A Problem Squared - 130 = Sly Skittles Claim and Why Sniffles Name?

Episode Date: March 16, 2026

🌈 Is it true that "No Two Packs Of Skittles Are The Same?”🤧 Why a cold called cold?🤫 And there’s some ASMROBHead to our socials to see Matt’s Mission Patches, Matt’s Calculator, and the Skittles Combinatorics!The Liberation Laser Software by Seb Lee-Delislehttps://liberationlaser.com/ The Skittle Maths by Clare Wallacehttps://www.clarewallace.co.uk/skittlesAnd some Norfolk Punch, if you’re so inclinedhttps://www.norfolkpunch.com/ If you’d like to see Matt on tour, all the dates, venues and tickets can be found here:http://standupmaths.com/shows Join 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.

Problem solving, Yes, you absolutely can. Can we stop this now? I'm trying to split the difference now between my normal voice. Yeah, because what we don't want is people to go, yeah, exactly, no jump scares.

Yeah. You know our policy. No jumps scares. That's what we said going into this. I'm going to be tasting the combinatorics. I'll be looking into colds. It's very chill. If I just whisper business, does that count?

Sure. Chills. I've got chills. Okay, can we just gradually fade back up? Should we just slowly start to pick up our long? Yeah, if we gradually... We just bring this up? Just, no, nothing abrupt. Not too strong. Until everyone's had a moment.

Just to just give it a second. Hello, Matt. No, no, hi, Matt. We just made it up. We could do a sleepy time episode. We could. We're not. I guess. This is, this is, 20206 is the year where I try and put in as many special episodes as possible. We hadn't asked me anything. We're going to have a tooth day, a rock day.

How are you, Matt? I'm good. Excellent. It's all systems go for Moonpie. Ooh. Now, have I mentioned the patches on the podcast? No, but I think just for anyone new or who's forgotten, give us a very quick rundown on Moon Pie. So I'm calculating pie on the moon. There you go. No further context. No further context.

So, okay, it turns out the sorts of engineers who work on space missions building like lunar rovers. Also, nerds who watch YouTube videos about mathematics. What? I know. Wow. And so I received an email from the company Astrobotic building a lunar rover. And they're like, hey, on one of our rovers that's going to the moon, we got some spare computers. cycles if you have any good ideas for what to do with them.

We thought we get you involved is a kind of like public engagement, space science, fun thing. And I said, yes, I want to calculate pie on the moon. And so a lot of people supported the mission because while they very kindly let us on the mission, we had to pay any extra costs that were the result of our mission. Because they can't just bill them to a different mission or part of the project or whatever, right? The money's got to come from somewhere.

And so I was like, fine. And so almost 5,000 people backed the mission. A subset of which, as part of the perks I promised on Kickstarter, was a mission patch. Like the one that you got on that parabolic flight. Oh, yeah, my Issa patches. So they're like official ones. I say official. Mine's official too.

Yeah, come on. They're more official. Let's go with that because ESA made them as opposed to the Matt space agency. Mitzer. Yeah. And so I was like, well, I want to have my own mission. Patch as well. Turner Prize winning artist, Keith Tyson, designed it.

He also watches my videos. Amazing. And he asked me for some math help on projects he's been doing. And I kind of had not a favour in the bank, but I was like, he's such a nice guy. He loves this stuff. I was like, I bet I get one dangle a cool project in front of him. And you get me to do the cards? You're an incredibly talented artist.

Yeah, look at Sold of the Perth. Exactly. But I feel like I can easily bait you into a project back. I was like, I reckon I got one big project where I can cash in a, hey, would you, instead of being paid a lot of money to do other real work, want to mess around for free? Yeah. And Keith was so excited about this project. I was like, this is the one. I was like, Keith, hey, if you got some spare time, do you want to do a submission patch and he did.

Do you want to see it? Yes. Oh, that is very. Isn't that a hang? That is That is very satisfying. So the patch says some moon with pie underneath,

some moon pie. Some is written at S-U-M. Yep. Just sound like that mass. Fun. And we're summing on the moon to get pie. And Keith really liked the idea of the sun and the moon, and this is the sum in the moon.

Yeah, that's fun. Yeah. So you've got, is it a dodecahedron you've got in there? Icosahedron. Icosahedron. How many, Faces is nice. 20.

Oh, so it's like a 20-sided die. Yeah. So you've got a D-20 in here. And the archa-hedral is because we're using icosahedral axes to work out positions on the moon. Oh. It's really nice. I talked key through all the mathematics. This is the design that came up with.

It's really beautiful because the way the patch is embroidered with the different directions of thread. And it's quite like a metallic thread. When you move it, you get these different shadings and contrasts. Yeah. pretty nice yeah it's partly Keith's incredible work designing it and I used the same company who make NASA mission patches made these what yeah well that for the match that is a above and beyond how often do you get to do your own mission I'm doing this properly I said yeah yeah yeah amazing there's only one slight problem on the patch there's a mistake I love this this is

I've never seen anything more Matt Parker I know Well, here's... So, we've discussed before how I do increasingly more and more ambitious, ridiculous projects. And this is a new record. But I simultaneously have a reputation online for trying ambitious things and failing. So I'm really nervous because this one can fail in some real spectacular ways. Yeah.

And so I've been kind of keeping an eye out going, like, how's it going to go wrong? Like, something has to go wrong. The patch. See, there's like blue, surrogens. arcs on each side. Each one in the design was meant to contain 3.14 stars. Ah. And the one on the left contains 3.14 stars.

Yes. And on the right, there's a star missing. And I checked and it was missing in the proof that the patch company sent me is totally my fault. I checked the proof and went, yep, that looks great. And I didn't realize in the conversion from design to patch all that shenanigans, that's a whole thing. Somehow just one star somehow got missed during that process. But they showed me their proof and that it was missing in the proof. So I should have done a proper overlay.

I didn't think to check if one of the stars had supernovaed. But one supporter has since pointed out that because they're missing one star, there's now 22 stars. And there are seven letters in some moon. So because the stars missing, it's encoded 22 over 7 as an approximation of pi. And I would have understood that even without you telling me. So if you look at all the symbols, you've got Pi symbol, and then you've got seven normal English characters, and then you've got 22 stars. It's amazing how easily you can convince yourself that... I can contrive all sorts of reasons to overlook mistakes.

And it's this level of optimism that really, I think, is why you're so successful. Blindly, la la, la. Most people would have given up. Oh, I can land. I can put a mission on the moon. Sure, I'll take that on with all this spare time I have. Yes. It's not like you've had any other life stuff happening.

Yeah, you've seen how this is definitely one project too many, 100%. In every objective measure, I should not have agreed to do this. Anyway, I'm not going to not calculate point on the moon. So this is happening. Yeah, yeah, yeah, yeah. And I'm very excited about my patches. It's beautiful. Yes.

She'd be very proud. Yeah, I know. So that's what's happening in my life. And I love it. How about yourself? I'm well. Recently, we got to go to the launch of our friends software. Oh, we did.

Yeah. Lovely Sebelie Deliole, incredible Lasarist. Yep. If you've seen our shows, you've seen Sebs excellent work. Yes, along with Abby Shum, who's now an incredible laserist as well. Seb has created some software, which is free to download. Yep. And you can create sort of laser shows and stuff like.

that. It works with a bunch of other programs and it's all about trying to make laser stuff way more accessible and I'm so proud of him and so we went to the launch. He's been talking about this for so long. Yeah, he's been working on a really long time. We went to the launch, which was so fun and got to see a bunch of laser shows. Honestly, I was sitting there like, how lucky am I that I get to go to the launch of laser software? Laser software of the future. Yeah, and then they had an incredible DJ and what this is what I love the DJ was amazing the music was incredible it's a Friday night it's it's like plah and it's a room full of very excited software engineers and laserists and nerds like us people yeah tinker's makers yeah so it was

you know real liveliness no one was dancing everyone who's chewing to try the laser software to control the lasers during the DJ set. Yeah. So no one was sort of dancing, but they're all standing to the sides. The line of people. Watching the lasers and being like, oh, that's good. And I won't lie. I played with lasers.

What did you do? I played with lasers. It was great. I would normally be dancing. Instead, I was playing with lasers. It was a lot of fun. I know. I mean, not for any bad reason, but it kind of had school dance vibes.

It did. Yeah. There was a lot of people standing at the side. It's a bit too nervous, but too self-conscious. Yeah, yeah. And then they also had some games set up with lasers that Sebs done in the past. I played a lot of asteroids. You did play a lot of asteroids.

I played Luna Lander. I got it on an eight. An eight? Yeah, I was all proud. That's a difficult spot. Yep. Wow. So, yeah, it was a really good night. Yeah, if people saw Humble Pie in my show,

Sebs did all the lasers in that. And in my show, I'll be back with a laser version of one of my flip chart. It's very funny. And on tour now, Abby Shum, Lasers and Coder Extraordinaire, is on tour with me. So I mentioned Abby. She's kind of running the Christmas tree in my shows. Oh, amazing. And doing the lights.

So if you're marvelling at the lights, that's her. And we both got quite sentimental because Abby was a venue technician. Yes. The year that we both did our shows at Pleasance. Yeah. And so Seb came up to help set up the lasers, but then had to go back down. because he was, I don't know, doing some gigs for someone called like, Fat Boy Slim or whatever, I can't remember. Norman.

Some Norman character. And so he was training Abby on what to do if everything goes wrong. And Abby took a real interest in it. We should have been a software developer. Got sick of that. Yeah. Or she'd go into theatre stuff and then happened to land just completely serendipitously working on our show. Yeah.

Which were accidentally in the same venue. That was not designed either. No. And so she rocks up going, I wonder what the career change from software developer to theater technician is going to be. And we're like, we need someone help us program this laser. Yeah.

Just when you think you're out. Yeah. And it was great. We got to see like these two meet and now they work together all the time. She's an amazing. She's won awards with it now. We can't take credit for that. But it is nice to have been there at that.

it's nice to witness that point of someone's life. Yeah. Like the sliding. It's when we had nothing to do with the sliding doors moment, but we're like... We were the ones moving the doors. Yeah. Well, we were like the driver. We were the train.

Oh yeah. Okay, that works. I'll accept that. And I'm just, yeah, anyway. So I'm in a good mood. I'm chuffed. I like my friends. I think they're great and talented.

I was just glad. Because said I put this incredible code together. It does all this wonderful stuff. Whenever I spoke to him about it, he was just sick of writing the documentary. That's the, oh, I'm so sick of it. But he really wanted this software to exist in the world. And it had been embated for so long. And when you're coding, it's not like you often get this kind of celebratory thing.

So I'm so glad he put a night on and did the whole thing properly to celebrate it. Yeah. Being released properly to the public. Yeah. So you're into lasers or that kind of thing? Check out Liberation. We're not sponsored or anything. No, we're not sponsored.

We're just big fans. Big fans. Download it, have a play. Design a laser show. Yeah, link in the show notes. Our first problem comes from Andy, who went to the problem posing page, which is a problemsquare.com, selected the drop-down problem. Yeah. And wrote, have you seen the thing on the skittal packs which says no two rainbows are the same?

I saw a short vid which debunked this by counting every possible skittle pack. I think my problem is, how many skiddle packs would I have to buy before I got a match? And will you do that, please? Hey, I'm on board No So the short version of this is Skittles on their packet claim that no two packets are the same

So did they get rid of Taste the Rainbow or have they got two things on there now Oh, you know what, I got some packets Let me get some Okay, here you go This is a packet for you Now I've got a packet over here Skittles, fruits

Oh, they have still got Taste the Rainbow Share the rainbow, taste the rainbow. Now, would you mind reading out the whole next sentence? No two rainbows are the same. Neither are two packs of skittles. Enjoy an odd mix. There's a lot going on in that sentence. Mm-hmm.

Like, I think they're confusing rainbows with snowflakes. Yeah, because rainbows are kind of like pretty uniform in terms of... Every rainbow is basically identical. Like, I mean, it depends if you're like, oh, how strong does it look for? from the angle that you see it? I don't know. Well, the rainbow you're seeing is unique because every rainbow is down to the exact point at which you're looking.

Yeah. And the position of the sun. But arguably, they're all the same spectrum. Yes. Anyway, so let's not unpack that. It's going to be the same colours as what we're saying. Yeah. What we will unpack is the pack because they say,

neither are two packs of Skittles, which is weird. And I was aware of this. They've had that slogan for ages, and mathematicians were rightly outraged. Because just very quickly, there's going to be a finite number of skittles in this packet. Yeah. There's not infinitely many. There's a number. There will be a number of skittles in every packet.

Now, you've gone for 136 grams. It's actually like one of the sharing packs. You've not gone for your uniform. This is a big in. Yeah. Yeah. And there's a finite number of flavors. Yes.

Yeah. So on here, they've got five flavors. Which means if you've got a finite number of things that are each taken from a finite number of categories, there's going to be a finite number. Yeah. So there can't all be different. Well, unless that's such an overwhelmingly big number. Yeah, if it's like you telling me about shuffling, playing cards and every time you shuffle them, it's so unlikely that. Anyone else has shuffled it into the same order?

Exactly. That the chances of it are basically none. And you did the maths, because I didn't believe you, and you did the math. And I was like, oh, that's fascinating. Yeah. So it could be like that, but I'm guessing it's not like that. No. So here's what I thought we would do.

I've got three packets for you, me and producer Laura. We're each going to open our packets. We're going to category. No, any. Put them into categories by color. And then count how many of each. Okay. And then we'll use that to do some calculations to work out how many packets of these would have to buy.

I'm starting to regret the half a pack of M&Ms and half a pack of candy kittens that I've already eaten before. Yeah, I'm going to give everyone a piece of paper so you can kind of dump them out on the bed of paper and then rearrange them into flavors. This is the optimal paper for doing maths on. It's like dotted paper, which I love them. Oh, it's almost like ASMR. They'll tip out the skittles. I'm just going to ask you both while we do this. Either of you experiencing a lot of salivation right now, or is it just me?

It's just you, my friend. I've pavloved myself. Okay, through the magic of editing. Yep. We just did that pretty instantaneously. Oh, yeah. Yeah. No messing around.

No one dropped any. Nope. So I had 30 greens. How many greens? So many greens. I've got 34. That's too many greens. It's too many greens, especially because it's not even an apple flavor.

It's lime, and I have feelings about that. I'm not even going with the flavors. I'm just doing colors. Make life easy. This is why you and I are different. Just Laura. I also had loads of greens. 33.

I see you just left yours in a massive clump. And Beck, like me, put them into a neat grid, a five wide stack. It would just make it easier to count them up. Sorry, I would you say, I was so distracted by your clump. How did you count them? Yeah. And twos. Oh.

They're all messed around like sheep. Yeah. Okay. So what do you think it is? I mean, I want to say here. I finish first. Yeah, I know. I know.

Yeah, anyone can finish. It's way easy to verify, though. Anyone can finish first if they're just guessing. All right. Give us the number. 33. I guess. I had 25 oranges.

Me too. Ooh, interesting. I had 20. 20. 20. Oh, I had 28 pebbles. I had 25 purples I had 30

21 reds 18 disappointed 17 oh maybe reds are scarce and I had 18 yellows I had 21 I had 22

okay so Beck that means you had 34 greens 25 oranges 25 purples 18 reds 21 yellows yeah so I've got 123 in total.

Correct. You've got 123. And Laurie, you've got 33 greens, 20 oranges, 30 purple, 17 red, and 22 yellow, which despite your chaotic system. It's 122. It's probably correct, it's 122. I also had some to 122. Huh.

So it feels like... It's almost like the weight, you know, it's pretty good at weighing them out. Yeah. So first of all, now we've got an estimate for how many Skittles per packet, which we need to know for these calculations, which is 122, 123, around there somewhere. Let's just say it's one of those two numbers. And we've now got a breakdown of how many of each color. And I haven't done any calculations, but eyeballing it, you could maybe say, well, hang on, there's consistently more greens and consistently fewer reds and fewer yellows

and more oranges and purples. So you'd have to do a bunch of calculations to work out if that's just natural variation or maybe they're not putting them in with equal likelihood. I propose for now we assume there's an equal likelihood of any given colour. So let's do the case for 122 first with five colours. So the question is, how do you work out how many possible packs of skittles there are, if you've got 122 skittles in a pack, and each individual skittal can be any of five different colours. Is it a shouty button? It's always shouty button.

It is ultimately shouty button, yes. Which is called, I know it's an exclamation mark. Yeah, it's a factorial. Factorial. That's a factorial. Yeah, yeah. A bunch of people listening will be thinking, well, that's easy. You just have five options for the first skittal times five options for the

the second skittal times five options for the third skittles. The issue with that is you've now identified specific skittles. You've got the skittal number one, skill number two all the way down. We don't care which is which. When you were counting the greens, all greens are equal. They're fungible. Yeah, right. And if you just did five times, five times five, 122 times, you're assuming the order in which you eat the skittles matters, or at least the order matters, but it doesn't because all greens are equal and all rows are equal. But now you have to divide out because you've accidentally counted multiple equivalent

packets as being the same packet. Got it. Because there's no ordering in the packet. They're just tumbled in there. Yeah. So you're like, oh, we'll have to divide by the number of ways to arrange,

the number of greens. Oh, but now that correction changes for how many greens there are and the complication gets super complicated. Okay. Thankfully, a friend of mine, Claire Wallace at Durham University, has previously looked into

Skiddle maths. Oh, thank goodness. For two consecutive years, Claire's done a talk at the Mass Jam weekend about Skittles. Get a life, Claire. No, she's got this is the perfect life. We need this. Never changed, Claire. Yeah.

And Claire came up with just a genius way of doing this because combinatorics, sometimes you've just got to think of it the right way and you're like, oh, that makes sense. Now, I'm kind of giving away the spoiler here. Claire didn't do it with this full-size sharing bank. She did it with the much smaller individual little packs. They've either got 16 or 17 skittles in them. Oh, so they're like the fun size ones. Yeah, yeah, they're like tiny.

Maybe. Yeah, way easier. Importantly, still have the same slogan on them. So it counts. She worked out how to do it for that one. And the logic is, the skittles in the pack, the order doesn't matter. Yeah. Because it all just tumbled in there.

When you get them out, there's no way to say this green one is different. to that green one in any meaningful manner. But you can put them in colours. And you can say, you know what, I'm going to get every packet of Skittles and put them into colours and then put the colours in alphabetical order, which is the order I read out a second ago. Because if you put these in alphabetical order and go green, orange, purple, red, yellow, for any pack of Skittles, you could put them in one long line, first of all, all the greens, then all the oranges, then all the purples, then on the reds, then all the yellows. and two identical packs of skittles,

if they have the same flavour distribution, will form exactly the same line if you do that. So we can safely say that's a way to take a pack of skittles and kind of put them in one nice, neat long line. So when you're saying, how many different packs are there, how many different ways are there to line up skittles in alphabetical order like that.

Got it. So what you're actually saying is, If I started with 122 blank skittles, at the beginning, they're going to be green for a while, and then I've got to pick a point at which the green stop and the oranges start. They're going to be orange for a while, and I've got to pick a point with the oranges stop and the purple start. Now, possibly there could be no oranges. So those points would be one after the other. Like the greens would stop and immediately the oranges would also stop after zero of them.

Okay. You've got to somewhere in there put in four dividers to separate out the five flavors. Yep. So you could actually imagine it, instead of being 122 skittles in a row, it's 126 locations of which four are dividers and the rest are skittles. Okay. And so what you're actually calculating is 126 choose four, which is the number of positions you could put those four dividers. Yes. And the way I'm picturing this in my head is if I had 126 blank spots.

Yep. Like divvits or something. Yeah, exactly. And then I've got four fence posts. Correct. Love it. And then I'm going to walk a lot. And then I'm going to go like, okay, if I put all four at the front.

Yep. Then 22 are going to be this way. And now I'm going to move one post. post across one each time, two each time, and then it's all the combinations. Right, got it. I'm with you. I'm with you. You nailed it. I love this. And thankfully, we have a formula for if you've got a number of things and then you've got to choose a certain subset, we already have an equation. It involves the shouty function.

And I'm just going to type into, I'm actually just going to use Woolfram Alpha. 126 choose 4 Oh that's such a nice number So choose 4 is the like choose is the Command. Oh it's the name of the function Yeah interesting If you've got n things choose k So in our case our N would be 126

Now K is 4 That's just the common ways to do it It's shouty n divided by Shouty K times shouty the difference between N and K. All right. That whole thing. Sure.

That's the equation. Okay. And there's a nice proof for that and you can work it out yourself, but that's a you thing to do later. 10 million 9,125 possible packets. Okay. That's a lot of packets. That's a lot of packets. Okay.

So I'm going to just make a little note of that number. Here's the thing. That's only for... 122 Skittles. Oh, because we've proved that it could be 123. Yeah. So we need to do for one more. So 127 choose four is for the one extra one.

Could you not also assume there could be packets with 121? That's valid. So for packets with one more, it's 10,334,625. So it's basically the same number again because they're roughly the same size. Yep. So basically each time we allow for a different number of Skittles, it's about another 10 million. Okay. Would you say we should also factor in 121?

I think we should. Because if it bumps up, it might bump down. Yeah. Yeah. Okay. If we did 100, let's get the exact number. Let's do this properly. 125.

She was four. Yeah, just shy of 10 million. 9,691,375. Now, when Claire did this for. the smaller packs, because she started doing this as a workshop with school students. Great. Which is such a good idea. Claire has now used child labour to open 425 packets of skittles.

I've never thought of it that way, but that's genius. Yeah. It's so clever. All of them, all of them have had 16 or 17 skittles in them. So the number of skittles is super consistent. So I think in our case, we should open more packets, but shall we just say a range of three? Yeah. Which feels about right.

I mean, you've got scales. We could. We don't. We can't. And see how much it weighs and work out how many, on average it would take to do 136 grams. I should get my scales? Yeah. You know you want to.

Oh, I really do it. Okay. So how many grams are these packets promising? 136. Oh, which is, yeah, pretty close to the number of Skittles. Hmm. They're gram-ish. I'm going to weigh all one, two, two of mine.

Oh. 137.4 grams of skittles. And would they promise, 136? It's pretty close. And we can actually now give us an exact, um, skittal weight. So they're like 1.128 grams per skit. So they have gone slightly over. So given this is ever so slightly above,

Now, I believe they would rather be slightly above than under because if they're promising 136, they probably... I know there's regulations around the distribution of how often you can go below the stated mass. I think they're always going to go a little bit more. One fewer skittal, one-to-one that you pitched would be 136 and a half grams of skittles. So that's cutting it real fine. Yeah. But would technically be okay. So I think every now and then, a one-two-one will slip in, and that's fine.

Maybe they're mostly one-two-ones and we just happen to get some good ones. That's a whole different calculation. It's doable. So we're going to assume there's either 121, 122, 123 skittles in one of these big packets. Yes. Each of them, we do the number of skittles plus four, choose four. Yep. To work it with the dividers go.

That actually gives us about 10 million each time. We then add them all up. And it means when you buy a pack of these 136 grams skittles, there are 30,035,125 possible packets, which is not infinite. No. But it is a lot. It is.

It's a lot. Yeah. So now it becomes a question of, is this like the birthday problem where you're going to get matches more? often than you expect? Or is it like the pack of cards problem? Hmm. Where even though the number of arrangements of a deck of card is finite, I said with great confidence, you'll never get the same shuffle twice.

Yeah. And possibly Skittles, that's what they're doing. There's just so many combinations. It's unlikely that the same pack will have come up twice. I used the same formula as last time that approximates the birthday problem for bigger numbers. And I worked out how many packets of Skittles you need to buy, and this is what we were being asked. Yeah. Before there's a 50% chance, you bought the same pack twice.

Okay. You would need to buy 6,454 packs. That's a doable amount. It's a doable amount. Like, it's a lot. It's a lot. And if you generalize that to everyone buying Skittles packs, because the packet isn't just saying just you, it's saying every pack. Yeah.

I can say with some certainty there's been more than 6,500 packs of Skittles. Yeah. I mean, I looked up to see if there was any information about production of Skittles. It goes by individual candies. Oh. So obviously they don't all make the 136 grand packs. They say that the annual production is about 70 billion Skittles. 70 billion skittles.

Yeah. Now, bearing in mind that we're basing this on UK, which is a different set to what you might get elsewhere sometimes. Like there are different flavours in different places. Some of them have an additional flavour. We only have five here. Yeah. But that would be if they were all sold in this size pack, that's like 57 million packs. Yeah.

So I would use to say 100,000 of these packs easily. And that gives you, oh, that's 100%. There will be a match. That's like, you can't distinguish that from one. There will be that. By the time you get to 20,000 packs, 99.9% chance there's been a match. Right. So it's false advertising.

It's false advertising. So when do we start the class action course? The moment I convinced Kellogg's to update their Frost. a donut holes packet, which I don't think we've discussed glazed, glazed holes. Don't say that, please. That I've talked about at evening of a ziridio. I don't know if we discussed it on the podcast. We did mention it briefly.

Okay. YouTube video exists. If I get that done, then we take on. But Skittles, they've had this for a long time. And I did think about doing a video about this, and I spoke to Claire about maybe we collaborate on a video. Yeah. But a lot of people have talked about this Skiddle problem.

Yeah, but they're not you guys. Yeah, I know. That's also true. And people want to hear you and now I'm putting it. I don't know who Claire is, but I want to hear from Claire. That's great. And when Andy wrote in with this, I was like, oh, I was, I'm not aware of this thing. It's been around for ages.

And I was like, you know what? I never got around to making a video because I've got a lot of videos I want to make. But I was like, yeah, I could do it. I could do it in the podcast. This would be fun. We'll buy some skittles. We'll have a go. Yeah.

But even the biggest pack. I mean, maybe they're bigger packs They must have like sacks of Skittles, right? Yeah, so you can get commercial-sized packs that are like 1.6 kilos. Oh! You'd put those in those big gumble-type machines. You know, you're putting in 50p

and you turn the thing and get a little handful. I think general packets, there's a 190. A bit bigger, yep. There's the 136 that we have. Then there's the 45 grand packs, which are like your standard ones that you generally get in the confectionary bits. Yeah, if you're getting a snick.

or a Mars bar, that would be the Skittles equivalent. Yeah. And then there's 18 grand packs, which are the first size. Which is the one that Claire's using. Because giving every teenager a 136 grams of Skittles is a terrible idea. Oh my gosh. 17 grams is acceptable. The teachers would be so angry.

I mean, we could run the numbers again for 190. But, I mean, I think the point is there's going to be matches. There's matches. Well, look, we're using a pack that has that advertising on it. And they put the advertising on the smallest packs. It's outrageous. But you still got the big ones. I'm just going to wash down all this Skittles with some coffee.

It's going to be a fun end to the podcast. So kind of in conclusion, Andy, it's very likely. And individually, 6,454 packs, 50%, but globally, definitely. Yeah. And we know Claire has opened and made children count 425 packets. Yeah. She's now got a very good data set. It's on her website.

I'll link to it in the show notes. Right. You can download all of them in Excel. Amazing. Have a look. And the distribution, she's getting matches way more often than we'd expect. Right. Which probably implies they're not put in completely randomly.

Well, no. And the thing is, we're counting possibilities that some of the packs might be 122 greens. Yeah, exactly. Which is highly unlikely because unless it's some limited edition when they're doing, They obviously want to put roughly the same amount. Because people get annoyed. It's the classic shuffle versus random problem. Yeah.

So of those 425 packs, no pack has ever had more than 10 of any one flavor. So they've obviously doing something to stop the extremes. Yeah. They want to keep it looking like it's a mix of everything. Yeah. I would be fascinated to know if some of the flavorings used are more expensive than others. and it's interesting or some of the colourings even so there has been a deliberate choice because we all found that we had more greens and fewer reds yeah is that a cost saving thing because at first you'd be

like oh the cost would be so insignificant it wouldn't make a difference but if you're producing 70 billion that is a difference anyway i feel like that's much like eating a couple skittles doing this as sated my need. Yes. I'll tell you what. Doing it as a video or doing it on a larger scale will be expensive because I have a feeling that Skittles will not sponsor. I don't think they're going to give us three packets in order to check if they're advertising is bogus.

Yeah. No. Anyway, I'm going to consider that case reclosed. Let me know people, specifically Andy, if you're happy with that or if you think I've missed anything important. Next problem was sent in by Tomas, maybe Thomas, who went to the proposing page and typed in blah, blah. Why a cold, cold, cold, cold, cold, cause cold, temperature makes sick, temperature make weak, blah, kind regards. Thomas, P.S. Blah. So.

Can I read it the way the voice in my head did it as well? Okay, that's how the voice in my head did it. A cold, cold, cold. cold cause cold temperature makes sick temperature make weak now i know we're both ozzy but these rising inflections are question marks yes at the end of every sentence why are cold cold cold is maybe one of my favorite opening it is great so beg do you have an answer to why are cold cold cold cold why are cold cold cold cold cold cold it's so tempting to answer in the same type of language i feel like we've had just as much fun imagining that as we would have doing it possibly more

Well, the earliest recording of what we know is the common cold being referred to as the cult. Because the actual cold that we get, that sickness, that illness, they reckon it's been around since 16th century BCE. Oh, about to say, 16th century, I'm like, no, it's older than that. Oh, B, C.E. Yeah, yeah, yeah, yeah, that makes more sense. Symptoms and treatment are described in the Egyptian Ebers papyrus, which is the oldest existing medical text. But the actual term that we call it the cold came into use in the 16th century. Oh, there it is. On the other side, it's been suggested that that's because of the similarity between its symptoms

and those of exposure to cold weather. When you're in cold weather, you get runny nose. Oh, when you come back inside, yeah. Okay, yep, yep. Things like that. You might get a bit of a cough. You know, when you go outside, it's very crisp and cold, and it restricts the blood vessels, and you're like, like that.

Yeah. So you might feel a bit like you have a cold for a moment. However. However. Interesting fact. A lot of people assume that you get a cold from exposure to the cold. And statistics suggest that people do get a cold more often in winter. Oh, checked out.

But. Well, another. Oh, wait. There's more. Yeah. They reckon it's because, not because people are cold more often, but because people are staying inside more often. Oh. So there's way more chance for...

Oh, correlation again. Exposure to the cold in close vicinity of everyone. You know, you're being kept indoors with other people breathing their air, being around their germs, way more than you would if you're outside. So, yeah, to answer why a cold, cold, cold, it was because people thought cold cause cold. Right. Temperature doesn't necessarily make sick. Temperature doesn't necessarily make weak. It's more that what happens due to the change in.

temperature that has that effect on us. That's great. Well, Tomaz, there you are. That is why a cold, cold, cold. Let us know, is ding. Is ding ding? Is ding ding? You're right.

It is, is ding ding. Okay, report back to us on is ding ding ding. Let's slowly bring us up to talking volume. Please do. Because I know that you won't want to whisper everything else, even though I'd be well up for it. Oh, you would? Yeah, yeah. But on behalf of a decent percentage of the listeners.

Hey, if you're listening would like us to do a sleepy time episode that's super relaxing with the most boring problems that we could find. Only if we do that immediately after eating all those skittles. Yeah, yeah. Then go to a problemsquare.com, choose solution, and write sleepy time. Okay, we heard from someone who also went to problem posing page and said their name is Tweakley Drinker, which is adorable. Tweakley being twice weekly, as we discussed in a previous episode,

they said, I'm a social drinker, went out with friends or on a date with my partner. Back in episode, blah, blah, blah. Great. All the information we need. Laura has diligently done the research and said it was episode 108. Beck said, paraphrasing here, I've never regretted skipping an extra drink. Yes, I think my exact words were I've never woken up and regretted not drinking. Yeah, yeah. Yeah, and that has changed my behaviour.

I now think, what would Beck say? Oh, no. Don't think that. Don't think that. No. Really work on how you're summarising that motto. Because one in ten charts, it's something to do with farts. So I now think what would Beck say and stop it too?

I like their policy. they say all-day events three. Yep. But since hearing the Beck advice, they've never had a composite number of drinks. So I feel like a composite number is a non-prime. Two and three are primes. Yeah. Four is not prime.

It's a composite number. Yes. And so they've never hit four. It's a fancy math way of saying they've not had four drinks. But they could have had seven. Yeah, I was just thinking that through going, Would that have involved having had four at one point? Yeah, yeah.

So maybe it's a barrier you can't get through. But that's a good policy. Yeah. I'll save it to drink more knowing that I have a limit because I can anticipate the next day being a pleasant experience instead of being a painful reminder of a non-prime number. See? Yeah.

We've had some business sent in about episode one to six, where we were looking at non-alcoholic uses for fancy glassware. And we were talking about using champagne flutes for things like drinking coffee as well as your recipe for mold wine. There's some chat here and there about other types of non-alcoholic mold-esque beverages, of which I want to flag up Trevor here, who said, big fan, blah, blah. For Beck's non-alcoholic mold wine, have you tried Norfolk Punch? It's been around for ages. And then they link to Norfolkpunch.com. I love this as a kid.

Yeah. So what's Norfolk Punch? I've had a look at the website. I love this. Original Norfolk Punch is a healthy non-alcoholic herbal drink first made by the Benedictine monks of Well Manor in the Fenlands of Western Norfolk. I love this because looking at the bottle and the sound of it, it has smacks of Buckfast.

It has got that vibe in the packaging. Now Buckfast is made by... It is alcoholic. Monks. Yes, in an abbey. I want to say in Devon? I think that's right. Maybe this look is just monk core.

Yeah. That's true. I love the idea that like in some abbees, they're like, let's put caffeine in port and call it tonic wine. Yeah. And then in Norfolk, they're like, can we just put some herbs and stuff? And herbs have a good time. Yeah. I'm fascinated.

It's a monk for every season. It looks like they've got a few different flavors and stuff now as well. We'll celebrate together for our next in-person record. Yes. Also, looking at it, it looks like I can only always always. order in cases of six. Right. But I will look into this.

I'm fascinated. In the meantime, send us in your Norfolk Punch stories. I bet they're not as interesting as Buckfast ones. No, no. Now, in the same episode, I talked about how I would like a champagne flute for every occasion, other than alcohol. Yep. Including wanting a champagne flute I could put coffee in.

Yes. Quite a few of you sent in suggestions. for a particular product. Oh. Since looking into this product, I've been inundated with online ads for this product. We're going to look into it, watch this space to see whether we recommend it. Suspicious. You're not even going to name drop it until we know.

Well, that's integrity back. Yeah. Although we did mention Skittles a lot on this episode. And final bit of any other business. We've got a ding. All right. Love it when a ding comes home. I'll read this exactly as it's written. I am Frederick.

Okay. I posed the problem mounting sea level rise from episode one, two, three. That's like how much would we have to scoop out of the ocean bed and pile it up somewhere to stop sea level rise increasing? Yep. Hi Matt and Beck or Beck and Matt. Feel free to use the order you prefer. They put that in brackets, yep. I would have liked to give you a very large amount of...

of mole dings or dinghills, but I do not know how many it would be. Instead, I will give you one giant mound ding. Hey, thanks, Frederick. Then he goes on to say that he likes the show, blah, blah, blah, and that he is sorry to admit that he had gotten quite a few episodes behind, but was happy when he heard a question that rang like a bell, like a ding in his head. You said you were going to read a word for word back.

And the words you read out sound like someone's summarizing in the third person, what someone has written. Have we trained our audience to become a large language model? They're training us. Eventually, they're going to be able to guess what we would say for everything. And then we wouldn't need to be here. At the moment, they've pushed it one, maybe two layers of abstraction. Then they'll start writing things like, oh, and then the person wrote out,

what they thought I would say summarizing their message to me so they can trick me into sounding like I'm summarizing it but that's what they've written Yeah yeah yeah Yeah Or they'll say

And that's concluding any other business Here are the people We want to the entire end credits They'll make up the other Patreon members we're going to thank No I think everyone should just stop their Solutions partway through And just right I'm not reading all that

Great. And speaking of altros. Oh. Wait, is this still? No, this is me. This is Beck Hill, I swear. I'm saying every word from my mouth. This is from my brain.

How do I know mouth is mouth? My Beck called Buck. It's mouth, mouth. We like to thank everyone. involved in making this podcast a success. So that is you are listeners, everyone who tells their friends and family and colleagues to listen and spread the love and the learning. But we especially like to thank our Patreon supporters who make the podcast possible by financially supporting us. If you would like to become a podcast Patreon, go to patreon.com

forward slash a problem squared where you can get access to a bonus podcast every month called I'm a wizard. I think it's quite good. I think you should check it out. Matt is ambivalent. It's fun. For us. Yeah, yeah.

And you get a couple of other nice little perks and benefits as well. So do go check that out. Please support us if you are financially able. We will also choose three Patreon supporters at random to thank by mispronouncing their names at the end of every episode. And on this episode, those Patreon supporters are... Cleamy. Riz. B.B. Rizh.

Yazi. Yach. Thank you very much for supporting us. Thank you very much for listening. I'm so sorry. You're here to listen to us. I also want to thank my co-host, Matt Parker. Ah, jeez.

I'm Beckhill, and your triggering sound, like nails on a notebook, in a nice way, is producer Laura Grimshaw, who is great. Thank you. By the way, everyone, she does the face. I've never watched myself. I would do some hair brushing, but my co-host makes that difficult. Oh, too soon. Goodbye. Okay.

Regular volume connect four times. Regular volume connect four. Okay. Now, you went last time, so I'm going to get producer Laura to hold the... Okay, and this is from my point of view. That's interesting. Okay. I would like to go.

in the 33rd hole from my point of view, reading left to right, top to bottom. No, no, no, keep counting further. From my side, not yours. Why are you making this hard for long? Tell what, keep moving it and I'll say stop. Yeah, and then the audience goes. Yeah, that one. No, no, back.

One more. There, yeah. Oh no, they're just guessing now where you've gone. I think we leave it totally. From left to right top down, sure. It's correct.