A Problem Squared - 133 = Oeuf-Bran Geometry and Huffman Decoder Tree

Episode Date: April 27, 2026

🥣 What percentage of a box of Weet-Bix is wheat again?🥚 What shape is an egg? 💬 What’s the most efficient way to write your name on a Pop-it Fidget Toy?👎 And would you like some AOB? We won’t take no for an answerHead to our socials to see all the Weet-Bix Pix, lots of names efficiently spelt out on a Pop-It Fidget Toy, lots of Girl Scout cookies, and a sheep being sheared by a robot…The Sheep’s Back Museum, Naracoortehttps://thesheepsbackmuseum.org.au/Creation: Between Art and Mathematics Exhibition in Paris: https://www.ihp.fr/en/news-science-and-society/creation-between-art-and-mathematicsLaura Taalman’s Granny Life Crochet:https://www.grannylifecrochet.com/ Get your own Egg-Shaped Spinning Top:https://mathsgear.co.uk/products/phitop Eve’s beautiful cross-stitch:https://www.instagram.com/p/DWY-_qzivz6/?utm_source=ig_web_copy_link&igsh=MzRlODBiNWFlZA%3D%3DMatt has extended his tour - and filming the show in London in October - all the dates, venues and tickets can be found here:http://standupmaths.com/shows And there is a Kickstarter to fund production of the filmed show, which you can get involved with here:https://www.kickstarter.com/projects/standupmaths/getting-triggy-with-itJoin us on Patreon for early releases and our monthly bonus podcast I’m A Wizard!If you’re already on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on our pinned post!  If you want to (we’re not forcing anyone) please do leave us a review, share the podcast with a friend, or give us a rating! Please do that. It really helps. Finally, if you want even more from A Problem Squared you can connect with us and other listeners on BlueSky, Twitter, Instagram, and on Discord.

Hey, just before we start the show, it's me. Self-promotion, Matt. I'm back on tour in October. If you want to come and see my show getting tricky, and more importantly, I'm going to film it. And I've got a Kickstarter to fund the production of that stand-up special if you want to get involved. There'll be a link in the show notes. Appreciate your support. And now on with the show. Hi, everybody. You're listening to yet another episode of a Problem Squared. This is the Problem Solving podcast where we try to solve your problems. And it is the podcast that doesn't take.

No for an answer. Nor does it take yes for an answer, because both of those are way too simple answers with a complete lack of detail. This is the podcast only takes long, complicated explanations as an answer. I'm joined by Beck Hill, comedian, writer, performer, and doesn't take slow down for an answer. It is currently recording this balancing near a... railway station hot spotting to a phone in Melbourne.

But yet, it's still with us. What we're trying to say is that quality is probably poor. And we apologize for that. But hey, you're here. And I'm Matt Parker, mathematician, performer, and I don't take O for an answer. It's pronounced zero. And I won't go through this again.

And on this episode, I'm going for a breakfast theme. That's what I'm going to say for now. Oh, intriguing. I've worked out the most efficient way to put your name into a children's toy. After a friend of mine wouldn't take no for an answer. Oh. And there's any other bo's-ness.

I will take Bo as an answer. So, Beck. We've already foreshadowed this, but how you doing? Do you know what? I'm, yeah, aside from difficult connections and doing the best we can to bring this podcast to our listeners despite obstacles, I'm doing well. So I'm in Melbourne now, but I just spent the week in Maracourt at my dad's place. And when I was there, so my dad volunteers at a museum called the Sheepsback Museum. A little shout out to the Sheep Back Museum.

and he had to go do some stuff there in the evening so while it was closed and I went along with them and he was like oh yeah I'll show you some of the exhibits the sheep's bank museum is a largely sheepshearing dedicated museum I'd guessed as much so a lot of the exhibits are in old sheep shearing sheds yeah that checks out and there were definitely moments where I had It's nighttime. He's like taking me into these sheds where it's like, you know, those like fluorescent lights blink on. And there's just like loads of sheep shearing stuff like hung from the sides.

Rusty shears and stuff like that. Yeah, it's got a real horror film aesthetic sheep sharing equipment, particularly old. I found it so amusing because like it's not scary. and my dad's a delightful dork. You come from a long line of delightful dorks. Yes, that's right, from the delightful dork dynasty. The old DDD, so I say. The old triple D.

Yeah. You know, I wasn't scared. I was fascinated generally. It's very exciting to be in a museum at night. I felt like Ben Stiller. Not only that, but there's like a sheep shearing, machine in there that was made in the 80s and it has like the instructional video for it. The instructional video makes it look like it was a clockwork orange for sheep.

Can I? Yeah, can I just clarify here? Because there's a range of possible machine levels for sheep shearing. Yes. On one hand, you've basically got fancy clippers on an arm that a human can kind of to help moving around. Yeah. On the other end, you've got a giant box with a hopper at the top into which you can

throw a sheep. I just want to know where on that range are we talking. Oh, it's like past the box. Oh. It's like we're talking like Wallace and Gromit level. I'm going to send you a small clip that you can describe. I'm not going to put it, we're not going to put it on socials because I don't know what the rights are, but I would like you to describe.

I don't know if I want to. I've seen the holding thumbnail and I'm already regretting so I'm going to watch this. But here we go. A sheep is automatically captured and loaded on the shuttle. The operator attaches the head and leg restraints which holds the sheep in a suitable position for machine shearing. The leg restraints clip on very easily. Oh my God, that is jaunty music for a sheep is automatically captured. Okay.

I'm seeing, oh my goodness, okay, I'm just pausing that for a second, it's too much at once. I'm seeing a sheep strapped into a machine. So its head is put in like, not a giant muzzle, but not dissimilar, all its legs. It's like being strapped onto a... Like a pommel horse. Like a pommel, yeah. So I was watching this and I was like, oh gosh, this is terrifying. Because I always imagine, whenever I think of wool, I think, it's the same as,

like when you give kids like farm toys to play with and all the animals are smiling and they're never like crammed into tiny cages and like you know that you never see like the sad part of farming right yeah and i think this is similar because in my mind i always got that sort of mental image of you know like the the guys with the shears and like yes the sheep might struggle a little bit But it feels closer to like trying to give a toddler a haircut, you know? Like it's like I imagine they're not traumatized for life or anything. It's uncomfortable. But then, you know, they're all shorn.

And Australia's hot. So they're probably grateful for it. And then we get these lovely jumpers for winter. You know, like that's how I imagined it. And then this machine made me so sad. And then I was delighted to find out that only one of these machines was made. So it was called the robotic shearer. And the funds ran out before the project reached a marketable system.

The failure of oversees markets for wool and the removal of the floor price saw the industry go into deep depression. Some key funding was withdrawn and the project was closed down. Yeah, whoever invested in that got fleeced. Hey. That's my one joke for the episode. Yeah, you've hit your quote. No more, please.

Oh, now it's being rotated into the machine. It's going, it's on like the world's worst merry-go-round. It's been designed to remove the fleece as efficiently as possible. There are now two robot arms, shearing the bolted-down sheik. Close-ups of the blades. The arm movement is controlled by computer software. I think it's more 80s than the shearing arm is controlled by computer software. software. Wow. That is just a sheep torture device. Right. Can you believe they only made one of these machines?

This is like sore but for sheep. Wow. Okay. Thanks. I wish I hadn't watched that. When they were using it, like get more funding and stuff. They turned the wool from it into some nice socks and then they sent out the socks to like, you know, guess of honor at events and stuff. Yeah, because in marketing, as they say, socks sell. Oh, it's two jokes. That's exactly what they say. You're too funny for this, Matt. I don't like it.

Incorrect. Because the machine never actually, like, made more. The money invested was obviously lost. So technically the pair of socks cost. cost like $10 million. And there's a note in the museum that's like, the museum is eager to obtain a pair if any still exists. So if anyone listening has a pair of socks from this robotic shira in the 80s.

Promotional wool socks from the 80s. What about you, Matt? How have you been? I've been doing well. I've just had my second of two lots. of American visitors. I don't know why people from the USA are keen to not be in the USA at the moment, but a lot of my American pals have been heading to Paris because there's a big kind of illustrating mathematics, math art crossover event that's been running this year, culminating in a big math art exhibition,

which is very exciting. If you want to go along, my friend Laura Talman has a huge... It's a crocheted, you know, granny squares where you crocheted granny square and you put a bunch together to make a blanket. Yes, I don't think I ever knew that they were called granny squares. It's illegal to make them if your offspring haven't also procreated. And Laura did a version of these. You can get cellular autonomy. There's a whole thing called Game of Life where you start with initial states and there are simple rules that allow them to evolve.

and you can get 2D ones. And so Laura did Granny Life instead of Game of Life. And people all around the world crocheted Granny Life, Cellular Autonomer Squares, sent them all into Laura. And she, I forget how many, so many of these things. And she put them all into a giant double-sided blanket. If you do go and see it, the exhibition is called Creation. It's at a place in Paris.

I think it's the Harry Ponqueray related thing. I love those books. Somewhere in the show notes. Yeah, there you go. Harry Ponqueray and the Sorkai-Seris is Sloan. That's the one. Yeah, yeah, yeah. It's the French knock-off version.

Yeah. It's the bizarro world Harry Potter. Yeah, which is probably less bizarre. It's all super inclusive. Yeah, yeah. Yeah. Anyway. Oh, to go to Bizarro World.

Bizarro World. If you do go and see it and you marvel at how well aligned the squares are on Laura's artwork, it was because we spent a fantastic afternoon and evening on my dining room table, working out how to lay out a grid on a massive bit of material that was going to be the central load-bearing part of the artwork. And that's now, it's now suspended in the exhibition, which is on, right through until 25th of July. But I also had some other friends visiting. My friend Alyssa was like, hey, do you want anything from America?

Because they were flying over. And when we visit them, we'll often bring, you know, British or Aussie things. And I was like, I'll just bring anything super American. And she's like, oh, do you want some Girl Scout cookies? Oh. And I was like, okay. I don't think I've ever had any. I had never had Girl Scout cookies.

And I was like, it's such a staple of like American culture as far as I can tell. Yeah, I know. about them, but I couldn't say I've ever had any. Exactly. I was like, let's do it. Bring some Girl Scout cookies. Now, here's a question for you, Beck. When you imagine Girl Scout cookies.

Yeah. Are you imagining A, cookies lovingly baked by Girl Scouts that they can then sell to raise money for charity? Or are you imagining B, cookies mass produced in a factory and packaged down? up so they can be sent to Girl Scouts to learn the value of capitalism.

I'm afraid I know it's B because I've watched so much American media where I know they're like, put me down for 20 boxes. So I knew already that they don't, it's not like, it's not like a bake sale. It's the Avon of, it's to get little girls into Avon early. It's my first pyramid scheme. Yeah. My first multi-level marketing scheme. Yeah.

So I'm holding a box of thin mince. Are they any good? Which I have until September to eat. Ooh. They're fine. Do you want me to save them for you when you get here? Please. I love, is it like mint chocolate?

Yeah. I love mint chocolate. Great. Well, because they came with two cylinders, two racks of thin mints. They're like disc-shaped cookies. And we already opened and consumed one stacks worth. But the other one still separately sealed. And they're good till September.

So I'll wait to a both in the same country. But I did like, there are five essential skills that these cookies are designed to teach Girl Scouts. Do you want to have a guess what any of the five skills are that Girl Scout cookies are designed to pass on? Entrepreneuralsam? No. Oh, social skills. Like the idea of being able to talk to people. Correct.

Skill number four, people skills. Yeah. Girls find their voice and build confidence through customer interactions. Sure. Now, entrepreneurial, I'm actually going to give you one because skill three is money management. Girls learn to create a budget and handle money. Okay. I mean, yeah, that's not quite what, but yes, thank you for giving that to me.

I could also give you point two. Point two's decision making. girls learn to make decisions on their own and as a team. No, I don't, I'm not accepting that as a skill that you're not taking that one. That's not. Okay, fine. They're really reaching there as a. Well, there's two I haven't read out yet.

So get ready. So the other ones that I would do, stock management. You know, you've got to look at supply and demand. No, they get given huge quantities of these and they don't go off very quickly. So they're great in that regard. Great stuff. Marketing skills, I guess. Marketing would be that, would be self, the ability to.

Lying? No. I'm afraid that's a winner. What? Yep. So you skipped right over. The first one is goal setting. Girls learn how to set goals and create a plan to reach them.

Okay. I guess. Uh-huh. But number five, business ethics. Girls learn to act. ethically both in business and life. Yeah, there's no ethics in business. Selling cookies.

Selling cookies teaches you ethics because, I don't know, what are you going to blackmail your family into buying them? You're going to lie? Yeah, there you go. So I'm going to give you that for lying. I would like to learn more about this. I can look it up, but I suspect that we have some American listeners who either have a lot to tell us about it.

Maybe we've even got some Girl Guide, Girl Scout leaders in. Yeah. If you know specifically about this or have heard a very interesting episode of a podcast about it or something like that, please go to our ProblemSquared.com, select solution. I would very happily just look into that. It'll take a while before we loop back around to this because we'll wait until Beck and I are in the same room. so we can both enjoy eating these crisp chocolatey cookies made with natural oil of peppermint.

There you are. Next time we're physically in the same space, Beck, we'll check back in on the Girl Scout cookie mystery. Our first problem comes from Beck, who's done more Wheatbeck's research. So it's the second installment of our... now long-running feature, Bix and Pieces. Bix Hill, just call me.

So last episode we heard from Notster, who wanted to know what percentage of a box of wheat bix is wheat. And I stupidly thought that the fact that the box says 97% wheat was enough. And Matt, you refused to take that for an answer. answer? That was deemed insufficient for it was the entire box we believed. Not still was talking about. So Matt, you gave me some suggestions of how you wanted me to check this. Now, unfortunately, your request to fill an entire box with milk to work out the volume. Yep, the volume of the gaps. With the bicks in there was vetoed by my dad, who I was with that week, because he was like,

that is a waste of food. There are other ways we can do this. You're going to then eat them all. That's why you use milk. In one sitting, I think not. By the way, wheat bicks now have a recipe on the side of the box for overnight wheat bicks, and that can fudge right off. What?

Okay, I have feelings about overnight oats. To me, overnight oats is cold porridge, or that is just lazy musely. Oat Oats is left over granola, like it's granola at its worst. Yeah. I'm angry, right? I love porridge. I love granola. I love musley.

Overnight Oats, I don't have many enemies in life, but Overnights or Outs is one of them. You've never been eating like granola or musely and thought, if only this was way more soggy. Right. Properly mush. And then we pick so like, oh, we'll get in on that action. Wee Biggs, get back in your box. Trend chasing rubbish. No deal, Weebbix.

Absolutely. For any UK listeners who are like, isn't it Wheatabix? No. In Australia there is a brand called Wheatbix, W-E-E-E-T-B-I-X. We are not sponsored. This is not an advertisement. I'm merely going by Nautster's request. If any British people want to put in a Wheatabix problem,

No, no, Matt, don't you dare join the same pile as overnight oats in my enemy list. I don't know. My dad buys a lot of wheat bics, so he had 1.2 kilogram pack, which was the other reason he vetoed the milk option. It would just be so much. It's a good amount of wheatbacks. So we weighed the whole pack, which came in at 1.317 kilograms. Excellent. So the empty carton weighed 60 grams.

Yeah. The plastic liner was another 7 grams. Yeah. That brings the weight to the weight to the contents to 1.25. 50 grams for free. Yeah. Well, 50 grams in a 1.2 kilo pack. You know, don't get too excited.

Yeah, it's not much. Actually, they're pretty close to the line in that regard. Yeah. Yeah. So we measured the. entire pack to get 4,800. I'm rounding just for the sake. Otherwise, it's just a lot of numbers.

Close to 4,800 cube centimetres. So you basically measured all three dimensions. We measured as many dimensions. We could, yeah. So the weekbics, 72 weekbicks and a pack. We divided the full dimensions of the pack by 72 and got 66.6.6. cube centimeters is a maximum upper volume per bix.

Yep. And then 1.25 kilos divided by 72 gave us an average weight of 17.36. Now I think on the pack, I might be misremembering where I feel like the average weight on the pack when it says like per serving is closer to 15.5 or 16.5. But anyway, close enough. Anyway. So we took the least. damaged looking bicks from the bottom row as our sample.

We measured the dimensions of the individual bicks. This is so good. My dad very kindly typed up the steps that we took because he knows that I would forget that. That's how we do it. So I will take a photo so that if people want the exact dimensions afterwards. We took the measurements and then got the volume of 54.18, cubic centimeters. So that's about 81% of that upper range that we got earlier.

Of the volume, yep. Yes, of the volume. To check how our sample bics compared to the average, we weighed it as well. So the one that we weighed came in at 19 grams. Oh, that's because it was the most intact one. It's almost 9.5% heavier than what it should have been based on our earlier calculations. But because we were like, hang on, there's quite a lot of air in these, you know? Yeah. They're just sort of layered flakes. So we stuck it in a blender. And we reduced a dry

bix to 30 milliliters of powder. It's so small. Like when you blend a bix, you don't realize how little amount you've got in there. It makes me feel less. less bad for eating six. I'll say that much. I don't think that's the moral we should be taking away from this. But the measuring cup that we had was one of those like medical sample cups that had that had been unused. It was clean.

Oh. But I do have a photo of it in there, which we will post on social. So I'm just explaining why it looks like someone's had some dry urine sample. To be fair, you should seek medical. advice if that's what your urine. If that's what your urine, I mean. So it was a 45% reduction in volume. And even then, like, obviously there's air between the particles, but, you know, we didn't

have an official weight of vacuum packet. So then we wanted to double check that this wasn't like a one-off bix. So we took a new bix from the top of a brand new box. And that weighed to 17 grams, which is much closer to our original, like, oh, this is what we think it would weigh. then we compressed that powder you know stuck that in a blender that came to 25 mils so we thought why not just take an average of the two so we came up with 27.5 milliliters doing some great size yeah then we multiplied it by 72 bicks per pack and we got 1,980 mil the packet says the ingredients

are 97% wheat so removing 3% we got 1,920.6. milliliters of pure wheat that as a percentage of the box volume that we got earlier from our dimensions is 38.6% so that means that no more than 38.6% of a 1.2 kilogram box of wheat bicks is wheat by volume contrasting with 92% of the box is wheat by weight. That's great. And I guess the remaining 8% or 61.4% is pure Bix. I figure that's the... Yeah, that's right. Yeah. You're either wheat or your Bix. That's what they say.

Because I just put like roughly 40% is wheat because I was writing down, these are my rough notes that my dad so kindly put into better notes. So I had like 40% wheat in a box, 1.2, kill. the ground box. 60% equals air, other stuff and box. Now, I don't want to speak on Nostas behalf here. I really like the doing it by volume way. I feel like that's the most honest way of breaking this down. I agree. So I think 38.6% wheat is a really nice answer.

Just over a third. That's good stuff. Thanks. Now, I think that's excellent work. And I'm sure Nost will be in touch. with a ding very soon. But there's still the open question of did your dad have one of the collectible metal tin wheatbecks boxes?

Oh, yes. He did. Excellent. I'm so excited. But I believe it belongs to my stepmother, Yvonne. So I think that also might have been the reason that the filling it up with milk was vetoed. Now, look, some listeners might be like, that's all very well in good, Beck.

But now this wheatbecks problem has taken up the space of two problems. We don't want to get ripped off. We want our problems worth. They're thinking what percentage of these problems is wheat? Yeah. Too many. Too many is the answer. So I've chosen one other problem, which I've got to say the cursed words again,

but I think is a relatively easy solution. Rebecca. I know. Oh my goodness. I know. I've manifested it. But I've chosen another problem if you would like to announce it, Matt, because I thought, why not?

We'll go with the whole breakfast theme. This easy, quick problem that we're going to bash through was sent in by Josh, who went to the problem posing page at a problemsquare.com and said, hi, Matt and Beck, I recently, and they clarify about two minutes before writing this problem. had a problem where they cracked an egg that annoyingly cracked along the long dimension of the egg, which, they say, led to a less than desirable fried egg outcome. I guess it kind of tumbled out the wrong way.

Now, Josh then thought to themselves, I hate it when an egg cracks along the semi-major axis. I think it's probably the major. Anyway, along the major axis. Josh then wondered whether an egg could even be said to have a semi-major axis, as it's not an ellipse. Their train of thought led them to the much more philosophical and mathematically interesting question of, what shape is an egg? Oh no.

Oh, no is me. That's my director's commentary. Is there a more accurate description for the shape other than egg-shaped? And Beck, you're going to do this in a quick, neat and tight. package off you go. So the quick answer is that an egg is an oval. That's where the word oval comes from, like ovoid. Oh, interesting. Oval comes from the Latin Oven, literally meaning egg. So you could argue whether you're talking geometry or technical drawing or things like that. They all have like different ideas of what the shapes are called.

and it depends in like what term you're using it. But you could argue that because Oval comes from the word over meaning egg, that whenever you use the word oval to not mean egg, that is technically wrong. Okay. Now, here's my take. Because you also, I think you said Ovoid at one point there. That's a three-dimensional version.

So technically an egg, like if you're talking about an egg shape, two dimensions, that's a, you know, oval. In three dimensions, Ovoid. What I'm saying is, Oval and Ovoid both come from OVim, which mean egg. Ovoid is the much more recent egg meaning word. Oval has drifted away from its original eggness. Oh, certainly. But technically, that is what it's supposed to describe.

So apparently in geometry, it's not super well defined. Like, oval can mean egg-shaped, oval can mean like the sort of a sports oval, which we've talked about before, like the stadium shape almost. Like it's... We're back to our friend, the disco tangle. Yes, yeah, exactly. It can mean any of those things when it's sort of used more generally. Agreed.

And then as a... the same before, Ovoid is the three-dimensional space by rotating an oval curve about one of its axes of symmetry. So a circle, a sphere, has the same radius or diameter in every direction, whereas once you've got an oval, one's bigger, one small, which is why Josh referred to the major, major axis, or semi-major, which is the radius, for the long direction on the egg as opposed to the short direction. Yes. So we would say axis to mean diameter and semi-axis to mean radius. That's the translation. Yes. Now, if you say ovoid meaning three dimensions, then that is still something or even ovate

is still used to describe like a three-dimensional egg shape. So you could just say that. Josh, that's your answer there. If you're talking about like a drawing like a two-dimensional egg shape and you're like, oh, oval, that could get confusing, which I get. Egg shape, very much accepted. Egg shape. Yeah. Great answer. And I did find that in technical drawing,

oval is a figure that is constructed from two pairs of arcs with two different radii. Oh, those rebels, come over here, take our words, hear them new meanings. Outrageous. Well, I mean, or going back to the original meanings. All that, all that true, very true. Now, if you want something that's really egg, like proper egg, and you may have come across this in your research back, I'm 97% sure there is a shape called a super egg.

And I haven't Googled that, but I feel like, and I feel like it's more of a design, fun looking shape that's not necessarily egg shape, but I think a super egg is a very well-defined shape in mathematics. I'm going to Google it right now. I'm already way ahead of you. Oh, great. What do you got? A solid of revolution obtained by rotating an elongated super ellipse with exponent greater than two around its longest axes.

Yep, that's it. Ah. I don't understand any of that, but there is a picture, and to me it looks like the capsule that you get in a kinder egg. Yeah, it's way too squat to be a real egg. But it's super. It's like extra egg. You need space per extra eggness. I don't understand what makes this extra egg.

I don't. It's just really so much egg. Would you say it's been over-egged? It's been over-egged. The amount of egg per egg is off the charts. I wouldn't call this a super egg. I would call it an over-egg and I would be happy with that. It should definitely be called an over-egg.

You're absolutely correct. I'm just looking here. This is fascinating. The shape was popularized by Danish poet and scientist Piet Hein. Super eggs of various materials including brass were sold as novelties or executive toys in the 1960s. Who writes this nonsense? The volume of a super egg could be derived via squigonometry. You're just making out words now.

I've got a golden ratio ellipse spinning top, which is just a very nice machine bit of metal. shaped a bit like a super egg but pointier. And it's just a fun thing that you spin. I guess that's basically still an executive toy. It's fun. Hey, I just found out where I'd come across the fie top. It's because I sell it on Maskier. There we are.

So, mystery sold. I see. All just a ploy. Oh, now that's some organic marketing. So Josh wanted to know what shape is an egg? The answer is egg shaped. And is there a more accurate description for a shape other than egg shaped? Well, you could say Ovoid.

Beck, again, I don't want to speak on behalf of Josh, but that is a ding if I've ever heard one. That's a nice, neat, comprehensive answer. So, well done. Yes, we did it. We've closed it that. Forever. The end of the breakfast era is upon us. We did it.

We've fulfilled the most basic promise that this podcast makes. Our next problem was sent in by none other than Jay Foreman, friend of the show. People may know from Matt Man on YouTube. Yes. So he sent it in by a text and then pestered you in person, Matt. Yeah, he messaged it to me originally. and then we happened to be catching up in a pub last week and he brought it up again. So I feel like I have to deal with this now. So he said my son was playing with this and you've shown me an image of,

it's one of those fidget toys where it's like a popper, I think they're called. It's a bit like a bubble wrap. Yeah. Basically someone invented the tension sheet from from Red Dwarf? So it's the thing where you poke the little round circles inside out and I've played with these, I've had them on key rings. And Jay couldn't help but wonder,

what's the most efficient way to turn this into a device you can write your name in? I understand. I've tried to do this myself. So the least efficient is obviously just to draw one letter. The most efficient would be to drop a very, very, very, long list of names. Each one assigned a number that can be expressed in binary. Then said, or sweet spot, some kind of clever Hoffman tree optimized for letters that appear

often in English names. I will say, I have no idea what that last one means. I'm sure you're going to tell me. Over to you, Matt. We can. Now, I sent you some photos while you were saying that, as we are recording remotely. So I had the photo of Jay and I in the pub, and Jay had brought up the messages he'd previously sent me on his phone and we got a shot of him reminding me about this. Can I just say, by the way, this is very cheeky of Jake, because we've had several like map related problems that I have tried to get him to answer for us. And we chased him and he was going to record stuff and then it just kept getting left. And he never ever solved any of our map problems for us for the show. And yet here we are solving his problem. Unbelievable.

bullied into it. He did apologize for the map stuff when I saw it. Very busy. And often he just didn't have an interesting answer. But if we do this now, Beck, we'll have a J favor in the bank. And so next time, we can deploy that on any map problem of our choosing. Yeah, send us your map problems. Send us map problems because we're about to have a lot of J favors. So in the pub, I actually ordered one of these, I haven't got a child, but I ordered one of these children's fidget toys. I put an M-M-for-Matthew into it, and it's kind of fun. So it's a six-by-six array of poppers that can go up and down, and you can just view it as a 36-pexel,

six-by-sex, on-off thing for making very low-resolution images and indeed letters. And I may have got a little over-excited. I ended up getting four of these, and so I quickly knocked out a full mat so we have the whole the whole thing there

I've gone for inconsistent orientation while doing that I don't know if that's going to bother you I sent you a photo of all four some of them are horizontal some are vertical It does slightly I feel like the orientation could also come into play with this

Yeah yeah Yeah in my defence Not all of them have the dividers running the same way. By divides, I mean there are like lines. So they're clearly split into rows. And for the three on the left, they're split into rows where each row is a single color

and the whole thing is like a rainbow. But there's one where they're split at 90 degrees. You're right. So every row gets one of each, which again, a little displeasing, but what are you going to do? This does bring me to the point that split into rows.

So for any one, you've got a set of six rows, each with six poppers in it. You could try and encode one letter of your name per row, because there are fewer than 32 letters in the alphabet. I picked 32 because that's 2 to the power of 5. So there are 32 ways to in or out five of these poppers. So you could have the binary from all the numbers from zero to 31 just by using five in each row. In fact, you could use the sixth one as the uppercase lowercase bit. So it's actually just the last six bits in ASCII code for those of you or your ASCII heads out there.

So it is actually a very tempting like encoding device. If you wanted to encode up to six characters, case sensitive. that would work really nicely on this. But obviously some names have more than six letters. But in the extreme, Jay's like, well, you could just have a big list of every name and then just assign each name a number and then just put that number in in binary

where like popping it out is one and in is zero. And then you can encode a giant binary number. And that actually works really well because there are 36 bits of data on. this thing and two to the power of 36 is just over 68 billion so you you can encode numbers actually you can code numbers anywhere between zero and 68 billion 719 million 476,735 that's your full range and that's more than the number of humans so Not only could you encode your name.

We could all have our own pop sheet. Yeah, you could encode a specific person. So even if you've got multiple people with the same name, you could still be precise to the individual if everyone on Earth was assigned their own binary index number. And goodness, that's the world we all want to live in. Are you telling me that if every person had one of these six-by-six popper sheets, that every single person on Earth could have their...

own pattern on the publisher sheet and that is only true to them. Yes, not only am I saying that. I'm also saying, as I frantically do some work on my laptop here, every single person on earth could have eight each. Why aren't we using these instead of ID? We don't need passports. We just need these. No.

Everyone gets eight. They're their unique eight patterns. And that's it. Job done. And then it just checks it in a system and then there's a photo of you. and they go, oh yeah, that's you. That tracks. Yep, that's you.

Yep. And I don't think anyone's ever raised any objection to some kind of global government database indexing every human. I feel like... Hang on. Is this why these are popular now? It's why they're popular and it's what the Book of Revelation was trying to warn us about. That's what you heard it here first, folks. Now, that's kind of a proof.

ridiculousness where it is possible to encode every single human onto one of these. So somewhere in the middle between using it as a screen to display one character to using it as a binary index record to identify any unique human on earth, in the middle, there must be a nice balance because using it as a screen, you don't need to know anything else. You can just look at the popper and read the letter. Whereas a number that indexes every human, you then also need the giant database of every single human and what number matches to them. So in the middle, there's going to be something which is a bit easier to read than needing the entire database of every human, but has a bit more data than,

a single character. So there's going to be a trade-off in the middle somewhere. Okay. And I'm guessing this is where this Hoffman tree thing comes in. Please explain to me what a Hoffman tree is. So a Hoffman tree, so in regular ASCII, every character has eight bits. Although they're not really all needed. You could do case-sensitive characters with six bits. Then that's what I was referring to earlier. That's a little boring because every single character gets the same length, code word, we call it a code word, you know, number assigned to it.

And that is like nice and unambiguous, but it's not very efficient because you've got to use six poppers every single time you want to put in a new character. A Hoffman tree is like, oh, what if the really popular letters, you know, your A's, your E's, what if they had shorter numbers and the less frequent letters or even combinations of letters have longer codes associated with them. And so what you can do, and Morse code does this, because if you look,

actually, let me just check. Morse code, the shortest things in Morse code, I believe, are the most frequently used characters. Let's have a look here. Yeah, so E is a single dot,

and T is a single dash, and they're very common letters. Whereas, like, your Zs and your Ys are like four dots and dashes. And in between ones, like A and they're much shorter. Now, Morse code has to have spaces so you know where one character ends and the next one starts. So, in fact, Morse code has three, has dot, dash, and, you know, pause.

Your friend of mine, Eliam MacDonald does a fantastic thing about ambiguous Morse, where if you move the spaces around and the same stream of dots and dashes, it changes the word into other valid words. It's very interesting. Yeah. We can do a same thing with buying. Actually, I did, not to get ahead on our game here, I did download a file with all the names in it. Of course you did. Everybody drink. Matt downloaded a file with everything of something in it.

Let me just real quick here. The most common letter in names by a long, not a long shot, but a decent, decent margin is A, followed by I, followed by N. they're your really common ones. So we could give them like two, two or three digit binary numbers each, and then the less common ones can have much longer ones. The only issue is to avoid the problem of needing a third symbol for gap, because otherwise we're back to one per row, and that's not going to help in terms of efficiency. We're about to pack these things together, maximize our space.

We can't have another symbol for gap, because we've only got pop in and pop out. So what you need to do is pick your longer ones, so none of them start with any of the shorter ones. And that limits what you can choose, but it means it's unambiguous where they start and stop. So if A is, for example, 1-1, you need to make sure no other code word starts 1-1.

So if you see 1-1, you know, oh, that's not the beginning of a longer one-one. one, that's all of A. Right. And then you start again looking at the next one. And so actually the process of generating the codes, people had done it for like just normal English language. I then went and found the biggest text file of common as many as they could put together

first names in the single file. So I could download it and analyze it thinking I could then try and turn that into a Hoffman tree. You got to kind of do a frequency analysis first and then you roll it into a tree. by combining nodes with the least common ones first joining. And then the reason it's called a tree is because that's the kind of diagram you use to work out how to assign the code words without accidentally clashing. So none of the longer ones start with something that is also used as a short one.

That's why David Hasselhoff is just called Hoff, but they've got like those are the starting letters. Now no one else can use them because they're the hoff. That's right. Yeah, yeah. David Houselhoff is the most common hoff. That's why they got the shortest, the shortest name assigned to them.

I think there's more, I think there's more truth to that than I initially expected when I started that as a joke. Now, at the end of all of that, I realized I couldn't be bothered doing it. Important thing to know. It was too much of a hassle.

Hoff. Too much of a hassle, exactly. So, I want to be all Hoff, no hassle. You know my mottoes. Yeah, that's true. And so I decided instead is just split. Like if you took all the names, okay, I've got 45,231 first names in a document. I've taken out non-character characters and I've removed duplicates and all the usual jazz.

And it didn't have Beck in it. So I've added Beck. Wow. I know. I mean, to be fair, Beck is not like the official name. It's a nickname, but still. I know, but still, it's a bit upsetting, isn't it? So it's now got Beck.

Thank you. And I sorted it into alphabetical order. So for this system to work, you would need that list of names. And then each popper just tells you left or right. So the first popper is, are you looking in the left, the first half or the second half, the left or the right of all those names? And then the second popper tells you within that half, do you want the first half or the second half, the left or right of those?

And then each subsequent popper just tells you, when you split it in half, do you take the first half or the second half? And eventually you go down to a single name. What's nice about this, unlike Hoffman trees or asking anything like that, you can't run out of space because you never need more than like 16 poppers to encode any name. So, do you want to give me a name? Like obviously I've tried Beck and Matt. Or I haven't done Laura.

Shall I do producer Laura? Do Laura. Do producer. Okay, here we go. I got Laura. So the first thing you do is you've got to find the absolute midpoint name in all the names. Which is the name Leff. It's like Jeff, L-E-F-F-F-L-E-E-V-E-I.

So the two middle names are Levi, L-E-E-V-I, and left, L-E-F-F. And that's interesting because you think like M and N, M-to-N is the middle of the actual alphabet, but this is weighted. There's more names starting with the first half of the alphabet than there are with the second half of the alphabet. Correct.

You look up left. Here you go left. Perfect. You've then got the middle of the first half. It's Edvard and Edvaro, but they look like Scandinavian D's. O's. Well, it wouldn't be a problem squared if we were pronouncing them correctly. So true. So true. So anyway, you get to the ADVARD split and you go right. Then you get to the

higher split and you go right again and you keep splitting and moving. The whole thing, from the beginning, from left, you go left, then you go right, right, right, right, right, right, right, right, right. left, left, left, left, left, left, right, left, and you're at Laura. And then you throw a Hadoican. And you're at Laura. Yeah, exactly, yeah, yeah, yeah, yeah, yeah. Yeah, and then you're done, then you get there. That's awesome.

I love that. You've created directions to Laura. Yeah, yeah, yeah, yeah, yeah. It just gives you turn left, turn right, turn right, turn left. Yeah, and at the end of it. What you've created is a GPS, but. for names. Yeah.

And after 16 or fewer turns, you're always at a single name. That's so cool. I like that. It means you can do, at the level I've done it with like 45,000 names, you can do two names per popper. So, or we could have a separate list of surnames. And you could find your last name by left and rights as well. The embarrassing thing is, did it take me more than 16 episodes to guess how many dice were in the jail? We could have just lift or write it on one.

You could play guess the name and we'll do it in 16 or fewer. Yeah. If you had to say, is it above or below this name? Yeah. Yeah. Turns out I'm not good at guessing. No one is, mate. Yeah, so it's still a tree-like search.

So I was inspired by Hoffman trees. But I just thought I'd do a binary search. And it is actually the index by a different name. name. It's just another way of assigning binary numbers to a thing, but I thought it was a nicer way to understand it that would make it more user-friendly. I mean, you say user-friendly. You do need access to a file that has all of the names. Or a printed book. Sure. You need a decoder, is what I'm saying. This isn't something that someone could easily read. Yeah. And once you're using a separate decoder, some kind of look-up table, the data can be way more dense, because all you have

have to do is encode an index in that lookup table in the book. Whereas if you're doing it as a character or ASCII or something, you've got to encode all the information has to be actually encoded into the thing. You can't just point somewhere else. Okay. And so to get every name, there's not enough memory. I'm talking about the children's like a baby toy here. There's not enough memory in this fidget toy to encode it entirely on toy, some of it has to be server side in a book, in the cloud. That's what I'm trying to say. I think the only way to get a resolution on this problem is you need to put in Jay's name

onto one of these, J-A-Y. Oh yeah, I can do that right now. and take a photo and don't send it to him we'll put it on socials and he should listen to this episode and he will realize that he needs to go to the post that we've done

to see his name on one of these and then once he goes there he needs to go left right right left right left left right left left left right left left left left left right left left left right left left left right left left right left j and really is there a better way to spell out a map man's name than with directions than a series of directions absolutely not i'm giving it a ding and now it's time to take bonus for an answer in any other bonus now to start with a lot of our aob this time is microwave themed. It seems

microwave chat was very engaging. It warmed people up to interacting. First of all, Madam Silver here, on Instagram. Look at them, hitting us up on the socials. They said, no idea if this is true for all microwaves. But if you hold down the

two button, it turns the beeps off. What? A much safer way of de-beeping than deconstruction minus ding. They're saying the microwave means that you're minus ding. There's no ding.

You're minusing a ding. That's very funny. I thought they were undoing my solution of dismantling a microwave. I mean that too. Well, hang on. If you just hold down the two button, at what point do you get to crack out the screwdriver

and open up the microwave? That feels like it's kind of removing a lot of the fun. Though that's way safer. Okay, everyone. Can you check on your microwaves? Because I haven't got a microwave to check. If you can hold down the two, I haven't got one because of the previous dismantling.

Anyway, hold down the two and see if it turns off the dings. That's amazing. I've never been so excited for a lack of dings. We also heard from Rob, who said I've used a microwave for almost an hour, if not over an hour, several times. When de-frosting a large piece of meat, I don't know if that counts as cooking, but it's certainly food.

well you know it's certainly you've used it over now that's what we're interested in Miles in a similar vein to Rob said that they used their microwave for 35 minutes to cook some brown rice and at some point in those 35 minutes it stopped working and wasn't able to start again oh no go that they bricked their microwave so miles says that 35 minutes of brown rice cooking we should all take that as a warning wow and Michael said I don't think I think I've ever hit one hour, but I do periodically have to run the microwave for tens of minutes to melt metal. Okay, that sentence took a...

That's a ride. I don't need to melt metal often enough to buy a dedicated furnace, but I use a small silicon carbide crucible in the microwave and it will melt most metals in 20 to 40 minutes. That's amazing. Now, I feel like this isn't advice that most listeners should take. As far as I'm aware, you shouldn't put metal in a microwave, but I'm guessing there are some circumstances where it's okay. I don't know.

That's opened up a world of home metallurgy. I'm going to start casting stuff at home. That's great. I mean, you've already broken one microwave. Why stop there? What? I'm going to cast a new microwave out of molten aluminium. Thanks, Michael.

In other news, we've had quite a few folks still saying they want a sleepy time episode. Those people are wrong. We've also had a lot of folks saying, please do not ever do that again. Never do an ASMR theme again. Those people are right. We hear you? We won't. If we were to do one, it would be a very specific one for those people.

You would have forewarning. You're not going to stumble on it by accident, is what we're saying. Exactly. We're not going to sneak up on you with any of this whispering stuff. But we did have some questions about that. and I have someone I'm going to talk to about it on a later episode. So just to let you know, we've heard you, thank you for writing in, and we will address this in a later episode, not in an ASMR style.

And finally, a listener who goes by Evie Outdoors, they decided to cross-stitch something we said on episode 1-28, where we were discussing things you change in your life to try and have a positive impact and the limits of what one person can do. And they've cross-stitched the phrase, something isn't nothing, which is a phrase I live by.

So thank you very much. They've done a little chicken with a love heart. A little happy chicken. I don't eat chicken because I think we're jerks to chickens. Evi outdoors. That's a fantastic cross-stitch. That's amazing. Thank you very much.

Yeah, well done. Well, that's it for another episode of Problem Squared. Thank you so much to everyone who listens along. We very much appreciate you joining us here. Your something also isn't nothing. But specifically, we like to thank three of our Patreon supporters, the people who enjoy my sausage-eating stories on the bonus podcast. I think that's really overselling what we do.

But anyway, thank you, Patrions, for supporting. this and we pick three of them at random every episode to mispronounce their names, which this time includes Thebo E five-five. Anthon Wipo Netan Zed Yes

Haas Haasab Arab Aleu Nowed it So thank you so much to all of them And indeed

Everyone else And we are done I've been Matt Parker You've also listening To Bechell And finally The person Who doesn't take

Oh no For an answer But will solve, fix and hide all our problems and mistakes as producer Laura Grimshaw. Bye. Okay, Beck, you've got to take Go for an answer.

What color am I again? You're green. I'm green. Right down the middle. Oh! Oh, bosh. Boom.