I'm going to take partial credit. And they've now confirmed they were happy with the solution. And that's the podcast in a nutshell. That's the service we provide. One fewer problem in the world now. And that's why we're here. So this episode, we have a collection of outstanding problems that we've been putting off because we had to deal with

you being quarantined in a hospital. Starting with solving the problem of what went wrong with some of our audio encoding from episode 003. We'll also be looking at the right way to take a backpack onto the tube. We've had a problem sent in from someone in air traffic control asking how many Boeing 737s can fit. Fit in what? Stay tuned to find out where they want to fit Boeing 737s. And finally, I'm going to be helping you solve the problem, Matt, of what you should be doing with your spare room. All right, let's do it.

Our first problem is one of our own making. So when we put out episode 003, a lot of people replied to say they couldn't hear Beck or she was very quiet or she felt very far away. Yeah. And it wasn't to do with the fact that I had a husky voice. No. Because I did. I was sick and we recorded remotely that time too, but I didn't have the setup that we have for this episode. And something went wrong along the way. So what we're going to do, actually, we're going to play in a bit of the unfixed audio from that episode.

Whatever device you're listening on, you might hear it a bit different, but see what you make of this. Oh, wait, wait, wait. Before you play into it, Matt, I want to point out that some people won't notice a difference because I didn't notice a difference on mine. So some of you are going to hear this and it's going to sound fine. I'll sound a bit sick, but the sound will be fine. It'll sound normal.

Okay. For others, I'm going to sound really quiet and far away. Do you want to lead us in with a previously on? Previously on A Problem Squared. I'm like a novelty nerd comedian and I'm okay with that. You do maths and then comedy is sometimes a byproduct. Whereas I do comedy despite the fact that maths exists.

With no additional byproducts. Okay, so for some of you that sounded perfectly normal. Are they lucky winners? Are they? Of a type. It sounded to me like you were distant. Like you were in a different audio space. That's because i don't like

you that well i wasn't trying to take it personally it sounded like you you you'd separated yourself from where i was in the recording and not like in a slightly panned left or right job just in a it's out some people said you sound like you were phoning in from the international space station oh yeah yeah and we don't have enough patreon supporters yet for that kind of extravagance but but it did it did it sounded like you were somehow removed yeah but it sounded fine for you back didn't it yeah yeah what we did when we realized people were having issues we got the episode fixed well our fantastic producer mr john harvey um fixed the problem. We've actually, for one special time only, we've issued a microphone to John, who's also dialing in from home. So John, what happened? We recorded, apart from you guys being

remote, we recorded the episodes, you know, kind of normally and I edited it as normal and it all sounded fine when we put the edit out and we listened to it all and we thought everything was fine. So when listeners started hearing the problem, we were a bit confused and not sure what the problem was. And so I analysed the waveform of Beck's recording with a colleague of mine, Eloise, and we noticed then, which is something you wouldn't normally notice on an edit program that Beck's waveform was out of phase and that is a problem because it means that the as I think Matt's going to explain there's a maths and physics reason why that affects the final sound that comes out of some people's listening device when they download the podcast so although it sounded absolutely fine to us some listeners

experienced Beck on the space station so you phased me up to the space station is what you're saying accidentally so what we've done is the entire broken version of the episode we'll link to it in the show notes for this episode so if you want to download it you can get it and try it on different devices see what it sounds like and then the fixed version i believe john all you did was just flip the phase for one of beck's channels right and then it all worked yeah that's right so all we had to do was isolate beck's edited waveform yeah flipped that and then re-exported the edited program and it worked fine okay i need to interrupt here because you're talking about flipping me and i do not appreciate being spoken to about that also normally i'm the

one doing the flipping you are the flipper not the flippy i am the flipper so what what what's this what's this dealio why why are you saying these things okay so i have two theories for what i think went wrong and first of all when john saying your audio was flipped if you imagine a sound wave yeah the kind of classic stereotypical sound wave is like you know the wave goes up and down and up and down and up and down like like a wave yeah flipping just means you turn that upside down whenever it goes up it goes down instead okay whenever it goes down it goes up instead so you're literally either like a mirror image or you're just flipping it around the middle and the reason that's important is sound waves indeed any waves can add and cancel out each other because if you have a wave that's going up and it hits a different wave, which at the same place is going down, when they line up, they will cancel out.

Oh, because isn't that how noise cancelling headphones work? Exactly how noise cancelling headphones work. So a noise cancelling headphone effectively has a microphone to hear the sound before it gets to your ear. Yeah. Because they're quite big. It then plays it back, but flipped. And that exactly lines up with the sound coming in or cancels out and doesn't get to your ear. So you're absolutely correct. It's exactly like noise cancelling headphones. The other place it's used is if you want to remove vocals from a song. Oh, like how

you create a karaoke track. Yeah, exactly. Like if you listen to a song with headphones or in stereo speakers, you can hear different instruments in different places. The vocals tend to be bang in the middle, which means that there's an equal amount in both channels. The left signal and the right signal have the same amount of vocals, exactly the same. So when you listen to it, it sounds centered. And all the other instruments are different in the right and left, which makes it sound like it's coming from different places. Actually, there's a friend of mine, mathematician Ben Sparks, who pointed this out to me. He said, well, that's what this software does. When you click remove vocals, what it's doing is flipping one of the channels,

but not the other one. And then it's putting them together. And because the vocals originally were identical, if you flip one and then add them, they perfectly cancel out. Whereas the instruments, which are different on each side, don't cancel out. Wow. And so the vocals disappear. And there's other things you can do where you don't flip certain frequencies because they're outside the vocal range.

So you don't lose your bass and a bunch of other stuff. But there's more audio engineering things we have to worry about. But just by flipping one channel but not the other. And then when you recombine them, it'll cancel out that sound. So I think some people were listening to it like in mono or in a way it's been mixed down and one of your channels was flipped compared to the other one and so your audio was cancelling out but mine because they were the same in both channels weren't cancelling out weird to fix it we just had to flip one of them the other way around to stop you from cancelling out and then that solves the problem let's hope

that's the only time i get cancelled that That's the, yes, flipped off and cancelled. My other theory, and actually I would really appreciate any contribution people can make to this because it's slightly outside my field of knowledge. I think we might have accidentally tapped into the way that surround sound is encoded in a stereo signal. So surround sound, you know surround sound, you've got like a center speaker and left and a right and a rear left, rear right, all that. You get four or five, depending on the system, channels of sound. And normally if you listen to a music or you watch a film, they just encode all five or whatever channels. They're all there. Sometimes, however, it's encoded down to two channels because then you can

broadcast it over the radio you can put it on cds only have two channels you can have a stereo signal that some systems can decode back into four or five different channels and the way they do that is by messing around with the phase or how things are flipped. Oh, is that what the phase is, the flipping? Phase is flipping, yeah. Oh, okay. So, well, okay, because out of phase means it's like completely off, whereas phase can be slightly off, but not totally off. Phase is like an offset.

Gotcha. Sort of. Yeah, I need to be careful because I tend to talk about things in terms of pure sine waves mathematically, but once you're doing it with audio, it's a lot messier. It's not quite as clear cut. So I need to be a little bit careful, but I know some of these old stereo systems, some of the matrix decoding it was called, would do things like to get the rear channel, you would invert some of one of the front channels and add it in a certain ratio to the other one and so by having weird combinations of the two stereo channels you could pretty much not perfectly but you could largely reconstruct the surround channels the center

channel that kind of stuff so i have a sneaking suspicion we also may have on some players accidentally put you into a weird place in the surround sound space i was in the matrix you were literally lost in the matrix that's great that's my theory so anyway we'll make the file available could people play it on different systems people have old matrix decoding surround sound systems or anything or people are audio engineers who know more about this. I've kind of exhausted my research. I would love to hear from other people what they think happened. So I think in terms of fixing the problem of the audio, that was solved. That's solved.

And that was you, John. Well done, John. Ding. Yay! Look at him, he's getting involved, right. But while we're on this subject, as Vat said, if anyone has any stuff to add to it, please do get in touch with us on social media. We're at a Problem Squared or via our Patreon page,

which is a Problem Squared. Basically everything is a Problem Squared. We've got a website, everything. I'm going to add in an extra problem for the listeners, if anyone's able to answer this for me as some of you might know I do stuff with these flip charts and one of them is a song by Edith Piaf called Non Je Ne Regrette Rien and sometimes when I'm at certain venues usually ones with a smaller desk sound. When I plug that in from whether it's a phone or an iPod or laptop or whatever, sometimes the instruments come out fine, but her voice is really warbled.

It sounds like she's singing from underwater. That's interesting. So she's not been removed, but it sounds like like that. Can we provide a link to that file? Yeah, yeah, we can. So I'm sure it's probably something to do with this phasing slash flipping stuff and to do with mono and stereo. But I'd really like to know what is causing the problem because there's been a few times where whoever's teching has been able to fix it and I don't know what they do. And a lot of the times in the places where that happens, there isn't

an actual technician. So what would I need to do in order to fix that? That's my problem for the listeners. Love it. Okay. So we've solved one problem and we've got another one for our listeners. Yeah. Get onto it. We have a problem sent in on Twitter from Bridget B, who is, by their own words, a three-time listener, first-time questioner, I guess, problemer. And they say, if you're on a crowded tube train, so that's like the subway in London, with a backpack, where is the best place to put it? On the floor, people assume it's a space to stand in. That's true.

That's happened to me. In my hand it lurches into people and that i guess depends how tall you are how can i get in people's way the least problem from bridget b and so beck you've looked into this yeah so i had a few theories about uh ways we could deal with this because i am a big backpack person both in terms of wearing big backpacks but also being a big fan of backpacks. Would you say you like big backpacks and you cannot lie them on the ground in the tube because that is a recipe for disaster? So I've also wondered about this problem quite a lot and I think there's two different ways that we can

solve this problem. So the first one is I think they need to have dedicated backpack carriages where 50% of people are really tall and the other 50% are really short. Wow and you've got to buddy up. Yes you sort of like tessellate so so that the head is just under the bag for the short people. And for the tall people, it doesn't, you know, like the bag's not really in the way if they just bend their knees a little bit. Wouldn't you rather have everyone standing back to back? So one person's standing back and their backpack's high. Oh, yeah, yeah. And the other person's standing back and their backpack's low.

Oh, yeah, yeah. And the other person standing back in their backpacks low. Well, I was thinking that, but then I was like, the other thing you could do with that carriage is, instead of worrying about people's sizes, if you treated it like Tetris so that you put some people in upside down. Now you're talking. That would work.

And then they would slot in together. And then, I mean, I think if you can manage to make a line of people that way, then they should just instantly appear at their station. I mean, that think if you can manage to make a line of people that way, then they should just instantly appear at their station. I mean, that would be fair. The tube struggles to get you to eventually appear at your station. I don't know if instantly is on the cards. No, no, it'd be like that line disappears from the carriage. Oh, no, I get it. No, I'm just saying.

I'm just saying. I'm happy with just, you know, within the hour I appear at my station having had to get off the tube I like how your issue with that isn't the fact that it is physically impossible but just like maybe we should just be a bit more realistic about the logistics of how the tube works it's not so much impossible as currently physically implausible with our current scientific knowledge oh yeah no that's fair do Do you know what? I knew you were going to say that. Oh, okay. So I've scratched the carriage idea. That was one solution I had, but I don't think it's the one. I think the other solution I have is the way to go.

So I think the best option at risk of maybe offending some people is to wear your backpack on your front yep and then if you put your top or jumper or whatever over it and wear one of those baby on board badges oh my goodness then not only will people stay clear of your bag but also you'll probably get a seat i can't fault you from a sheer practical point of view like i'm literally view. Like I'm literally solving the problem. You are literally solving the problem. I didn't say it was morally correct. No, I've got some ethical qualms, but I can't argue with your practical solution. So your solution is to feign pregnancy by putting the backpack up your jumper and then get a priority seat.

Yeah. Okay. Well, I reckon we throw this back into Bridget B's court. No, I think that's it. Problem solved. Ding. No, I think Bridget gets to decide if that solves her problem. Well, hang on. To be honest, their last sentence is, how can I get in people's way the least? And your solution involves kicking them out of their seats. Yeah. And then you're not in their way. They've moved.

Okay, Bridget, you get to adjudicate. Yep. If you like it, don't say anything. Just reply to us and say ding. Deal. If we get a ding from Bridget, then that counts as solved. Well done. This next problem comes from Rob via email, who says, as an air traffic controller, I am bound by certain restrictions for safety, five nautical miles laterally and a thousand feet, which let's be honest, is a lot of room. Go out and run five miles. That's how close I'm allowed to have two aircraft at the same altitude. That's a ton of space, right? I could easily fit more in there. But then I wondered, how much more? So my question is,

in a three-dimensional space with a radius of five nautical miles and 1,000 feet high, just how many airplanes could I cram in there and have none of them touching? Not traveling per se, Thanks. I love that question, by the way, because I like the restrictions they've placed on it. So Rob's sort of said, here's the problem. And just so no one's complaining about the size of plane or whatever this is what we're working with yeah it's great rob's done like half the work because at the beginning of a problem you've got to make a bunch of assumptions to decide what you're going to solve and they're like no here's the aircraft here's the situation here's the spacing it's just it's great there's the level of precision and attention to detail we want from our air traffic controllers.

All I have to do is the maths. So here's the deal. First of all, I did not go out and run five miles. I've decided that wasn't part of the problem. I have, however, crunched the numbers. So the area of three-dimensional space that Rob is describing is a cylinder because for planes at any given altitude, there can't be any other planes within five nautical miles. I also looked up five nautical miles. It's 9,260 meters. So 9.26 kilometers. There can't be any planes closer than that at the same altitude. So that's like your circle around the aircraft.

Yeah. But then you've got the height. So you've then got a thousand feet, which is 304.8 meters. And you can't have any aircraft above. I've not done a sphere because I think it's that shaped disc at each altitude. So I've done it as a cylinder. shaped disc at each altitude. So I've done it as a cylinder. I've also just done the cylinder 1,000 feet high, because that's what Rob put in the question. A radius of five nautical miles, 1,000 foot high. Because I was wondering, is it 1,000 foot above and below? But they phrased the

question very clearly, it's just 1,000 foot high. So I've just done a 1,000 foot high cylinder, which is made up of circles that are 9.26 kilometers across. Which makes more sense of the way than that I took it, which was that they have to fly at a thousand feet, which I thought was very low. That is very low. You were right to think that. But then dismiss your concerns.

Thankfully as well, Rob has specified it's a 737 aircraft. Now, the Boeing 737 has been flying since the 60s. I hope it stopped to refuel at some point. Yes, it stopped to refuel at some point and get bigger. So I've picked the biggest version, the 737-900. So the 737-900 is 42.1 meters long. It's 35.8 meters wide and it's 12 and a half meters tall. So that's the size of the aircraft. So now you've got to work out how many of those you can fit in the cylinder. At this point, I got a little lazy and I just thought, well, how many can I fit

per layer? And then how many layers are there? So if you divide the height by the height of the aircraft, you can fit in 24 layers of aircraft with just enough room for gaps between them all. Oh, like a cake. Exactly like a cake. I've left room for icing between each layer. Yeah, with the jam and the cream. Yeah, yeah. I've actually left. So this is me doing a live calculation in my spreadsheet.

They've got just over 20 centimeters between each layer. That's loads of space. Yeah, that's loads of cream. Yeah, please. In the next episode, I want you to work out how much cream you could put into those layers. How much cream that would be. Different problem. Not doing that.

Okay, so I've now got 24 layers with room for cream between. We're at a giant cake. And I now need to work out how many there are per layer. So the long bit in the middle of each circle, because if you just had a big long row of planes, like across the diagonal of the circle, you could work out how many you can get by just spacing them out. And you actually get 438 along that line from beginning to end. Is that all facing the same direction? All facing the same way. Although it doesn't matter if some of them were facing directly backwards, as long as they're like the longest way lined up down the line so

it's just plane after plane after plane all the way down but then if you do a line next to them it's going to be a shorter line yeah because the circle is a bit smaller there but actually you can still fit as many on the next line there's still loads of space in fact it takes a while you have to go a few rows out before the circle starts to get too small after about the 25th row. Is that because of their noses? Because for me, their noses are really long and pointy out and their tails point out. So there would be more space on either side, left or right, before it got to the point where the wing is. Well, actually, that's a good point.

So my first round of calculations, I just did them nose to tail all the way down and then i had the next row far enough away that the wings wouldn't touch at all like they're a totally separate queue yeah where they could be forwards or backwards they wouldn't hit the ones next to them which is the least efficient way to do this yeah and if you finish doing all the numbers on that all the layers i got just over 4 million planes. Wow. That's a lot of planes. That's a lot of planes.

What? On all the levels and in all the layers? On all the levels. Yep. So each layer has 517 rows. They start very big. They get smaller and smaller as they go out in the circle. That ends up with 177,987 planes per layer and then you multiply that by

the 24 and you get just over 4.2 million planes whoa but then you made a good point though that what if you tucked the wings in like what if you interwove the rows so the wings of one row went behind the wings of the one next to it like a a zip. Like a zip. Yeah, perfect. Yeah, what if you interlace and zip together or... Yeah, yeah. So I did a rough calculation on that. It's not perfect, but I kind of assumed you could fit all the wings in and the number goes up to 6.3 million planes. Wow. So you could fit, by my rough calculation, 6,334,728 Boeing 737s in the same amount of space where you're only allowed one, which now feels very inefficient. But that's assuming they're all going the same direction in this snapshot. Yes, you're absolutely right.

So could you potentially fit more in if you tessellated them? Oh, definitely. Or if you had some of them going vertically, like what if you shuffled them around a bit? Oh, yeah. And got another plane coming in this way. And actually, these are called packing problems in maths, and they're notoriously difficult. There's loads of open, unsolved problems in maths

about arranging things in the most efficient way to fill a space. And so you could then do some simulations. You could get a whole bunch of aircraft 3D models and try to simulate different random ways of jumbling them up in the cylinder to see how they all fit. But then I was like, wait a minute, Rob at no point specified that these are functioning aircraft. So my next thought was I should look up the total mass of a 737, what kind of density materials it's made from. What if you got one and crushed it down into the smallest possible shape and make a shape which fits really well inside a cylinder?

I could calculate the actual maximum number of planes you could fit in. But then I looked up on the Boeing website how many 737s they've made. And so far, across the entire lifespan of the aircraft, people have ordered 15,115 of these things, of which 10,575 have been actually delivered. So there's only just over 10,000 737s in existence. So we could put all of the planes into Rob's cylinder. Yeah, exactly.

The answer is just all of them. You could fit all 737s that have ever been made in the same space where currently you're allowed one. So I didn't need to do any of those calculations. Doesn't matter how you arrange them. They got loads of room each. All of them, Rob. There's your answer. Get them all together and they can all fly in the one safe region so there you are the the the end all

of them i hope that helps i think that's definitely a problem solved thank you ding i have a problem for you beck yes so in my house i have a spare guest bedroom. All right, show off. And I know it's pretty special. It's reasonably new. We bought a house that required a lot of work. And in the process of fixing it up, we designated one room the spare guest bedroom. However, it's still pretty blank, I guess, underdeveloped. Blank slash storage. I've stayed in that room.

Exactly. And it was. Blank slash storage. I've stayed in that room. Exactly. And it was very comfortable. Thank you. But it was also clearly a room where the things go that you don't know where else they go right now. That's also very true. Now, it's got a sofa bed in it, which is very comfortable. Very comfortable. Yep. It's also got like a temporary wardrobe for overflow clothes. It's got a pile of boxes in one corner. And then it's got a few amenities for the guest.

My problem for you is what do I need to do? What do I need to get? Add what has to happen to make that the perfect guest bedroom for people who stay over. And just to recap currently, bedside table with a lamp. And just to recap currently, bedside table with a lamp and it's got USB power outlets built into the wall socket. And then that's it. So can you help me out? And the bed.

And a bed. So, yes, I can help you out. The first thing I'm going to say, which seems like a no brainer, but if it's going to be a proper guest room get rid of them boxes okay okay yeah get rid of them boxes yeah i think if if we're talking when we say spare guest room are we talking like the quality that you would expect if you were like airbnb-ing someone or are we talking like when you go home to see your parents? I want it to feel like people are welcome. So when they get in the room, they're like, we're not imposing. Like the room is obviously here. They've not had to, you know, sort out a whole special room. The room is here and functional and we're not getting in the way. We're very welcome to stay, but not that we've gone,

you know, unnecessarily above and beyond. So you're right. There was a pile of boxes in the corner. Just for the record, one pile of boxes, which you are correct. We can move that up. What type of guests are you expecting? Close friends and family or acquaintances? It is almost overwhelmingly close friends and family. The ages range from, it's always kind of young adult through to probably people in their fifties. Not that we're ages, older people are welcome. It just hasn't occurred yet. And we've not had a family with kids yet, but we do have my study and we've got like inflatable mattresses for overflow kid storage. Okay. These are good things to know. And my final question before I go any further is how long would you say the stays are that you're expecting? Obviously, bearing in mind

occasionally there might be emergencies or whatever, but the ones you're expecting, how long on average do you think those stays will be? The vast majority are a single night. Every now and then we'll have someone for like a week, but normally it's like a working week if it's a colleague who's like over from like a Monday to Friday. All right, cool. Well, those are good things because the reason I asked that last one is because if you're expecting people to stay for a few nights or more on average, you'd probably want more space for them to hang things up or fold things up. But if they're only staying for like a night or two, most people are probably just going to live out of their suitcases. So the good news is you don't have to start investing in more cupboard or drawer space. Sounds like

what you've got is going to be fine. We could, on that note, we could clear up a bit of hanging space in the temporary wardrobe, which is largely holding coats and jackets and suits and stuff. Yeah. I think creating just a little space where someone can have it as their own is always a nice thing, regardless of where you are. And on that note, what I also did is I asked my followers what their favorite thing about their bedroom is to find out if there is a common answer of things that should be in a bedroom. Oh, that's a great idea for research. Would you like to have a guess at what the number one thing was in that list? Favourite thing in the bedroom?

A comfortable mattress. Yes. Correct. Really? I'll also expect a bed. That was by far the most answered one, which seems like the obvious one. And for that reason, I wouldn't have said bed. I would have felt like that was a given, which it already is.

You have one in the room and it is very comfortable. I will attest to that. Oh, good. So you're sorted for that. The second most popular was a toy. A toy? popular was a toy a toy huh there's a lot of people that had a cuddly toy or a figurine or something they were given but something that i would classify as a toy because it's either there for decorative or comforting purposes two of those things were for let's say other purposes but i

would still classify them as toys. Yeah, toys, technically. Well, I'm thinking, because I thought of like puzzles when you said that. I've got a few very ornamental looking puzzles that could go like on a shelf or something in there. So they make the room look more homely. And if people are bored, you can try and solve the puzzle. Well, it's interesting you say that because one of the other common ones that people said was a quilt, which I actually don't count as the bed. A lot of people said specifically it was their quilt or blanket that they liked.

So I think you could go a step further. And if you were to wrap that puzzle in a comfortable blanket or quilt, or indeed turn a quilt or a blanket into a puzzle, then you could have both something huggable and something you could play with. Yeah, because number one, people want to be warm. But you're right, that kind of coziness and some kind of feature quilt. The next most popular, and I find it quite funny that this came after bed quilt and toy, was partner.

People who said their favourite thing in their bedroom was their husband wife boyfriend girlfriend significant other so i i guess you put lucy in there i guess i is that how that works i find the opposite when you're staying somewhere else it's nice to have a bit of space that's your own like a place you can go and not have to interact with people for a little bit but they know that varies from person to person well then the other one after that was a pet oh and i won't look into the mental thing of the fact that pet and partners came quite closely in this but yeah pet well the majority of the pets were people who said cats right yep like loads of them said cats and then a couple of people said

different types of pets so i added them because i was like they're all pets i think i did also two people said they're kids and i think i added that to the pet pile as well that counts as a pet yep that's true if i'm staying at someone's house and they've got like a pet cat or something that's pretty exciting yeah we need to get a pet we haven haven't got a pet. That's the problem. What if I just befriend like a neighbor's cat? Yeah. Just like leave little treats in a line. Yeah. All the way up to your spare room.

Let me just get that down. Steel cat. Got it. All right, next. So most of the other answers I got were all quite specific and I couldn't really link them with other answers. Um, some favorite ones, someone said a spider, which they don't count as a pet because it's just the spider that lives in the

room and catches all the flies. I thought that was quite cute. Someone said their Star Wars pillowcase, which was just so specific. I didn't want to combine that with any others. That's uncategorizable. Yeah. The other one was a Picasso butt. It's a print of a picture of a butt that Picasso did. Wow. Which obviously I like. And we got two people who do not know each other answering this. One of which actually included pictures. I think the other one was saying it as a joke. Who, when I said, what's your favorite thing about your bedroom, joke who when I said what's your favorite thing about your bedroom said their Beck Shrine right and one of those people had three framed flyers of mine with a couple of other things from my previous shows that counts as a shrine in fairness I was aware of this shrine and also they do collect

things from other shows that they see as well but I've got my own corner and and yeah someone else said a Beck Shrine so I think obviously what your spare room is missing is a Beck shrine. Beck shrine. No, what I'm taking from that is whenever someone stays over, they walk into the spare room. They're initially distracted by the spider living in the corner. Everyone loves that apparently. But then I've set up a shrine for the specific guest.

Yeah. In such a way, it looks like it's always just been there. Yeah. Like, oh, oh, and of course. Oh, yeah, sorry. Yeah, that's the shrine I have for you. Oh, wow. That's awkward.

Anyway. Even better. This felt like it should be your room. It kind of is. We call it your room. So here you are. I think even better is don't reference it. Go in slightly ahead of them.

And as they follow you in, go, and then try and clear it up as quickly as possible. Frantically, like blow out all the candles and try and slide it into a drawer. Got it. Yeah. And then try and distract them with a stolen cat. Love it. It's going to be very welcoming. So I actually have something for your spare room, which I can't give to you in

person because we're both recording from home at the moment. We are. We're working from home at the moment. But if you could read out what I'm about to show you in the camera. Yeah. Oh my goodness. What's this? A futuristic garden. So I think I've covered a lot of things with this. So it's got like a gel. And I think what this does is this covers both toy, because it's from the Science Museum. It says ages eight plus. Definitely a toy. It's a toy, but it's got life.

So it's a pet. It's a pet. Oh my goodness. And it's space related. So it's related to your partner. Hey, that's everything in one. Oh my goodness, Beck. That's incredible.

As soon as we're allowed out, next time we record in person, you can pass it over and I'll install that in the spare bedroom and we're done. I mean, I'm going to have to move the Beck Shrine out of the way, but that's...

If you could Sharpie onto it on loan from the Beck collection, then I think that would be absolutely everything. Yeah, done. I won't lie. I bought this for myself ages ago and I've tried it twice and it kept growing mold instead of the plants. So I've repackaged it. Hey, even, even better. I mean, that's, it's got back written all over it soon to be literally. So thank you. I feel like that's going to make the room far more welcoming

for everyone in the future. I'll remove the boxes, steal a cat and put the moldy plant thing in the corner. That's officially a problem solved. Ding! And we're nearly at the end of this episode, but before we leave you, I had a little bone to pick because in the previous episode before this one, you made an assumption when doing your mathematics about putting rice in houses. Yes. That I live in a 10 meter cubed home. Void. Yeah. Yeah. Yeah. And I measured my flat as soon as we finished recording that episode. So I think I sent them to you, Matt, so you could double check your maths. You did.

So you claim your house is actually 8 meters by 6 meters by 2.3 meters. And we should recap. This was episode 004, which we recorded this morning. So over our lunch break, I went and put that into my calculator. First thing up, because I replied to you straight away and went, oh, I'm off by an order of magnitude. Because if you multiply those together, the total number of cubic meters volume in your house is 110. And my assumption was a thousand. So the correct answer is 10 times smaller than what I had actually put into my calculations. And you said to me that your calculations were off by an order of magnitude.

And I realized I've heard you say that a couple of times and I've just assumed it's a cute way of saying off by a lot, but I don't actually know what order of magnitude means. It sounds like a Harry Potter book. So will you explain that to me? That is a good point because I love things like this where it's a mathematical expression, but yet you can use it in normal language and people get the right idea.

So in mathematics or in science, an order of magnitude is a multiple of 10. So when I said I'm off science an order of magnitude is a multiple of 10 so when i said i'm off by an order of magnitude i was 10 times too small so if you think something is like uh oh that that looks like it's about you know that will cost you know uh that spending budget was a million pounds versus 10 million pounds that's an order of magnitude difference and you get this in in science all the time where people like oh that's like three orders of magnitude bigger or smaller than something else so does that mean like 30 times that would be a thousand times so three orders of magnitude is a thousand times difference because it's times 10

times 10 times 10 which is a thousand but yet if you say order of magnitude in normal conversation people kind of get the gist it sounds like a big amount well you say mag so i'm like hmm mag means big magnitude that's big magnify magaloof really big version of loof more to follow so um that's the difference between a billionaire and a millionaire very very different things because the difference as we've said before between a million and a billion is about a billion like it's a million is insignificant it's 0.1 of a billion right so so i was just trying to ballpark the order of magnitude of your house. And so I was like, it's obviously not a meter wide. It's not a hundred meters wide. It's about

10 meters, give or take. And because I was working out how long it would take for something to happen, I went for the worst case scenario. So I erred on it being bigger than it is rather than smaller, because if it takes that long to fill a 10 by 10 by 10 meter cube, your house would definitely have been filled by then. So I assumed it was bigger than it was to make sure I wasn't going to give you an incorrect answer. But because it was an order of magnitude off, your house would have filled with rice a lot sooner. So this will make not a lot of sense unless you go back and listen to the previous episode. But I was looking at exponential growth, comparing it to throwing rice into a room, and you will have filled your house not in 20 days, but rather in 18 days.

So there you are. Your house will have been full of rice two days sooner. Do you know what, though? That still says a lot about exponential growth because you were off by an order of magnitude as to the size of my flat. Yep. And yet it only shaved two days off. Yeah, it's great, isn't it?

And I could kind of ballpark that when you said it because that was showing if the multiple was 3.5. And I'm like, well, three squared is about 10. 3.5 squared is about, well, three threes are nine, right? So I'm like, eh, it's about 10 if you square it. So it would take two of them to make a difference of a multiple of 10. And that's why it's two days difference in the amount of time. So, yeah, I mean, it's just the power of exponentials.

Once you're raising things, it makes a big difference. Yeah, so there you go. And now after 31 days, you'd have enough to fill 18.6 million equivalent households to yours. Whoa. However, after 32 days, you could fill 65.2 million equivalent households. And there are only, I looked up the most recent stats from the government, there are roughly 27.6 million households in the UK. So you've done more than twice as many after 32 days. So I've redone my calculations and I'm pleased they're more accurate now,

but exponentials are still just as terrifying. And we're now at the end of this episode. Thank you so much for listening. This is just a little reminder that we aren't getting sponsorship or anything for this. The only money that comes in is from some of you Patreons

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It's all linked below. We would very much appreciate that yes if you tell 3.5 people about this podcast and they tell 3.5 people and so on and so on and so on that's great actually if we did that we would have the entire population of the earth listening to a problem squared in 18 days wow in fact if the transmission rate was only 1.5, put that in my spreadsheet here, then so you've only got to convince half a person to listen to this podcast.

And if everyone does that, the whole population of the earth, 54 days. There you go. Within two months. So get onto it. As always, we are looking for problems for future episodes. So if you have a problem for A Problem Squared, hit us up on social media. That's at A Problem Squared.

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