A Problem Squared - 042 = Plate or Bowl Guesses and Faster Processes

Episode Date: September 12, 2022

In this episode... * When does a plate become a bowl? * And, five five-letter words with twenty-five unique letters: Some mind-blowing solutions.  Juat a reminder that you can now buy APS merch! Head on over to: https://a-problem-squared.teemill.com. As always, if you've got a problem or a solution, hit us up on our website aproblemsquared.com. And if you want want even more from A Problem Squared, find us on Twitter and Instagram.

sup dings dong and welcome to a problem square the most extreme gnarly podcast on the podcast platforms that solves i've already used gly. I was going to use gnarly problems. That solves your problems. Radical. Wow. Sit tight. You mean hang 10. Hang 10. Sorry, hang 10.

Stay loose because I'm joined by comedian, performer and author, the rad Beck Hill. And that's rad as in radians, because she always brings a new angle to all the problems. And myself, the radical Matt Parker, because as a mathematician, most of my solutions to the problems involve the square root of a number. That was my intro this time. Congratulations for having an intro that is the audio equivalent of that Steve Buscemi clip.

Oh, the fellow kids. Yeah. equivalent of that Steve Buscemi clip. Oh, the fellow kids. Yeah. Hey, I was there in the 90s. So I feel like appealing to people who were children the same time I was a teenager. Is that legit?

Or is that still? The 90s is coming back around, isn't it? I have seen several people wearing pretty much exactly Spice Girl outfits without irony. Oh, wow. I was wearing that stuff when I was younger. Now I know how stupid I looked. We are maybe seven or eight seasons of Stranger Things away from everyone discovering this unknown band Nirvana.

Yeah. On this episode. I'll be getting into semantics on some crockery. I will be overloading any other business with follow-ons from the five letters, five words problem. And that's it. And that's it. Strap in.

So, Bec, how are you doing these days? I'm good. I'm good. I mentioned this on the I'm a Wizard Patreon. Oh, Patreon exclusive. Bonus podcast that we do. Yeah. But I'd been to Edinburgh Fringe.

I didn't go to perform. It was my first time going as a punter since. Oh, wow. 2005. I thought I was going to get FOMO and I absolutely did not get FOMO. Oh, really? Just seeing how stressed everyone gets. I was like, oh, yeah, I've done the right thing.

So you can just go to the Edinburgh Festival Fringe and hang out and see people and see shows. You just go. Yeah. But what are you going to do for like three whole weeks if you're not doing a show? I know. It's almost like there are more things to do and see than there are people to go and do and see them. My goodness. Yeah. You're going to revolutionize the Fr do and see them. My goodness. Yeah.

You're going to revolutionize the fringe. I know. I thoroughly recommend it. But while I was there, I stayed with the guys from Mr. Thing. Excellent. How's their show? Oh, it's really good. It's really good.

I'm pretty sure this episode will come out after the fringe is finished. So the up plug is unhelpful. You'll miss it. Oh, my goodness. It's such a great show. I really hope they bring it to London, Matt, because you'd bloody love it. While I was staying up there, Gus, who does some of the behind the scenes stuff for Mr. Thing, as soon as I arrived, he said, Beck, I've actually got a present for you.

And I was like, what? For me? Why? Why do you have a present for me? And he was like, well, I just think you'd appreciate it. But I'm going to hold it up in front of the camera. All right. So you ready? So Becca's holding up a piece of metal. Some would say it looks like a surgical kind of precision engineered bit of metal. And it's got three massive claws on the top. And when she spins it, the claws open up. It would look like the claw in

like a game machine, except way more vicious. And Beck is spinning it in what can only be described as a menacing fashion. Yeah, this is a grappling hook. Oh my goodness. Basically, I'm obsessed with the idea of grappling hooks, like on a weekly basis, because I've always wanted a grappling hook because they're cool. But I also constantly try to think about what the physics is in order to make. So I've got the hook part, but I don't have the retractable that bit. All hooks, no grapple.

Yeah, that's right. Isn't a grapple like the actual action of the hook hooking onto something? Like you grapple with a subject. I thought it was climbing, and that's where the phrase, a grapple a day keeps the burglar present. Yeah, that classic saying. But whatever that thing is, I'm always trying to think about the physics needed behind that because when Batman has it on the utility belt.

Where's the motor and the winch? Exactly. And then I'm always thinking how strong would the motor need to be? And what material would the cord be made of? It pops into my head a lot. And I had mentioned this in passing when I was doing some special little filming for a bit in their show. And turns out that they had a spare grappling hook. Yeah.

And I keep spinning it. It's like a very, very big, dangerous fidget toy. Yeah. In a way, anything can be a fidget toy. Like a very dangerous fidget umbrella. Yeah. Wow. Well, I acquired no burglar tools or accessories.

Sucks to be you. Since we last spoke. I did, however, go to Finland. Oh, yeah. What were you doing out there? I went to a math art conference it's a conference called bridges didn't invite me it didn't invite you you know what you would have really enjoyed it i gotta say it was a lot of fun there's a lot of it's people who use math to do art oh and some of it is like

arty people who happen to incorporate math but a lot of it is just math people who like to express their math discoveries via the medium of art and i've been wanting to go for years and they keep inviting me but it never lined up because it falls during the edinburgh festival fringe so i can never really go or like summers are always quite busy actually in 2020 i was like i'm gonna do it and then i got delayed so i finally made it along and i did a talk about incorporating mathematics and into performance and videos and youtube and that kind of jazz. But I was also super interested in people doing things with sculptures and knitting and all sorts of cool stuff.

My favorite session was about randomly generated mitten knitting patterns. So as you're knitting, you're still randomly generating the pattern as you go. It's very cool. But the highlight of being in Finland was I went and measured some steps. I don't think I've mentioned this before on the podcast. Stop me if I have. A friend of mine has the world record for the most steps a slinky has gone down. Yeah, yeah.

Well, I know about this, but I believe maybe we've just talked about it in person. Yeah. So this is it, right? So it was part of my process of trying to find a long set of stairs such that we could really extend the world record for most steps a slinky has gone down amazing i want to knock it out the park on the order of 100 steps that's that's my dream because the slinky can't like you can't use like a spiral staircase so it bounces off the side you can't put it on an escalator very funny doesn't count it's got to be a normal static set of stairs. But finding a set of stairs with a hundred linear steps. I had one

candidate set of stairs in the UK at Cheddar Gorge. So I went there, good set of stairs, measured them to a regular because you want nice consistent stair size. So yes, Slinky will keep on going. And the issue is modern stairs have a landing every like 10 or so steps. You're looking for kind of old sets of stairs or unusual sets of stairs that have lots of regular steps in a row. And I had looked online and found a candidate set in Finland, just outside Helsinki. And so I was like, perfect. While I'm over there, I'll head over to, actually, I'm going to put the name of the hill in the chat, if you don't mind just quickly reading that out for us. That's the hill that I went to.

Okay. Maumankatanonhupu. I think you nailed it. They recently refurbished these steps, so actually they're nice and consistent. Took a tape measure. Measured a bunch of them. And there were some landings, but there's a stretch of 121 consecutive equally sized steps. However, they are quite shallow.

So they've only got like a 18 or so centimeter drop, and then they're about 40 centimeters wide. Oh, so there's long ones. Yeah. There's no off-the-shelf slinky that can do that. We would have to custom make a slinky. And there's an amazing set of stairs on St. Helena can do that. We would have to custom make a slinky. And there's an amazing set of stairs on St Helena,

I think that's how it's pronounced, an island, but it's real difficult to get to. And so at the moment, I think my only real option is custom-made slinky in Finland. But I thought I would throw it open. Can everyone keep an eye out for a set of stairs that has about 100 stairs in a row, straight line, equally sized. And let me know what the ratio of the tread, like how deep the stair is, and the riser. So risers up and down and treads backwards and forwards.

Let me know the ratio between those. I should warn everyone, this is not like a burning project. Whenever I happen to be somewhere or traveling, I'm keeping an eye out for this magical staircase. So I'm sure with our listeners all around the globe, let me know. Your prize will be me coming to visit you with a slinky or whatever the staircase may be. Yeah, if anyone wants to cheat and just make that staircase

so Matt has to come to you. Oh, 100%. Yeah, if someone wants to build it, I will come. That's my mathematical promise. You can email me or go on to the problem posing page at a problemsquared.com. Select solution. Tell me about your stairs. We have a problem here, Bex. We have a problem here, Bex, sent in by Sam Griffiths via our problem posing page at aproblemsquared.com. And their problem is, at what point does a plate become a bowl?

They then go on to qualify that they have a bowl that's quite flat and kind of splayed in the middle, that their family claims is a plate. Aha, they've called it a bowl. Their family thinks it's a plate. They would like to know when it's a plate, a plate, and a bowl. Well, I'm glad they sent this because we also had pretty much the same question from someone called Patrick as well. Well, Sam was the first person to raise this apparently quite common issue. Yeah.

Of when is a plate a bowl and a bowl a plate? So that one was sent in late last year. We did also receive basically a similar problem in July this year. So I thought we should chat about it because I want to know too. So I've got some plates. In fact, I'm going to hold this one up here. I would count this as a plate because I store it with other plates. For people who are at home, Becca's holding up a plate.

It's got a real flat base for the centre. I'd say two thirds, maybe even three quarters of the radius. Then a real kind of steep lip on an angle around the edge. I would honestly say if you just took it as the outside of a shape, it's practically a frustum. It's a section of a cone, really, that's been sliced off. It is literally those big plates you get in a restaurant because the restaurant at the National Theatre quite some time ago redid all their crockery and allowed the staff to take home any of the older... So your husband brought home ex-restaurant plates. Yeah, they're sturdy.

Commercial grade, yeah. They definitely contain more depth, I guess, but I do call them plates. So I was trying to work this out as well. And the consensus on the internet is that basically anything with a lip is technically a bowl. No. Yeah, which I disagree with. I would argue that majority of plates have even a slight lip, you know, just to stop your... Your peas rolling.

Yeah. I would call that the soup test. Right. I'd thought, okay, what denotes a plate in a bowl is whether it holds soup, but not just that, because you could put soup in a plate and it would be fine, but it should be that you can get your spoon into it and bring it up. Oh, a spoon step. Yeah. Like you shouldn't have to tip your plate. You should be able to put your spoon in and take the spoon out and take soup with it. Yep. I feel like in the same vein as the soup test, there are a lot of plates that you could

technically put cereal in and add some milk and there's enough of a lip to hold the milk there, but you wouldn't. No. It would be a suboptimal way to eat cereal. Yeah. Maybe there's a tip test. Maybe how easy it is to spill. to eat cereal. Yeah. Maybe there's a tip test. Maybe how easy it is to spill.

As a friend and fan of a dirty dry martini, it's my favorite cocktail. A martini glass, traditional martini glass, is an awful receptacle. It's just a cone. Yeah, it's a wide cone as well for anyone trying to picture one if you're not entirely sure what I'm talking about. I always spill at least 12% of my drink as soon as I pick it up. I would say martini glass is the glass equivalent of somewhere between a plate and a bowl. It's very shallow, but very wide.

I think a tip test is a good idea. So I was thinking that's my test is can you eat soup from it by dipping your spoon in? It's not a bowl until it has the depth of a spoon. But then I was looking up different types of crockery online, you know, because you get salad plates, bread plates, and you get fish plates and slightly different sizes where the lip around the plate changes as well. And then you had also like salad bowls, cereal bowls. But then, then I've got the version of the plate that I held up before where it's a bit deeper inside. So I do use my soup in those. Well, according to the website I was looking at that was telling me about crockery,

it's called a soup plate. A soup plate? A soup plate. Ah, it's just throwing everything out the window. Yeah. So I was developing my own mathematical way that maybe we could determine which is which. And one thing I was working on was maybe the ratio of flat to gradient. However, the soup plate throws it out the window

because I would look at it and say it's definitely a bowl. But if you combine the middle flat bit where the soup goes and then the rim, that's definitely more surface area than the slopey bit. I was going to say whichever there's more of, that determines what it is, but looking at a soup plate, that's a bowl. So you're counting the flat section in the center as well as the flat section around the edge. Yeah. If you discount the edge, then I think my theory stands. Ignoring rims, if there's more area on a slope than flat, it's a bowl and vice versa. And because area scales as the square of the width, you'd have to take the square root of two to work out how much you'd have to increase the

radius to double the area. So the threshold point, like roughly two thirds of the way out. I'm pleased because you're solving this problem far better than I am. No, that's definitely not true. So in that case, if roughly the outer third of the bowl or more curves, it's a bowl. If less than the outer third curves, it's a plate. So what happens if there's no curve? What if you had an upside down hat? An upside down hat? Like a top hat, sorry.

Oh, gotcha. Oh, okay. So it's a plate with a depression in the middle. That's like a dip platter, surely. Come on. Now the focal point is on the stuff on the rim being dipped in the center. At what point is it a ramekin? Well, my other theory was that to be a bowl, the curvature has to change.

A plate, like the plate you held up a second ago, the outside bit is on an angle but it's a consistent angle it's like a flat slope yeah it's a steady slope whereas a bowl you've got the increased curvature like it's a section of a sphere or something but not necessarily a sphere so i was like maybe it's the second derivative the gradient itself is changing as you go out bowl if the gradient for any most local areas is consistent, plate. I think it comes down to whether we feel that it is your formula, the amount of flat surface versus angled or curved surface.

Discarding rim. What do you mean when you say rim? Your soup plate where you can balance your toast on the outer rim. Oh, I see. Yeah. So why are you discounting that again? Because that's basically an attached side plate. What if, though, you had like a one inch flat bit followed by half an inch of curvature and then like 10 inches, basically a plate with a little dimple in the middle. Yeah, exactly.

Bowl equivalent of a spork. And that's fine. Just because sporks exist doesn't mean you can't categorize spoons and forks, right? So I think that's a special case hybrid. Does this mean that if you had like a cheap plate or a faulty plate that had a dimple in it, like a divot. Yeah. It technically is classified as a bowl.

No, because the bulk of the surface area is flat. Not if you're not counting the edge. Oh, yeah. But there needs to be a flat bit in the middle of the, that would be a bowl. But what if the flat bit, there was a flat bit, it was just very small. Yeah. This is why I think we have to go back to my spoon theory i will do a poll which is a poll central surface versus curves without edge then i'll do central

surface versus curves with edge with edge you know counting as a surface yeah yeah and then i'll do the depth of a spoon and we'll see what you think. So we can't ding that one yet. No. But we will. I'm certain we will come back to this. We will find an answer. I actually did do the etymology of the words. And plate comes from the armour aspect of a flat disc of metal.

Yeah, so you would use it. Because when you think about it, yeah, you would have had metal plates before you had ceramic ones. It's not linked to a plateau? Is that a whole different word? Oh, I didn't see it when I was looking it up, but that's a good point. People will tell us. People will tell us.

This podcast is just us saying, we don't know now. Yeah. Yeah. Oh, people right now are yelling the answer at their podcast playing device and they will let us know. Yeah. Oh, and bowl comes from the, like a Germanic word, but then linked back to Latin again, I think, but basically just means round, which is also where like bowl as in bowling and everything comes from.

So problem as of yet undinged. Yeah. Gonna have some soup in this plate now. Now for all you fans of business, which is otherwise uncategorized, it's time for any other business. Yeah, so in episode 038, Matt, someone with a question about Wordle wanted to know if it was possible to find five letter words with no recurring letters yes 25 unique letters across five five-letter words and you solved that problem we dinged it

i did thank you and then a lot of people had things to say well a lot of people thought they could do better so as i mentioned in the episode and it's fine if you haven't heard it, the crux is I wrote some code. I ran it on my laptop. It started with like the biggest list of words imaginable. Like I just got a text file with every word in it. And then it searched for sets of five, five that are words that fulfilled this property. And my laptop took 32 days to do that. In fact, it took just over 2.76 million seconds. Yeah, we released that episode

and approximately one day later, someone named Benjamin Passen replied to our problem squared account on Twitter to say they'd written some code that could find the same solutions faster than 32 days. So I downloaded their code and I ran it on my laptop. And guess how long it took? The other one was what? 32 days, did you say? 32 days. Mine was 32 days.

Okay. Three days. 15 minutes. That's so much faster. It's so much faster it's so much faster just outrageously faster so

so it's like the equivalent of you being like I'll walk I'll walk to Scotland and there's no faster way. And someone's like, oh. There's a train? Yeah.

So Benjamin just knocked it out of the park, right? So way, way, way faster, found exactly the same results as me and did it within a day of the podcast coming out. And I know I said my code was bad, but oh my goodness. Now, I spent a long time in that episode explaining how I tried to prune the number of options to get it down to a searchable amount. Well, Benjamin did it a whole different way. They took all the five letter words that each had five unique letters in each word, and

then they built a network of how those words linked to other words that have no letters in common. So they turned it into what we'd call a graph in mathematics, which is this basic network of how all the words link together in terms of if they have letters in common or not. And then they used some graph theory to search that network for five nodes, five words that are all linked to each other by these no letters in common links. Would it be like if you had a circle made up of all those words and then you ran lines between all the ones that it doesn't have letters in common with? Exactly that. So the five ones we're after form like a pentagram kind of thing with a circle on the outside because everyone's linked to every other one. Yep. Got it. Yep. The technical name

for that is K5. It's the complete graph on five nodes. It's what it's called in graph theory. And so what Benjamin was doing was searching for a subgraph, which was K5 on this network built based on all these words. Now, in my defense, Benjamin's code came in two sections. One bit of code builds that network and the second bit does the searching. So you've got to run two bits of code, whereas mine, you just got to set it going once and then come back a month later. Well done, Benjamin. And then I thought, you know what? Because you were there, we filmed a video about the same problem the day after we recorded the podcast. Oh yeah. No, I wasn't there. That was photos of me.

Yeah. Oh, sorry. Sorry. I had stock footage of you in my video, basically talking about the same stuff, but because I could show graphics, I just covered slightly different things than what I did in the podcast. I had already filmed that when Benjamin came in with this 15 minute winner. And actually I was in Greece. And so I sat in my hotel room and filmed an extra scene for that video explaining what Benjamin did.

Now, while that was happening, it turns out someone else named Neil, Neil Coffey, was also working on a version of the code. And Benjamin and I both used Python. Neil was using Java. Neil Coffey used something called Java. Used Java. Yeah. Fantasticey used something called Java. Used Java. Yeah. Fantastic. That makes me very happy.

Their surname is spelled C-O-F-F-E-Y. So I apologize if I've pronounced that incorrectly. But anyway, we go with Coffey. They wrote code that was faster than Benjamin's. So do you want to, in the spirit of this guessing game, guess what Neil got it down to? Oh my goodness. If Ben got it from 32 days to 15 minutes, it's quite the jump. Yeah.

I mean, so I guess seconds? 15 seconds. 15 seconds. Now I was unaware of this. My video went out and then all hell broke loose. Aha. Everyone took that as a challenge. Within a day of my video being out, someone called Ilya got it down to

5.86 seconds using C++. Someone called Guy got it down to 2.58 seconds using C. Kristen got it down to 1.045 seconds, also using C. And then Orson was the first person to break the one second barrier. Oh. And they got it down to 0.48 seconds oh my goodness using a language called rust half a second from 32 days and you had to leave your laptop running constantly the whole time well didn't stop there oh no people kept going oh my gosh sylvester sylvester got it down to 0.006761 seconds. Ah. So we now, people had to start measuring the speeds in, well, they were measuring it in milliseconds.

Now they're measuring it in microseconds. I think as we speak, the current record is like 2000 something microseconds. Oh my gosh. Less than 1% of a second. Imagine what we could do if we could harness this for good. I know it's so good. They hit the point where reading in the text file was the bulk of the time. Like the actual processing was happening so fast to speed the code up. It was the read that was the issue. And so people started writing code that would, that would commence doing the computations

and calculations while the file was still being opened. So it was computing it as it was being loaded. Just incredible stuff. So actually Sylvester's code, which got it down to 6.76 milliseconds, it took it 4.3 milliseconds to load the words, 2 milliseconds through the processing, and then 0.4 milliseconds to save out the results. Oh my goodness. Just incredible. People started running the code on iPads. So the record on an iPad is 13.1 seconds. That's still very good. This is ridiculous. Yeah. And then, so Benjamin, good old Benjamin, who started this whole thing with the 15 minutes, downloaded everyone's code. So I was keeping track.

We had over 20 different versions of the code at this point. Benjamin downloaded them all, ran them all on the same environment several times, took the averages. This is where I'm getting all the rankings from. We did a full analysis of it, analyzed all the things different people were doing in their code, like different techniques and optimizations. And some of the techniques were mathematical, like smarter ways to do the maths. And some techniques were like

computing focused, ways that computers are fastest. And the single greatest improvement. So my code I was using, and this is not super important so if people aren't familiar with coding it's fine but in python i was storing the words as sets of characters and i was using set operations to calculate the union of two sets and then look at its size to see if there'd been any duplicate letters in the two words in the first place which is a long way to say yeah i was using an off-the-shelf built-in operation, which is very slow. People then started looking for how they could make the checking as convenient for a computer as possible. And do you remember the menu problem we had? Yes. Where people had to turn a menu order into a number. Yes. People did that.

They took each word and took it as if you were ordering those letters off a menu. did that. They took each word and took it as if you were ordering those letters off a menu. And so they turned them into numbers using exactly the same process, except now you're guaranteed you can't have duplicates of the same letter because every five letter word has five unique letters. So they could turn it into binary. So a 26 bit binary number, each bit is a zero or a one based on if that letter's in the word or not. And then you're doing something called a bitwise and to compare them to see if the two orders have anything in common.

Just incredible. And so that was the biggest speed up that people discovered. And don't get me wrong, there's loads of other great things that they did. So they were doing it in a way where basically they had to teach the computer how to do its own analogy. So it could understand and solve the problem and then spit out the solution that would translate back into it. They basically go to the computer and say, oh, forget the whole words thing. Just imagine it's a bit like a binary number.

Yeah. And then the computer's like, ah, why didn't you say so? Gotcha. And then it's off and racing. I was just thinking we should just find some actual meaningful computational problems like protein folding or something and i will just do it badly in a youtube video and by the by the end of the week people will have nailed it one other fun thing yeah is this whole kind of this word or problem we were working on which isn't actually useful in Wordle.

Well, people actually have been using some aspects of it, but it's Wordle inspired. Turns out people first asked the same question called the Jotto problem in 1968. Wow. There was a game called Jotto, very similar to Wordle, because there's been different variations of this game for a long time. And people had the same question. They're like, oh, I wonder if there's five words, each with five different letters, that use 25 letters between them. 1968.

Now, that was before computers could really be useful for this. So they didn't find the solution I found, the Fjord, Vibex, Waltz, Nymph, Gux solution. But someone revisited the Giotto problem in 1996, and guess what? What? They found exactly that solution. Whoa. So my exact solution was in a paper from 1996, and I'd rediscovered something that we'd already known

for about a quarter of a century. But do you know what I love about this? Is that even though your thing went way longer than it needed to, took ages, and even though technically the answer that you needed was already out there. I hope you're building up to a point here. I am, I am. By mainstream standards, a lot of people would see that as a failure. But by doing it that way, we've learned so much more than we would have if you hadn't done it.

So true. It definitely inspired a lot of people to have a go at solving this programming problem and develop skills and techniques and experience that they wouldn't have otherwise. I think, if anything, you deserve extra dings for that. Oh, thank you. We did find one new thing, though. So even though I rediscovered an old thing by everyone else turning over the soil, they uncovered a new thing

because people started to wonder, forget five letter words. They're like, what's the fewest words that covers the maximum amount of the alphabet? So people adapted the code that people wrote to show that they could write much better code than me to look for words of any length. And first of all, they rediscovered a pre-existing combination of two 10-letter words that between

them have 20 unique letters. Blacksmith and gunpowdery. Ooh. Blacksmith, gunpowdery, two words that cover 20 letters. And that was up until people tried to do better coding than me. I was going to say, I like how they're both like sort of connected to Old West. They are. And they're kind of linked, which is really nice.

In fact, I would do it the other way. Gunpowdery blacksmith. A gunpowdery blacksmith. That was the only known example of two words that between them had 20 unique letters. We discovered show jumping veldcraft. Veldcraft is being crafty on a veld, and a veld is like a grassy plain in Africa. So not wildly different to like orienteering

or like, you know, being able to navigate and follow animals on the veld. That's veldcrafting. So you could have veldcraft showjumping, could be another two-word combo. And veldcraft has nine letters, showjumping has 11 letters, between them no letters in common. So there's another two words, nine and 11 letters,

20 unique letters between two words. And we discovered that because people had to show they could do much much better code than me wow i'm just wondering whether we can do better than 20 letters well on the word lists we've been using there are no better combinations how about if people can come up with two words that between them contain all 26 letters and they sound like words, we will then assign them definitions. And we will have two words that use all 26 or more than 20 letters between them. Let's say two words that sound like words with more than 20 unique letters between them. Yeah. You know what?

If you're going to the trouble of finding it and you feel very strongly that you already know the meaning to that word. Oh yeah. Oh, that's true. Feel free to suggest meanings. Otherwise we will happily. That's the other way to solve the problem. We will happily chat about it and see if we can come up with something.

All right. Deal. Wow. If you haven't got an answer, go to our problem posing page at a problem squared dot com. Instead of picking problem, pick solution. Give us those words and yeah, we'll we'll pick out our favorites. Thank you so much for listening to a problem squared. We very much appreciate everyone who listens to this podcast.

But some people are able to financially support the podcast by supporting us on Patreon. And that's what makes it possible for us to make the podcast in the first place. So thank you very much to those people who mean it is free and commercial free for everyone else. And we like to pick three of our Patreon supporters every episode completely at random. Well, as far as the rand function in Excel is random, and we thank them by name, which this episode includes... Kim Larson. Anders Ort. And potentially Ivan or Ivan JH.

The JH is connected to it, or Ivan or Ivanji. Ivan JH, all one word. That one. Thank you, that person. And indeed, everyone listening. This has been a Problem Squared. If you're not looking forward to the barren wasteland of two weeks before the next episode, we are on the vast majority of the social media platforms as at a Problem Squared,

or however they format their names on that social media platform. My name is Matt Parker. My co-host is Beck Hill. And this show is produced by Lauren Armstrong Carter. Thank you for listening. Hello, Matt. Yeah. Guess what time it is.

It's stale knockoff twisty time. Do you miss the, is this your card? I do miss, is this your card? So these are called knickknacks. Now for the record, there was the pack that was already open. Yeah. And I said, let's just get rid of that one. Yeah.

Then you have not got rid of it. No. No, you've still got it. Yeah. Yep. So opening it was easy. Yeah, it was already opened. It was already opened from when it was given to me. It was given to me by Philip Alexander, a fellow comedian,

who I believe his wife got it from South Africa. They're called knickknacks. They're related to the not the uk they're by a company called simba and they've got a lovely yellow and pink design on them that is that yeah i would wear that is arresting yeah and they went off in May 2017. Oh, good. Good, good, good. That's our wood anniversary. So you smell and I taste. Yeah, they're the rules. They look like twisties.

Very mild smell. It's not pleasant, but it's not overwhelming. Yeah, all right. I guess they've had time to air. They've out-gassed. They have, yeah. That's probably why my kitchen smells so weird. Here's a snap test.

Not bad. These things really hold their snap. I just put my teeth into it and it... It just gave? It just gave, but not in a... It just formed around your tooth. It just went around my tooth. I could use that as a... It's now a mouth guard. Yeah.

Flavor's not bad though. Oh, okay. Yeah. Oh. Very greasy though. We should get fresh ones. My fingers are oily. Yeah.

Yeah. If anyone listening has heard of any of these chips and they're like, no, you've got to try them the real way around. Like send us some. Send us some. We'll find a way. Drop us a line. Drop us a line.

We'll give you a postal address. All right. Bye. you you