A Problem Squared - 049 = Grand Theft Auto Five and Girlfriend Digit Size

Episode Date: December 19, 2022

In THIS episode:  * How do you get a billion dollars on GTA 5 as fast as possible? * What are some sneaky but effective ways to measure a ring finger? * And some ANY OTHER BUSINESSSS! The three norths are aligned! Here's a map of the North by North North tour: https://www.ordnancesurvey.co.uk/newsroom/blog/magnetic-true-grid-north-align-over-great-britain You can find 'band merch' by Matt for that here: https://standupmaths.teemill.com/collection/north-north-north/ If you want to see more from DarkViperAU you can do that here: https://www.youtube.com/channel/UCV6mNrW8CrmWtcxWfQXy11g And the actual live-stream can be found here here: https://www.youtube.com/watch?v=SIvCHyy62ro&ab_channel=DarkViperAU As always, if you've got a problem or a solution, hit us up on our website aproblemsquared.com.  You can buy A Problem Squared 'DING' t-shirts here https://a-problem-squared.teemill.com.  And if you want want even more from A Problem Squared, find us on Twitter and Instagram.  

Ladies and gentlemen, today we are going to hear some of the most anticipated problems and solutions in the history of professional podcasting. Are you ready? Podcasting, are you ready? Podcast fans, are you ready? For the thousands listening right now, for the millions listening at different points in time in the future because you've just discovered us and you're going through our back catalogue, from the comfort of our individual homes because we're recording this remotely,

let's get ready to grumble did you say crumble rum grumble grumble yeah because we solve problems problems like grumbling like grumbling yeah good work i'd like to acknowledge that's very funny with rumble yep no it's great thank you if you're wondering who's these voices, who's these voices you are listening to? And where'd that announcing person go? In a cupboard in London, standing at five foot five and weighing 571 hodung beetle's strength worth. That's not a unit. It's the art assassin, the toilet tormentor.

It's the big heel, Berk Hill. Oh, we love you, Berk. And in an office in Surrey, standing at six foot something and weighing just over 850 horned dung beetles. That's true. Strength, not mass. It's the coffee killer, the mathematical murderer. It's the pie, Romaniac, Matt Parker. Ah, boo, we love Beckmore.

This crowd is weirdly biased. Yeah, well, I invited them. You didn't invite me. I did not. It's very true. That explains why I got a text message from you this morning asking me what my height is. Oh, that was unrelated. Oh, okay then.

That's just because I'm keeping an eye on your height on a weekly basis that's good it's a very flat plot i imagine um you know i didn't even question it i get so many context free messages from you i just think well i mean beck's either working on something or i'll find out in the podcast if anyone ever wants to know something random about matt ask me to to ask him and then he'll never ask any questions. I will respond immediately and truthfully with no further questions. I'm trying to get you to a point where you stop even thinking about it so I can just be like, what's your pin number again? What was your mother's maiden name?

Speaking of my mother's maiden name, on this episode... I've calculated the fastest way to get $1 billion in Grand Theft Auto V. I will be working out the best way to work out someone's ring size of their finger. And also their wrestling. Wrestling. Yeah. Maybe their wrestling. And in any other business, I have an explanation about the relative train speeds in new york that i was

too jet-lagged to do last time it's a knockout is that they say that wrestling i don't think so it's wrestling wrestling words so matt how have you been i've been I got very, very rained on the other day because we live in England. Okay. No, there's more. There's more. Okay. I had a time critical journey that I had to do to travel to the south coast of the UK.

Near, closest town is Langton, Metravers. I don't know if you've ever heard of Langton, Metravers? No, but it sounds like a great name for a character. Matravers. It's near Worth-Matravers. There's a whole family of them down there. Their names are Matravers. Matravers.

Langton-Matravers. So I was actually, I was right near, for anyone who knows the Matravers district, and for everyone who doesn't, if you picture the UK, at the bottom of the UK there's the Isle of Wight, which is like roughly in the middle. It's a bit of an island.

It's an island in so much as a very chunky river has basically become part of the ocean. And so it's an island. There's a bit to the west of it, which is effectively another Isle of Wight. It's just still attached to the mainland. It's like the next bit. Okay. So I popped down there and it was time critical because at the beginning of November, you know, a couple of weeks ago, for the first time ever, all three Norths lined up in the UK. And so I went.

What? All three of the Norths. You know the three Norths. What are you talking? The three Norths. North by North North. That's what it's called. It's not.

It's not It's not So There are three Norths There's Actual true North Which is The top of the planet Where it spins

There's Magnetic North Which is where the North magnetic pole Happens to be Where that moves around That's the love of the place Oh

What? Yeah so If you get a compass And it points At the North Pole, it's pointing at the magnetic pole, and that could be somewhere else. Wait. Wait.

What? Huh? Yeah. Are you ready for this? What? The South Pole. The actual South Pole is in Antarctica, in the Antarctic Circle. The South Magnetic Pole isn't even in Antarctica.

What? It's halfway between Antarctica and Australia. And it's moving towards Australia. Yeah. Oh my gosh. Wait, is this what people talk about when they talk about the poles like reversing and then everything like...

Yes. You know how doomsday preppers, they're like, oh, one day the poles will flip. And I'm always like, what are you talking about? That's stupid. But, oh no. The magnetic poles.

They move all over the shop. It's a mess. They're here. they're there. They're shifting around. Why? Because, so the true poles, that's just the axis of rotation because the Earth's spinning. Yeah. And that kind of defines the equator and everything because it's spinning around.

And then you've got the top and the bottom is the bits where it's spinning about kind of, right? Yeah, yeah, yeah. As far as we're concerned, don't go anywhere. They're pretty stationary because the Earth is just spinning on its axis. Now, inside the Earth, all sorts of gooey metal things that produce a magnetic field. And it's vaguely got a North Pole at the top and a South Pole at the bottom, magnetically speaking.

I'm just saying there's a North Magnetic Pole and there's a South Magnetic Pole and compasses point at the bottom, magnetically speaking. I'm just saying there's a north magnetic pole and there's a south magnetic pole and compasses point at them. End of story. And because the Earth and everything in the solar system is a big old slushy mess, the magnetic field is moving all over the place. And so the point... But why?

Because it's coming out of a fluid. It's the molten, not molten, it's the liquidy metal, whatever it is, in the center of the Earth that's producing a magnetic field. But why isn't it coming out at the spinny bits? Why would it? I guess, actually, why isn't it coming out at the non-spinny bits? Yeah, great question.

Like, why isn't it? It does come out near the spinny bits because the way it's spinning kind of lines up the field that way. But you're right, it will flip occasionally. They'll'll drift we don't even know what's going to happen i guess they drift around then they flip or they split up and they flip it's a mess wait so what does it look like is it just a big lot of metal that's moving around sort of yeah but it's under a ridiculous pressures so it's not like a liquid as much as we would imagine it because it's super high pressure. Fluid iron that produces the magnet. It's not fully understood as best I'm aware.

Is it like how if I drink water and then do a handstand, it won't just come out of my mouth? You can wrap that analogy up right there. Yes, exactly like that. It's precisely like that. But the water still moves around. It's not always going to be in my stomach. Yeah, yeah. And they're not even poles.

Not even poles. Not even that. Do you want to get... It gets worse. If you think about a normal magnet, you've got the field lines that go from one pole to the other, let's say, as a way of thinking of the magnetic field. The Earth's field lines don't go go from one pole to the other, let's say, as a way of thinking of the magnetic field. Yes. The Earth's field lines don't go straight from one pole to the other.

They wobble all over the shop. They are a mess. There they go this way, there they go that way. It's not even just that it's moving. It's just that your compass doesn't even point at the North Magnetic Pole. It just lines up with the local field, which could be pointing in a whole other direction. Oh my goodness. Magnetic fields are a mess.

The only reason we use them is they're easy to measure. You get a shiny magnetic rock and you hang it or you float it or something and it will line up with the Earth's magnetic field. But all it's telling you is which direction the Earth's field lines happen to be pointing at that one local location. Right. This is a conspiracy by the map industry.

Yeah, to sell more maps. To make sure that they, you have to keep updating your maps. Big cartography. Because the Earth's magnetic field is wobbling all over the place and is an absolute nightmare, every so often, often just by accident it will line up with the true north so it's not even pointing a magnetic north but it will accidentally point in exactly the right direction so the maps tell you if you're here your compass is off by three degrees too far to the west if you're here it's off by five degrees too far to the east or whatever and every so often there's a perfect spot where if you stand there, the field accidentally lines up perfectly.

And you can just look at your compass and it's true. And one of those... But you mentioned a third north. There was a third north. Third north is grid north. So if you look at the lines on a map, they don't point north because a map is a 2D approximation of the surface of our 3D spherical.

And north lines, the lines of longitude, all curve in towards the north pole, the true north. Whereas a map, you don't want the grid lines getting closer together as you go up the map. And so OS maps, who make the maps for the uk they want their lines to stay parallel so they ignore true north and they have invented a third north which is grid north and grid north changes depending on where you are in the uk because it depends at different points grid north is a different amount different to true north the only place that grid north matches true north is at two degrees longitude to the west the west of greenwich they picked the two degree longitude line to base grid north on and then all the other ones are slightly off and they pick two

degrees longitude because that line goes pretty much through the center of the uk so it's the only place where a maps north lines up with true north is if you're on that line and then the third north the magnetic one those places where it happens to line up by accident they move around and one of them is moving across the uk as we speak, and it just collided with two degrees longitude on land. So I went to the coast down near Langton-Matravers because for the first time in history, the Earth's magnetic field accidentally lines with true north at a location on the two degree longitude line, which is both true north and grid north. So it's the only place and the only time ever all three norths in the UK are all exactly in the same direction.

How often does that happen? Never. It'll be centuries at the soonest. Well, actually, so the point where they line up, it's going to move its way up the UK. And so it's going to take a couple of years before it leaves the top of Scotland because of the way the Earth's magnetic field is wobbling around.

The point where it happens to line up is moving up the UK. So triple north is on a tour. Yeah. North by north north is on tour. I should do it. I'm tempted. You should do t-shirts.

And then you have all the dates and places that they're going to be appearing at. You're a genius, Bec. Yeah. So it's going to work its way up the country. It's going to go through pretty much through Birmingham and then carry on up all the highlights of the UK. And then it goes out the top north of Aberdeen. Place called Fraserborough.

Fraserborough. That is the most it sounds like a made up Scottish thing. You know that place in Scotland? Fraser Bra. Yeah. So it's going to, a couple years from now it's going to pop out at the top of Fraser Bra.

So that's a very long time before it comes back. Hundreds of years. And we may have changed our grid north by then. And that's why you were at Langton. Yeah yeah so i went to where it was making landfall in langton matravers how about you beck uh i mean well an interesting week last week i went to the itv palooza itv palooza party right um is that what is it actually called that or have you just named it the itv no no it's called itv palooza that's the one way remember last year i made my own dress for it yes uh and so this year

i wore the eight pound charity shop dress that i bought while i was over at your place so i saw the dress at the window of the charity shop the night before when i went for a walk yes you did and it was so pretty that i got up early to go and buy it as soon as the shop opened. And that's when I saw it was eight pounds as well. And it was so nice. And so then I wore that to the gala. It did look like it was made for you. Like it fit alarmingly well.

It's the perfect fit. Thank you. And so I made a handbag to go with it that looked like a giant price tag that said charity shop dress, eight pounds. So everyone knew that it was a charity shop dress. That cost eight pounds. I'm against the fast fashion. So that was my Tuesday. And then the Friday, I had my third wrestling lesson because I'm doing wrestling.

That's why the commentator's here. That's why you've suspended your microphone from the ceiling. That's right. Exactly. Yeah. And that's why you've suspended your microphone from the ceiling. That's right. Exactly. Yeah. And that's why I'm wearing this Lycra onesie. I mean, that came first. You've just been looking for an excuse.

And I got to do my first flip bumps. I now know how to do a flip in the air and then land on my back without hurting myself. Wow. But I am covered in bruises. You should see the other flip bumper. You should see the mat. As. You should see the Matt. As in the crash Matt. Not you.

That's what they called me in high school. You know what the saddest thing is? No one called Matt in high school. That's not true. They ended up with their homework. This first problem comes comes from jason franklin by email announcer person's got a head cold now yeah it's just becoming more and more nasal i recently saw a live stream by another matt better known as the speed runner dark viper au in a quest to achieve $1 billion in GTA V, or GTA V,

Gatav, as fast as possible. Yeah. As fast as possible. He showed three ways to reach that goal, A, B, and C. So the question is, what's the best combination to get a billion

as fast as possible? Maybe this thought experiment interests you. I understand, though, if the topic isn't family-friendly enough because it's Gatav. Gatav which gta i should say it's a video game it stands for grand theft auto number five number five so jason watched dark viper au is an aussie streamer slash youtuber who does speed runs often in grand theft auto jason was right that i was interested by their thought experiment i saw their email i saw the email in the morning right when i

was about to get some breakfast before i took the dog for a walk and i thought that looks interesting i reckon i could solve that over breakfast so i sit down with a bowl of cereal and i open my laptop up and i start trying to write some code to solve the problem and by the time lucy's like we've got to take the dog for a walk i i was like i'm almost there and then i and it honestly took me so long but i finally cracked it now jason very interestingly translated the problem into maths now i don't play grand theft auto i'm unfamiliar with the game i'm aware of the concept i don't play it and so they didn't give me the Grand Theft Auto version. They just gave me the mass version where they're like, there's method A. Method A takes 52 seconds and gets you $25,000.

Method A. No additional details. Method C, and I have skip B, don't panic. Method C saves your current amount of money. So whatever you're up to, C kind of locks that value in. And then method B gives you that locked in amount again every time you do method B. Okay.

So at any point you can do C. Now C takes 10 minutes. That's like 600 seconds, method C. But it's like saving it's like a save point i've got this much money and then b takes 18 seconds and gives you that money again every single time you do it right so i'm going to try and put this back into video game language perfect because math language i'm finding it hard to hold on to all of that so and i love love, it's like when you translate something into a foreign language and then translate it back. I want to hear this as someone else.

Right, because I don't play Grand Theft Auto. Yeah, someone else put it into maths language and you're going to back translate. Off you go. So the first one, what was that first? It takes 52 seconds, but you get $25,000. Right. but you get $25,000. Right. So if you're using method A, you're doing a talent show to raise money to stop the local community hall from being closed down. That's exactly how Grand Theft Auto works. Yeah. C locks in the current dollar value of all the money you've got. Method A, you're

starting from nothing and C, you've got a place you can start from? Yeah, C, you don't gain anything, but it's like a save point, I guess. Okay. And then B- I don't see how that helps. Well, all that happens is once you do a C and you've locked in an amount, you can then do B, which gives you that amount again each time. Okay, I see what you're saying.

Yep, yep, yep. So imagine you start the game, you do A three times. So you do $25,000, $25,,000, 25,000, 25,000. Yeah, we've saved three community centers. So you've got three community centers, you've raised 75,000. You then do C to lock that in. It takes 10 minutes, but once you've locked it in, every time you do B, which is 18 seconds, you get 75,000 again.

So you get 75,000 and then another 75,000. So A is doing a thing. Yeah. C is saving the thing. And then B is like repeating it somehow. Yeah. Duplicating it over and over. Yeah.

Yeah. Yeah. Reimporting what you saved. Now I took a certain delight in not knowing what these things were. Because that's all. I need the math to solve the problem. Piece of cake. So then I wrote some code. took a certain delight in not knowing what these things were. Because that's all, I need the math to solve the problem. Piece of cake. So then I wrote some code that would explore every single possibility.

So I imagined the code as someone playing the game. And then the first thing they can do is do option A, because they've got no money. So all they can do is option A to get $25,000. Then they can either do A again, or they could do C to lock it in so they can start doing B. But I imagined it splitting. So the code then splits

and one version tries doing A again and the different version tries doing C to lock in the amount. And each time there's a choice, it splits again. So I then thought it would kind of span out and explore every possible way you could play the game so you start with nothing you do your talent show and raise 25 grand and you could do another talent show yeah and another talent show yeah you keep doing that but eventually it's going to get to a point where it's quicker to go okay let's do c

and save and look at that i've done 10 talent shows. I've got $250,000. And then it makes sense to switch back into B and then go, right, now let's just, this is what we're talking about, yeah? Yep, you're absolutely correct. And now we're going to keep, now we're going to reproduce the talent show all over the world. We're going to franchise it. Scale it right up. And everyone's doing their own talent shows.

All the community centers are being saved. And this is taking me a lot less effort than it did originally because I've only got one talent and that's announcing wrestling. Yeah, but what a talent. It's so versatile a talent it should count as three or four. But let's say you do A 10 times, right? So you've got $250,000. Then you lock it in.

And every time you do do b you're getting another 250 000 eventually you've got like a million you got one and a half million but then you're like well hang on what if i go back and do c again to lock in one and a half million because now yeah yeah it's like a macro thing isn't it yeah but but c takes so long you don't want to do it too often you want to yeah yeah too often. You want to... Yeah. Yeah. So the question now is how on earth would you work this out?

So actually, if you want to know my answer, I worked out that the optimal way of doing it is to first of all do A seven times. So you're going to bake seven very expensive cakes. Seven very expensive cakes, $175,000 for community centers. You then do C to lock that in, and then you do 17 Bs. So you're adding on that 175 every single time. Then you do C again to lock it in, another 17 Bs, a third C, 17 Bs.

That is the fastest way to get you over a billion dollars. Everyone gets a community center or a bake sale. I forget what our example was. Do you want to know what the actual things were? Because then once I worked it out, then I went and actually watched the live stream that Dark Viper had done. So A is swimming down to get a briefcase from an underwater shipwreck. Ah.

Didn't see that coming. I did not. There is neither theft nor auto. No. So far. Yeah. It's medium scuba. Larceny?

Ah, yeah. Plundering. I don't know how that. Yeah. Ooh. Medium scuba plundering. Yeah. It turns out C, locking it in. This sounds like a thing where it doesn't realize

that you've already accomplished that mission, and so now it's... Well, Beck, you are so on it. I would be amazed if I did not already have such high expectations for your video game intuition. Yeah, it's a glitch. What you've got to do is trick... Obviously, there's much better explanations out there than this. It's not a very well-known glitch because it's a glitch what you got to do is trick i mean obviously there's much

better explanations out there than this it's not a very well-known glitch because it's not super helpful normally in terms of speed running but what you do in um grand theft auto you can switch to director mode which i think just pops out and shows footage of stuff but you start director mode right as you're crossing the line on the ground that transfers you into the next mission so right as you're crossing into the next mission you also pop out into director mode and then you've got to blow yourself up or something but you can trick the game into thinking you're both doing the mission and you're not yet in the mission you know what yep i interviewed the actor who plays Trevor Phillips,

who's one of the main characters in Grand Theft Auto V at Brussels Comic Con. Really? Just... Steven Ogg. Yeah, like a couple of weeks ago. Wow. As a fellow video game voice artist, did you just chat about the biz? He got to do all the ping pong balls and green screen. It was a proper acting job.

Oh, wow. It's like a movie, the way they do it. And you have to, it's even harder because you have to do all this stuff with literally nothing around you. You have to guess what's around you. Not just because they haven't actually built the effects and everything yet, but also because they're so, so careful with not wanting anything to get out. Like you have to sign NDAndas but you don't even get full scripts really voice a character in a video game you have zero context for what is happening or who you are or what's going on like wow if you think video game voices sound weird and

unrealistic it's because you have nothing to go off like you'll find out later oh i was playing a mechanic but like your lines might not really have anything to do so you can't get a motivation in your head about i'm a mechanic yeah yeah exactly it's really really weird and on and so that's weird for just voice but with him it was like he knows some movements and actions he needs to do but he doesn't necessarily know why or what's there well there you go anyway that was a little little tangent for you good aside so anyway because the game thinks you're both doing a mission and not doing a mission it remembers how much money you had when you started the mission and if you fail the mission it resets so it gives you back

the same amount of money you had when you started but because it thinks you're not in the mission, it resets. So it gives you back the same amount of money you had when you started. But because it thinks you're not in the mission, you can buy shares on the in-game stock market. So what you can do, locking in the value is just doing the glitch. And then what you can do is buy shares equal to all the money you have. And then you can fail the mission

and it gives you back all that money. And then you can buy that many shares again, fail the mission, get back all the all that money and then you can buy that many shares again get back all the money buy the shares again repeat yeah so once you've set up the glitch in this weird superposition of both being and not being in the mission you can then just reset your bank account whenever you want but only back to the amount when you did the glitch which is why you've then got to do the glitch again if you want to reset it. Got it. Very interestingly, in the live stream,

DarkViperAU, Matt, Aussie Matt, initially had spoken to some of the people on his Discord about the maths, and they had just worked out how many times to do A, and then a single C, and then a whole lot of Bs. It was only during the live stream, someone's like, why don't you do C again? And they're like, oh, we didn't think of C again.

So then they crack out a spreadsheet and live in the live stream with all their viewers chipping in. They try to work out the best way of doing it in this new method. And I don't know if you've ever interacted with uh people on the internet beck but the signal to noise is not great so poor poor matt is wrangling all these occasional helpful but overwhelmingly unhelpful suggestions and eventually they got very close in the live stream they decided to do five a's then they worked out three of C, but they did 20 B's each time. If you work it out just using the exact times, their solution would take 52 minutes,

20 seconds of gameplay. My slightly optimal solution would take 51 minutes, 22 seconds. So my optimal solution was only 58 seconds faster than the one that they came up with using their viewers at the time. Which is just incredible. Yeah, that is impressive.

The power of the crowd. I like to crack that. And Dark Viper AU keeping a cool head and somehow putting all this information together and then executing it in the game. So I'm very impressed. It's absolutely amazing. I then, because I can't leave well enough enough alone because they'd previously done a million but just by doing a just getting

the briefcases which is ridiculous they've done done a billion and i was like well why don't you do a trillion and so i ran the numbers on the best way to do a trillion and i had to rewrite the code for all this so by then i got a lot smarter with the code because I kind of knew you had to start by doing A's and then you had to flip between occasional C's and then blocks of B's. And so I was able to whittle down to just those solutions. But it was interesting. Initially, I wanted to check there wasn't something I wasn't thinking of, which is the mistake that Matt fell the live the live stream because he had a good enough suggestion from his discord but in maths you're always like ah but what if there's another solution i'm not thinking of and so i did it the the less efficient but exhaustive way first on smaller amounts until i had a sense of no the best solutions are always

this format and then and logically it should be this so by now i'm talking to matt because i'm sure he was australian so i just dropped him an email and we had a good chat about it and he goes well actually you can't do a trillion because the maximum amount of money you can have in the game is 2 billion 147 million 483 647 okay he said he'd heard it's something to do and he quoted it here. 32 bits signed into during computing. And I'm like, yes, very familiar with that number.

Is this the like rollover thing? It's the rollover thing. Yeah. Yeah. But I'll let you explain it. Cause not everyone might've seen your shows a thousand times. Oh, so it's exactly.

So it's, it's a, it's two to the power of 31. If anyone's curious one below that it's because they're obviously storing the amount of 31, if anyone's curious. One below that. It's because they're obviously storing the amount of money in a binary number. And there's maximum values for certain length binary numbers. And Bex, familiar with this?

Because in my show, Humble Pie, I make a big deal of the 32-bit rollover, which is just over $4 billion. And this is exactly half that. Because this is assigned, which means you can store positive and negative values because you can have negative money in the game i guess i'm deducing the gameplay based on the binary limitations that people have told me about so i've now worked out we had a bit of a play and we looked at the various fastest ways that you can get to the amount where the game breaks and because the amount of time it takes to the glitch you can get better at doing the glitch like that 10 minutes was

just a guess on how many tries it takes so I then worked with Matt and I gave him for every single possible length of time the glitch takes on average the optimal strategy for that amount of time so what he can do is he can practice the glitch

work out roughly how long it takes him and then he can just look up the optimal strategy for that glitch time wow then to then um he did point out that you because it's a game that you can just you can mess around with you can just mod it or something to auto get the money but that's not nearly as much fun so yeah uh his video for a billion is out now. The pinned comment is him talking about the maths he was doing with me about it afterwards. If you want to chip in the conversation that's happening there. And I'm curious to know, will the game crash if you hit the max value?

Will it reset to zero? Will it roll over to be negative two billion? I mean, there's a lot of options. I'm hoping he'll give that a go. I think that'll be very interesting. Yeah, actually, I'm genuinely interested in that now. Yeah. But I had a lot of fun.

It started off as a pure theoretical mass problem, and later on I got the context in terms of the speed running. I had a lot of fun solving it. At a minimum, I was able to confirm that the on-the-fly solution they came up with in the live stream was achingly close to the optimal solution. And hopefully we can go for the $2 billion breakpoint next time. Yay! Five dings.

Ding V. In the meantime, I really want someone to do a... You know how Grand Theft Auto has a very specific front cover design? Yep. I really want someone to do that design, but for great treats. Great treats adventure. Adventure. Very delicious.

Very delicious has to be one word so that the V makes sense. Oh, yeah, one word. Very delicious. Yeah. Great treats adventure. Very delicious. Very delicious. One word.

Very delicious. Yeah. Great treats adventure. Very delicious. Someone named Ken got in touch with us via the problem posing page at problemsquared.com. And they say, hello! Exclamation mark. Great opening.

I'm planning to propose to my girlfriend, but just have one problem. I do not know her ring size! Exclamation mark, exclamation mark. Very liberal with the exclamation marks here, Ken. What are some sneaky but effective ways to learn her ring size? Question mark, thank you, exclamation mark. So, Beck, are you able to help Ken to work out their girlfriend's ring size without ruining the ring surprise? Yes.

First of all, I just want to say I love this problem because Can says they only have one problem, and we are a problem squared, and that is the exact type of problem that I want to solve. We're not problems squared. Yeah, exactly. Just one. Just one.

Yeah, I've got a few thoughts, but I was actually going to ask, Matt, you're married. When you proposed to Lucy, did you present her with a ring that she was aware of or had tried on previously? Oh, no, she was unaware of it, but I presented her with a ring that did fit. And how did you work it out? I had this problem and solved this problem. Oh. And my solution was to measure her other rings.

Smart. Actually, I think I looked at her fingers to work out, because I figured there's some variability in fingers, right? Yes, there is. So I wanted to work out other fingers that are roughly the same size and where she wears rings. I then borrowed, without asking, I stole one of her rings and took it into the jewellers and went, this size, please. And then they put it on the conical ring measuring device.

And they went, ah, that's... Make sure it's that one and not the comical one. Not the comical. That one's... No. It goes, whoop, whoop. A clown comes in. They put a balloon through the ring

it's complex no the conical ring measuring device I then managed to sneak that ring back in to her collection but then the engagement ring

was then sized to match that which then matched her own finger so that's some so that's my, from experience, but if you're proposing to someone who either has wildly different sized fingers

or doesn't already wear rings or doesn't leave rings where you can access them without being noticed, then my technique won't work, obviously. How about yourself? Were you proposed to with a ring that fit? I was. I don't wear jewelry much really at all so i don't really wear rings or anything basically what gav did is he chose a

nice ring from he got it from like an antique store and went oh she would like that one yep so it's nice and different and And, and then he just hoped. And then they said, if it's not the right size, you can come back afterwards and we'll resize it. Um, and so we were, he was prepared.

Well, he just went from what the ring, because it's like a second, you know, it's secondhand. It's just, it's whatever size it is. I guess it is what it is.

Yeah. It's a ring. Yeah. You can't be like, I want this one in this size. Yeah, exactly. Yeah. But he knew when he saw it, like I would like it. It's my, it is. Yeah. It's a ring. Yeah. You can't be like, I want this one in this size. Yeah, exactly. But he knew when he saw it, like, I would like it. It's my jam.

It's my vibe. So he went based on that and was like, you know, if it doesn't fit, then we'll go together and that'll be like a couple thing. We'll go and, you know, adjusted, which I think is a very romantic thing. Yeah. That works because the effort of picking the design like finding the second hand ring that that's all the effort and thought there and the size is you know an afterthought so yeah because that's the thing you can change but what you don't

want to do is propose with an awful ring yes so yeah if you if it's an amazing ring and there's there's a reason why it comes in the size it comes in and you have to fix it later, then you get away with it. Yeah, exactly. So I would say you don't need to stress too much about ring size. And we were weirdly lucky. It turned out that the ring is the perfect size for my ring finger. Oh, my goodness. So we didn't have to get it adjusted.

But that wasn't because he was this amazing guesser. It just so happened that the ring fit perfectly and i think that's the thing is i think a lot of people stress about it like as if you've got to get it on perfectly the first time and like we've talked about shoe sizes before you don't always know if shoes are going to fit usually you'll try on shoes before you buy them because you're aware that even though that the numbers are there they still might not fit right. Yes. And so I think the main thing is that, can you should be led by the ring itself and not so much the size.

However, let's say you're making a ring. And so you're like, well, while I'm at it, might as well try and get it the right size. Yep. I think, personally. And look, I know there's ways, you can Google, there's loads of different ways, you know, just somehow wrapping string around someone's finger or whatever. you can google there's loads of different ways just but you know just somehow wrapping string around someone's finger or whatever you know there's

loads of different that's the worst suggestion ever it's not very sneaky because i i was thinking because i like you don't want to get the surprise away because i mean if if you're in proposal town or the vicinity of it shouldn't be coming as a complete surprise to everyone involved everyone should kind of know it's on the coming as a complete surprise to everyone involved. Everyone should kind of know it's on the cards at this point in time. It's not the fact that it's happening that should be a surprise. It's just the minor details

in how it is executed. So you don't want to give away... Do you mind if I... I guess you could really ham it up, contrive something ridiculous to put a bit of ribbon around someone's finger and then sharpie the line where it crosses and then you're out.

But then everyone's kind of playing along i was thinking you want to get a photo of them holding a ruler oh nice yeah because i'm trying to work out i want to buy this ruler could you hold it up for that and get a good photo yeah exactly yeah yeah bingo yeah that's nice that's nice my my suggestion is, you know, you get those hand casting kits. So like people do them for like their kids' feet and hands and stuff, but you can get them for adults. And the adult ones, like you have, you're meant to like hold hands in the cast, but obviously that's not particularly useful if you want to get around the finger.

So I think you should be like, oh, I'd really like like a soap dish to have coming out of the wall wouldn't it be great if it was your hand your hand holding the soap yeah and so then so then you buy the kit and then you get her to do the the hand casting and then make that so it's like her fingers are sort of apart and then that way you can just take the whole hand in with you to the jewellery shop. It's the kind of divisive decor. I think I'd want to have my partner locked in post-marriage before I start pitching. Custom hands coming out of the shower wall to hold the soap. I feel like I want to be a little bit further into the sunk cost of the relationship before I start pitching stuff like that.

All right. Well, now I know not what to get you and Lucy for your next wedding anniversary. Oh, now we're fine. We've both invested so much in this relationship. We are not backing out now. Great. Good. Oh, it's not your hands.

It's my hands now. That's what I write in the card on Valentine's Day. I'm not backing out now. It's too late. Yeah. To my favourite sunk cost. Oh, yeah. My other suggestion

was I think can should talk their partner to be into getting into yo-yos. Oh. Because then they adjust

the string to match the finger. Yeah. And then you're like, oh, it's actually the best if you have to match the finger. Yeah. That's good. And then you're like, oh, it's actually the best if you have it on that finger. A lot of people don't realize this, but you should try it with that. Or you could take her bowling and work out what size holes that she uses. You know, obviously, you know, get her to do the one that's like comfortable for it. What about one of those places where lots of celebrities have put their hands in like handprints like at the chinese theater in hollywood oh yeah yeah

let's find out which celebrity has the hands the same size as us right oh that's great yeah you ring the celebrity up ask them what their ring size is yeah that's what you do i thought you're gonna say like you then just find some wet concrete and you both do your, like, we're celebrity hands thing and then go back after it's dried. Yeah, I would say. Or what about you get one of those, it's like a little rack with loads of pins and then you press.

Oh, the hand imprint. Yeah, or you could do your face or your hand against it. Yeah, very carefully carry it out of the room. Why are you carrying it like that? I just don't want to hurt myself. Now, going back to my practical suggestion of them being photographed holding a ruler, all you really need is them being photographed with something else the same distance from the camera as their hand that you know the size of

because you can then measure that other object afterwards that will give you a pixels to millimeter ratio for that distance in the photo and then you can measure the number of pixels across their finger is and that will give you the diameter of their ring size using that conversion bag. Yeah, that's an option. Someone did a very similar thing, but about me recently. I did a show a couple of weeks ago and someone brought me a t-shirt. And they wanted to work out what t-shirt size I was. And they couldn't work out what t-shirt size I was. But they found a photograph of me standing next to Hannah Fry.

Probably from the Christmas actions. And Hannah Fry's height is available online, apparently. So they used Hannah as the reference object because they knew her height. And then they could then scale that to get my height and then scale that to get my t-shirt size. Fantastic. And they were good.

It was slightly smaller than i would have gone i think they're rounded down rather than up but uh yeah a bit less give on a ring though than uh than a t-shirt yeah that's true yeah there's a little less room for error it's funny you're talking about the scale thing because my mom and my brother and i are in a whatsapp group and my mom baked a loaf of bread and she was so proud of how big this loaf of bread was. She was like, oh, here's a picture. And we were like, we don't really know how big it is because we don't know how big that chopping board is because she had it just sort of resting on a chopping board.

And so Mike, my brother, said, put it next to a banana for scale. Classic. And then she said, how big a banana? And then Mike said, good question. Then she sent us a photo of the bread on the chopping board with a banana. And then Mike said, how big is that banana? Use a banana for scale. And then she said, well, look at the chopping board for comparison and don't tell me to get another board for comparison. So I told her, don't be silly, mom, just take a photo without the bread so we can see how big the board is

next to the banana. And so now it's become an ongoing joke that whenever size comes up in our conversations on WhatsApp, it's a quick take a photo of an extra banana for scale. And a few times she's cooked things and sent us photos with just like a banana next to it just so we can, even if the size has nothing to do with the food. So I guess my answer is that maybe Can should just take a photo of his girlfriend's hand next to a banana. That would do it. And just go from there. Measure the banana after the fact or before. Just get smaller and smaller bananas until they look that they're about the same size. They're about the same size. So yeah, I reckon there's loads of suggestions there.

Oh yeah. Beck, I don't want to put a ding on it just yet because I feel like I want to see... It's going to be a long game, but I reckon we wait. Ken can try one of these and report back on how it all goes. Yeah. We'll find out if they're engaged. Or if she's just another dingle lady.

Hey, all the dingle ladies. So we've got so many other business, Matt. We do. As you all know, we like to address any sort of feedback solutions or anything that we've received to previous episodes. And hoo boy, did we get quite a few responses this is actually going back a bit it's to episode 045 a minute of new york and and hey i'm walking yeah where we were figuring out at what point if you live between two subway stops should you go forwards or backwards yes

if you're walking along a road, you want to get the subway. There's one behind you, but you've got to walk away from where you want to end up. So if you got the train, you've got to go one extra stop. Or there's a stop in front of you. So if you walk there, you can then get the train. Yeah. And during the maths for that, there was a formula. And I was like, how does that explain things?

And you're like, I don't know. And in my defense, very jet lagged. So the formula was, you take the percentage of your walking speed compared to the train speed. So we worked out, because we measured it, we walked 17% of the speed of the subway. You then subtract that off 100%,

so that would leave us with 83%. And then you half that. And so that gives you, in our case, 42 and a half. And that's the distance between the two stops. That's your split point. Anywhere behind that, you go backwards. Anywhere in front of that, you go forwards. And so I was like, it feels really neat.

Because I did a bunch of algebra and it dropped out super neat. And I'm like, I feel like there's an intuitive way to explain why it's that value. But I was too jet lagged to do it. A lot of people have now done that. And most of them have told us about it. So that's very nice of everyone. And so I'm going to give specific mentions to someone called My Ticket Burner, who drew a diagram with a great explanation, and someone called,

now I'm going to mispronounce, R-U-U-D-D-E-R-O-O-I-J. They didn't do a diagram, but did a very nice little explanation. Other people sent in diagrams and chat, and someone filmed a video. The video involved relative speeds, which worked, but I might think it's slightly over-engineered for what we need. But if that's the easiest way for some

people, that's great. The way I liked it explained is to think about, actually there's two ways. I'm going to do two ways. Two ways of explaining it. And let me know if either of these make sense. So the reason it's one minus that 17% is because if you travel at 17% of the speed of the train, you can be 17% away from the distance between the two stations, away from the second station, because that's the distance you can walk to get there that it takes the train to do the entire distance. Yeah. So if you start 17% from the end, the same time the train starts from the previous station,

and you go at once, you'll get there exactly when the train does, and you get on the train. Yeah. So from that point forward, you always definitely, definitely, definitely go forward. Yeah. And all the other cases are kind of in the mix.

And so you go from the middle of all the other cases, which is why you then take half of what's what's left because that's the in-between point of the rest which is a little bit hand wavy but that i that kind of made sense for me another way to think about it for the rest of it is if you because you got the 17 where if you left and covered that the train could do the whole thing the midpoint between the starting point and that 17% point if you start on that midpoint if there's a train that if you started walking backwards you got there exactly when the train got to that first previous station and then you travel forward together if instead of going backwards at the exact point if you walked the other way you'd do the other half of that beginning section.

That would take the time, it would take the train to get to the first station, except now you've walked the other way. And then you got the 17% for the train to do the rest of the journey and you got on the train. So actually that point, if you subtract off the 17% and then half the rest,

is the exact threshold point where you'd get the same train if you walk in either direction. Right. Got it. And so that's like the split point between getting the same train going backwards or forwards. And so if you're any closer to back, you definitely go back because you're going to get there even earlier. And if you're any further forward, you definitely go forward because you're going to get there even earlier. And if you're any further forward, you don't have to go forward because you're going to get there even earlier. Yeah. And so that,

that I think was the most intuitive explanation I came across. It's still, it's still a little bit, but I can see, and I'm convinced it's correct because I did the algebra. And I don't know if I would have trusted any of these explanations if I hadn't done the algebra, but I think a reverse explanation, they kind of make sense, I don't know if I would have trusted any of these explanations if I hadn't done the algebra.

But I think a reverse explanation, they kind of make sense. But I'm glad I've already verified the formula. I mean, there's a bunch of weird edge cases. Things like if you walk faster than the train, if the trains only come once every 10 hours, all these things. Where the solution is just to walk to wherever you're going. Yeah. But for everything else kind of in the reasonable range of values the average wait time is the same at either station it's why i didn't bother factoring in walking down to the platform another way of kind of thinking about it which is a bit like the first one i said is you should in general you

should be like walk to the closest one but then you're like ah but if i walk to the one in front i save the journey time in between and that's why you subtract off that the percentage you walk which is the equivalent distance you can walk in the time the train moves yeah and what's left you just walk to the closest one which is why it's the midpoint of that because the you you should always walk to the closest one but you should factor in that you're saving one stop's worth of journey by going to the front one everything else cancels out because it's the same at both stations hmm that's that's the vibe i was getting and you know what i'm happy to accept that unless someone who has done a paper specifically on this wants to correct us oh it's got to be peer-reviewed from here in otherwise thank you everyone who sent in your suggestions.

You can all stop now. They can still discuss amongst themselves. You can either go back to the previous stop now or you can go forward to the next stop now. The important thing is

we've arrived at the station. And our final bit of any other business is exciting. I'm excited. You look it. For those listening at home, business is exciting. I'm excited. You look it. For those listening at home, that's funny because I don't. I don't think I've ever seen you.

I've seen you vaguely excited. I know when you're excited, but you're. I've been mildly excited in your presence. Yeah, I've seen you excited about stuff, but you're excited. Like, you know, you're not like a bouncy up and down child excited. Yeah, that's not you. Calm. Calm.

It's time to thank our Patreons. So we like to choose at random three of our Patreon supporters and we give you a little personal thank you. So on this episode, we would like to thank... Kate Sherrard. Neil Fraser. Andreas. Thank you very much.

If you would like the opportunity to potentially be thanked, you can support us via patreon.com forward slash a problem squared. I said, because correct. That is the URL. Because that helps us continue to make this happen. It means that we can pay our wonderful producer, Lauren, and

that we don't have to have any ads and that other people can listen to this as well. So, with that in mind, thank you so much for listening. I have been back. You've had Matt Parker. And over in the corner it's world champion lauren armstrong carter Hey, Beck.

Yeah? We got some post. What? Someone posted us a Twisties substitute. No. From Canada. From Canada. Yes.

Here it is. Now, people told us about these. I couldn't find any. These are Hawkins Cheezies. Ooh. Much discussed. A lot of people have said Hawkins Cheezies. And you're saying discussed as in like people talking, not discussed as in much discussed.

Opposite of discussed. Like a doge way. They were not discussed, these. Doge way. They came with a letter from Tim. Please find enclosed a bag of Hawkins Cheezies. I hope you enjoy them. And then they provide some additional background information

on Hawkins Cheezies, originally developed in Chicago, but production was moved to Tweed, Ontario in 1949. Cheers, Tim. P.S. This box, the box they posted them in, came to Canada full of stuff from Maths Gear. That's my shop. So,

I shipped them the box full of maths and they shipped it back full of twisty substitutes. Yay! Oh, how wonderful is that? Tim, you utter legend. Who knows where that box will go next. Thank you, Tim. So, Tim, thank you very much.

Now, as people may have realized, we are recording this remotely today, but last time I saw Beck, which was only a few days ago, I gave her half of this pack of I was wondering what the bag of bright orange things were. Let me go get the Ziploc bag. Yes. That's them. Grab them.

They're just labeled as corn snacks. Corn snacks. Made with real cheddar cheese. Picture of a maple leaf. Oh my gosh, they're so orange. They're so orange. Mmm. They're so crispy. Mmm. Damn.

They're so crispy. That is savoury. Oh man, that is good. That's a new mummy of crumb. It does taste more like cheddar. Yeah. And you're right, they've got a real crunch on them. Mmm.

Oh my goodness. They're crunchy the whole way through. They are tasty. These are really tasty. They're not twisties, but they are delicious. They're very Moorish. Do you know what? They're a little bit like the Cheetos, but they've got proper...

You know how I was like, there's something quite dull about them. But this one, it's like the saltiness is there. Yeah. I could imagine growing up with these and finding twisties to be an inadequate substitute. Yeah, you're right. The other way around, I get, yeah. Don't get me wrong, Twissies are great, and I'll probably choose Twissies over these,

but I can imagine if this was your starting point, you'd be locked in. Yeah. Man, these are good. What a living legend. They're great. Hawkins Cheesies, delicious. Thanks, Tim.