A Problem Squared - 118 = Rolling Eyes and Juggling Highs

Episode Date: September 29, 2025

🎲 What are the odds of rolling snake eyes? (And does it make for good TV?)🤹How long does it take to learn to juggle with seven balls?🛌 And there’s some Any Other Bed’n’BoardnessHead to our socials to see Matt and Bec in action, rolling dice and juggling balls!To find out more about our juggling expert Darryl J Carrington, head to his insta:https://www.instagram.com/stories/highlights/17849564354111457/?hl=enAnd here’s Colin Wright’s video about Sideswap: “Juggling by Numbers - Numberphile” https://www.youtube.com/watch?v=7dwgusHjA0Y Here are Jasper’s links (in Dutch and in English) about the Belgian family and their children’s themed nameshttps://vrtnws.be/p.NvjDVZw5w  (Dutch)  https://www.reddit.com/r/tragedeigh/comments/17h7ka6/gwenny_32_is_pregnant_of_a_twelfth_child_a/ (English)  And here are the visualised shuffles of the card question in Episode 113Tom - https://tehtommeh.github.io/riffle-me-this/Bernhard - https://www.bernhard-werner.de/assets/cindy/applets/card_weave.htmlShaun - https://svermaak.github.io/VisualiseCardShuffle/ If you’re in the market for a phenomenal dwarf hamster set up, here’s Bec’s ebay link:https://www.ebay.com/itm/127379362494 See Matt on tour!http://standupmaths.com/shows  Here’s how to get involved with Matt’s Moon Pi Kickstarter:https://www.kickstarter.com/profile/standupmaths  And here’s how to volunteer for Calculate Pi By Hand with Matt: https://forms.gle/w44THpNJ3jWUPqHy6 If you’re 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.

Hello and welcome to a problem-squared, a problem-solving podcast, which is a bit like having your mother come to stay. Wow, wow, you reached a long way for inspiration. We may focus on solving problems you were previously unaware you even had, but you're nevertheless grateful because you know it comes from a place of love. I'm one of your hosts, Beck Hill, a comedian and non-mathematician who is currently hosting their mother in a one-bed flat in London for the next month. And I'm joined by your other host, Matt Parker, a comedian and non-non mathematician who is not currently hosting my mother in a one bed flat in London for the next month. Correct. Correct. That's so funny. Your mom's lovely. She's great. I love her. Your flat is small. It's very small. Actually, she's been amazing.

I'm sure. She's very understanding. So understanding that if she were to listen to this, I think she'd forgive me. Oh, good. Yeah. And on this episode, I've run the numbers on snake eyes. I catch up with a juggler to help answer another listener's problem. Oh, and we have any other bed sit with your mumness?

Boarding? Boarding, boarding, that's the word I'm after. Any other boardingness. So, Matt, we are in a different recording studio. We are in the new Dio. Yes. Okay, hang on. New studio.

I promised I wasn't going to call it the New Dio. Yeah, but it's happening. I said it once by accident. Because it's the new studio. Yeah, we know. And my brain just went, New Dio. And you're never wearing clothes whenever that's unrelated. Just an open kimono.

That's a whole separate thing. That's why I got kicked out of the old studio. It's a new space with flat floors. Like, we love the old space. Yes, but yeah, the floor was somewhat uneven. It was a very creative floor. Yeah, yeah. And it was doing its own thing compared to all of the walls.

Yeah, it's nice when you put something on a table and it rolls. Our mics aren't just randomly swinging around. Yeah, yeah. Well, they're attached to. Just swing away from our mouths. Like, I loved it, but it was in a 1600s building. Just nothing was level. And so we're now in a slightly bigger space, which is lovely, and everything is flat.

Yeah. Very pleased. I'm also moving on my YouTube work here as well. So people are watch my channel. Now we were shooting from the new deal. Yeah. Get ready for that. Yeah.

We get demonetized real quick. Yeah, but you can make money a different way. Yeah, so exciting times. And you were ill. I was ill, so that's true. I should apologise to everyone. I'm very sorry I was ill. We were meant to record in the new deal and we couldn't because I got back from Edinburgh from the fringe and I was instantly sick.

Yeah, you had no voice. So actually, it took a moment. I didn't get instantly sick. You finished the fringe and it's like cliche. to then like collapse at home and rest up and then immediately just come down with some kind of illness. Which I didn't get. You didn't do?

No, I get either sick and or the dread, the post, the post-edember come down. So it's like a real like, because I'm not having the adrenaline. Got it. Yeah, the adrenaline withdrawal. Yeah, fellow performer Alice Fraser podcast herself and very, very intelligent, incredible, funny person. And she said that after Edinburgh Fringe, she makes a point of going for a run at the same time her show was on every day. So that then she's getting that adrenaline hit each time. Because you go from gigging, non-stop, doing other gigs.

Yeah, it is a cold turkey thing. And for the last month, I then threw myself into redecorating my flat to distract myself from the dread. Yeah, the lack of adrenaline was a bit. I got back and got access to the new deal. So I started setting that up. And I had to do a talk a couple days later. Yeah. Oh, and I filmed with BBC.

Yes, you did. Very few people will have noticed I was part of the BBC's coverage of the women's rugby World Cup. Well, we were going to record on that day. Yeah. Then you had to move it for that. Yes. And then you got sick. And then I got sick.

Yeah. Yeah. So thank you for being flexible and sorry. Honestly, it was on the train home. after filming, because we filmed in Cardiff for the BBC. On the train home, I was like, oh, I just get ready for the podcast. And my brain just was like, nope. I'm like, that's weird.

I'm like, well, I'm exhausted. Like, I just spent all day filming. Yeah. I'm still recovering from the fringe. I was like, tomorrow morning. I woke up the next morning and my voice was gone. Yeah, yeah. That was it.

That was, yeah. I appreciated it because I was still halfway through all of my. Oh, I experienced very little resistance. Yeah. From anyone when I was like, shall we postpone? in this recording because I can't talk. In fact, you can still hear my voice as not 100% happy. Yeah, and our lovely producer, Laura Grimshaw,

had recently moved house as well. Yep. So it was in the middle of unpacking. I was redecorating. No one, except for probably you, our listeners, minded. Yeah, exactly. We were all on board. Yeah.

Like, hey, what if we just don't do it? That's easier than doing it. But it's nice to be here. It's nice to see you again. It's good to be back. I haven't seen you since, since Edinburgh. Yeah, we were staying in the same flat. Yeah.

Again, cold turkey. That's why you got sick. Yeah, if I got sick. Yeah, your body was like, oh, no. How are you feeling post-Edember about the show? Great, yeah. I ended up in, there's a ranking of the top reviewed shows. British comedy guide, comedy.com.com.com.com.com.

Ninety-two shows got over six reviews from recognised publications. You know, you can't get your mum to come and see the show. Legitimate. six or more, the legitimate reviews that gave a star rating out of five, as is tradition, and then they take all the shows that pass that criteria, and then average their star ratings, and 92 shows averaged over four stars, including this guy. Nice. So I am in the official.

There are like thousands of shows in the fringe. So the top 92 in isolation doesn't sound very impressive. I think it still does. But that's out of a lot. I'm roughly in the middle. I'm in the 40s somewhere. Yeah. Yeah.

It's higher. I didn't get that many reviewers. I didn't really promote it. I hired a whole person to convince reviewers to come in. Whereas I explained during my show that I did as little as possible to encourage people to come. No, I was going for reviews. That was one of my goals of doing the show. Yes.

Because then when I tour it, I actually can convince venues it's not a terrible show. I think that's the key to doing well in Edinburgh is to having like a realistic personal goal to get out of it, Not like something that you're like, yes, okay, reviews, you don't, you know, you're not in charge of that. But your thing was to get it tour ready, something that you can promote on tour that, you know, you're very happy with. You can't go up thinking, I want to get a TV show or any of that. I was like, I want to go up with a show that's good and end up with a show that's very good and ready to tour. Yeah. And get the kind of media coverage that means it's easier to tour.

Yeah. Whereas I had the opposite thing of, I don't want to tour this. This is a show to help me process and stuff and get back on stage. There was a few of you that came along to my show and an even fewer that came along to the last. That sounds bad, but there's a lot of listeners. I just want to point out. It's a lot of you, yeah. I was only in a 60 seat of room.

The top 92 of you came along. Yeah, yeah. Came along to the last show where I, at the very end of the last show, clicked the submit button on my divorce application. You got divorced live on stage. With the blessing of my ex. Everyone was involved. He was very on board for it.

So, yeah, that was a nice way to send off the show and now I've got to work on the next one. You achieved everything you wanted to achieve with that show? I did. Yep. And I really liked meeting everyone. Oh, and another little bonus, little bonus fact. Yeah. I didn't bring it with me because I was scared I might lose it.

But I bought more teeth since the last episode. I had more folks come along, including Thetler, who had the Messier dens. I think I'm pronouncing that right. The unusual tooth. Yes, the additional tooth, supernumerary tooth. Oh, wow. Yeah. I bought it.

I'm not surprised. Yep, yep. They could have provided it in a beautiful little sort of velvet pouch. Wow. And I got a photo of the tattoo that I could have gotten of the tooth, three different angles of it. So we'll put a photo up on socials. We got a real great. I'm not surprised.

Yeah. I feel like I made it. a lot of friends. You know, you think you're in it for the teeth? It's the friends you make along the way. It is. That's right. Yeah.

The tooth fairy never talks about that enough. No. If she was to make friends with the children, it would be creepy. That's true. That's, yeah. That's why being an adult tooth fairy is. Hi, new listeners, by the way. I'm not going to explain anything.

It's better without context. No, we're not doing it again. Our first problem comes from Andrew, who says, I recently watched the final episode of the reality show The Snake on TV. Now, just before we carry on. Have you seen The Snake? No, I'm assuming it's not a UK show.

No, it's American. Okay. And even there, I don't think a lot of people watched it. Okay. So don't, everyone listening, don't panic if you don't recognize the snake. Sure. This was a show where players competed in challenges to be crowned the snake. And then they decided who was voted out by a snake draw.

Oh, see, the word draw was on the next line. And I was really hoping it was... Voted out by a snake. Yeah. They did have an actual snake in one of the episodes. One of the episode? Or maybe more. You know what?

I haven't seen all of the snake. You do a show called the snake and I want either one of two things. One, an actual snake. Actual snake. Yeah. And the snake is involved in all of the challenges. Oh, yeah. The snake is hosting.

It's hosting. You've got to guess how long it is. You've got to be bitten by it. Knitter scarf for it. I don't know, whatever it is, right? The other thing I would accept if you, created a show called The Snake would be like playing snake on your mobile

but with humans. That would be hilarious. It's basically a conga line. Yes, yes. But then everyone has to go up faster and faster as you add more and more people to the line. Yeah, I'll watch that. Yeah.

Obviously, to win you want to have the longest line but the amount of money that you, the stays the same. Oh, you're dividing it between all the people. Yeah. So eventually at one point you could be going, you could end up winning the game, but if there's a lot of you,

then you're only going to make like a pound each. That would be a great show, by the way. I've just come up without the top of my head. We're not doing your problem. We're doing the snake. Beck Hill Edition. Yeah, thank you. Anyway, this apparently is not easy of the things.

No, neither of those. So Andrew says, with six players left, the challenge was for the contestants to roll a pair of dice one at a time and the first person to get snake eyes would be the winner. Yep. Now, this is fun because we used to call our other producer. Lauren Armstrong Carter?

Yeah, she was old snake eyes. Old snake eyes. I think that just came from us trying to come up with... It came because she had snake eyes. It's not the... Let's... Do you know what? Sure.

She can't remember. I think we did at one point go back and work out while we started that and then I've now forgotten... She's not going to listen to this. So, we can say what we want. And let's producer Laura dobs us in. Yeah, don't dobs us in. Don't dobs us in, Laura.

I mean, am I? Oh! Laura finally earned her snake-up. Anyway, the remaining five contestants would then continue rolling the dice one at a time until they got snake eyes. When four of the remaining five people rolled snake eyes, the player left would be the one voted off. So the six players, they all rolled two dice. Right. And snake eyes is if you get two ones.

Yes. And they keep going until five of them have all rolled snake eyes. They started rolling and the first person got snake eyes on their second try. They then continued, and the next four people all got snake eyes by the end of round five. Mm-hmm. Assuming that the dice they were rolling were standard, the odds of five of six people rolling snake eyes in five rounds is almost impossible. I would love your take on this, as I cannot find any information on if this was legitimate or not.

I'm thinking they edited it down, but it still would have taken a long time to complete. Yes. So, this was the finale episode of The Snake. Okay. And it aired end of August. So it's quite recent. This is a very recent show. Do you want a royal snake eyes?

Have you got some dice? I've got my dice. Your dice are here. I brought the jar of dice on permanent loan from the Beck Hill collection. Right. For newish listeners, we used to end the episodes with Beck trying to guess how many dice were in this jar. And when she finally got it, after many, many guesses, she won the dice in the jar. Okay, I got two red ones.

I've got two blue. Okay. Now, if we were the last two contestants, first person, to get snake eyes stays in and the last person is out okay so we're going to do is keep rolling these until one of us get snake eyes just start rolling over and over first person to get actually how many of we roll i wasn't counting five let's call that five each six seven eight nine i haven't been counting well we'll assume it's about the same as me i've done 11 now snake eyes would you want to keep going get your snake eyes or oops oh one's a one i keep getting

one and six you keep rolling them off the table to be accurate i got that in like 12 rolls i have i stopped counting some time ago oh close so while beck's doing that so each dice has six faces and there's a one and six chance of each one being a one so there's a one in 36 chance for every role, that you will get snake eyes. So if you did this, you know, thousands of times, you'd expect 136th of all the roles to be snake eyes. Now, the other thing we might notice from what you're doing back, this would not make good television.

No, you're right. Make a great YouTube video, as I well know. I would say it's not even making good podcast. Exactly. That's the point I'm making. Everyone's suffering. I got snake eyes way faster than I expected. I think I'm definitely past 30.

Okay. Two threes. Call it the old double mutant snakes. You really rolled them with some gusto, I got to say. They give them a good bounce. A pair of twos. Yeah. Snake eyes.

Right. So that was like, I don't know, 40 to 50. That was tedious. We definitely did more rolls than the entirety of the snake waiting for five people to get snake eyes. They did it in 24 rolls. Yeah. Five snake eyes in 24 rolls is deeply unlikely.

Yeah. Is this one of those things where, like, you would think each time someone rolls snake eyes, the chance of it occurring again gets lower and lower. No, they're all independent. Yeah. So it's always going to be one in... One in 36. Yeah.

Although, because lots of people are rolling to start with, it's almost a distraction to think about individual players. We just care about the number of roles because there's nothing special about one person rolling the dice. Yeah, it's a bit like when we were talking about the price is right, where people get distracted thinking about the product rather than just the game. So it's not really about the person. All this is saying is we're going to keep rolling a pair of dice until we have five snake eyes.

So if you start rolling a paradise and count how many rolls it takes to get five snake eyes, You do that in 25 or fewer roles, 0.05% of the time. That's very small percentage. It's very small. You do it in 50 or fewer, 1.2% of the time. And 50 is like twice as many, like what they did in the show. But I was trying to think, if you were designing this game, surely 50 rolls, like that's, you know, 10, 20 rounds, depending on how many people are, left when.

Yeah. That's a lot of TV rolling. Yeah. To have in. So, there is a tiny, tiny chance. They didn't think through the probabilities, and they got lucky with the 0.05% chance. It just happened to work out. Yeah.

Or, they did something different. Time is money. Like, what are the chances that it would happen to the people who need it the most? If the universe is as innately funny as I hope it is. This is like a full US production with a massive crew. Is there an audience? No live audience. No, but still.

But still. I can't believe their plan was just to keep rolling it until it worked. So if we think through the explanations, one is they got super lucky by accident. But I feel like they must, like I slightly believe they never bothered. checking what the actual probability is of rolling snake eyes until the day. Is this what a snake drawer is? Or is that something different? Because when they said voted out by a snake drawer.

Oh, maybe it's put the word snake in front of everything. It's like the smirfs, but snakes. I feel like a snake drawer is like a sock drawer, but full of snows. You need, yeah, you have two. Don't you hate it when your snakes aren't matching. Oh, I do. That's why I only own the same type of snake. Yeah.

It doesn't match. You want a knee-high snake. Exactly. No, no, no, no. To chip in, I don't think a snake draw is a thing. The internet doesn't seem to know it's a thing. I do have lots of lovely instructions on how to draw a snake, though, now. Lovely. Draw a wine.

Old snake eyes producer, Lauren Gimshaw there. That's what we call us snake eyes. So, here's what I propose. We ever think about how they could have done this? And then we watch it. Okay. So, option one, they just got. lucky. Yeah. I'm rolling that out.

Yeah, I doubt it. No. Option two. Having worked in television. Yeah, exactly. Yeah, yeah, yeah. Now, I definitely know of game shows who haven't bothered thinking through the mathematics. So I cannot completely rule out. They showed up on the day of filming and then realized what they'd done. Oh, 100%. That's extremely likely. They just got everyone to keep rolling the dice until everyone got snake eyes. And then they edit out loads of the rolls. Which I think is what they did. But that would involve sitting around for a very long time.

On average, it would take 180 rolls. Okay. So plausibly, they sat there. And that's the average. I think that that's fine. Well, I just rolled mine for about 50. So it's like just four times as long as that. So one option is they rolled it a bunch and then the edit they zoomp it down.

I think that's what happened. That's pretty likely. Everyone would have to be on board with, we're just going to do this until it works. Yeah. And then you're going to act like it was quick. Yeah. It's like the OK Go videos. Like the OK Go videos.

So that's option, option one. Option two, I think, because the dice they're rolling aren't real dice. Because the theme of it is like jungle aesthetics. Right. And they have lots of wooden crates for some reason. And I think they've 3D printed or made. tiny wooden crates that are the dice. Cute.

And then they've stuck a picture of a snake eye on one of the faces. Okay. So it's not like they're rolling real dice. They're rolling a dice substitute. It has five blank faces and one eye. Ah. I wondered if maybe they went to the contestants and said, hey, look, just to speed this up, it's still going to be fair, but what if each dice had two snake eyes on it?

And then... Again, you keep rolling until you get two ones. So one on top, one on the bottom. Oh, yeah, or two next to each other. And then just in the shots, we make sure you can't see both of them. Yeah. That's how I would do it. If I was in charge of, we want to look like everyone's got to wait until they're all snake eyes.

Yeah. But we don't want to sit around all day. I'll be like, well, more snake eyes. Yeah. And just be real ambiguous with the phrasing. It's still fair. Yeah. It's still the same odds for everyone.

They don't mention it any point. point, these dice have blank faces and ones. So yeah, it could easily be that. Could be that. I think, now, this could be being unfair to TV people. Now, I think that would make more sense. Yep, thank you. I also think that that would involve a certain amount of pre-planning. Thinking ahead. Yeah, good point. Which I think a lot of TV people don't do. No. No. We'll both been there. I think they're more likely to sit through all of it and film it for like, half an hour and edit it down, then they are to have done the maths first. Do you know what? Let's make special dice. I don't think any...

The props department are not thinking about that. No. The props department are just thinking... They've got spare snake eye stickers, ready to go. And I'd also say that the props department probably aren't making the dice in the sort of the way the casino, you know, we were talking about this, about the weights and all that sort of thing. They've just probably 3D print of them. It's very possible that the... there is a slight weight imbalance that made a difference that wasn't done on purpose,

but did change the outcome. So I think exactly what you said, what if instead of being perfect cubes, they're just a little bit flat, because that would increase the probability of two of the faces and reduce the probability on the other four. And if one of those was the snake eye face, you'd skew it. But I still don't think it would have been planned. No, it could have been completely by accident, 100%. I think anything like that would be an accident.

No, yeah, yeah. And I ran some numbers on that. So each face should be a one sixth probability. If it was ever so slightly squashed, and so two sides, instead of being 16.7%, were 20% likely, your probability of getting it in 25 or fewer rolls goes from being 0.05% to 0.2%. Quite a jump. It's quite a jump. Still, probably not enough to explain it happening that fast.

Closer, though. Closer. So a little bit more squashed. If the two faces were 25% chance each, then you're up at a 1.8% chance of it happening in 25 or fewer. And as they get more and more squashed, obviously, the probability gets more and more higher. But then it would visually look ridiculous. And the question of the geometry of how squashed for what probability is very, very complicated. But I think you're right.

I think they might have accidentally made them a bit squashed. I haven't seen the dice yet. I only got a copy of this TV show today. Because I saw highlights online and we got the stats from what happened. So I've been analysing that. I haven't watched it yet. So should we watch? Are we out of theories?

Maybe magnets in the table. Like there could be properly faked magic dice. Yeah, but I feel like. Now, without knowing the show, I feel like when something comes down to chance, they do need to be a bit more. Like, if they want a mechanic that allows the producers to choose a winner who they want, there are other ways of doing it. There are other ways of doing it. With RuPaul's Drag Race, as an audience member, you might go, well, that person definitely should have won based on the lip-sinking battle. I realize that some people won't necessarily

relate to this, but... It's a better cultural reference point than the snake. That's true. So watching it, you'd go, well, that was a better lip-sinking performance. However, I can understand overall, like, technically the lip-syncing performance is meant to be the thing that changes the outcome. But more often than not, you could tell that the producers had an idea of who they wanted to keep and who they wanted to get rid of. Yeah, but there's a mechanism within the show to be able to put your finger on the scale. Yeah, exactly. Whereas outsourcing it to dice would be a terrible way to then have to fake that to change she's going to stay in. So I don't think they would go to a special effort to do that.

I think they would just introduce something that would allow them to be biased. I think everything we know about TV as well, I don't think they've gone on to all that effort to. It would have been very complicated to fake it. Yeah. And also kind of problematic because then it could be revealed that they faked it. Everyone has to buy in and no disgruntled contestants. Well, shall we have a quick watch? and then see what we think

it's so good it's beautiful so we just watched and we're laughing because the person who doesn't roll snake eyes when they get voted off the show gets into the crate

And they've edited it with all the, like, sob story stuff. The music's really serious. And then the guy just crawls into a crate. It has such, like, 30 rock. Yes. Comedy vibes, not intentionally. It's great. I also watched that and went, I think that my snake game show has, ironically,

ironically has legs compared to this. Yeah. Yeah, like, yeah. It's pretty special. Yeah. So, I have theories. Hit me with your theories. Okay, first of all, I don't think there's two logos on the dice.

Gotcha. They're sort of moving the dice in their hand. There would have been far too many chances. It'd be too hard to do it proper, yeah. Yeah. So looking at it, I noticed that the crate dice has a diagonal sort of fake support being, yeah, going on all the other sides. except for the side with the eye drawn on it.

Snake eyes. So that does mean that technically that side would have had slightly less weight than the other ones. Probably not so much to make a huge difference, but might help account for why it happened more quickly than you would expect. I also think, because it does go on for some time at the beginning, you see everyone rolling and not getting snake eyes. Yeah. So I do think that they did do that, but as they go further on, the snake eyes sort of start

coming up more and more regularly. I think it's because the rounds, because you can't edit down the rounds that much when there's all five people. But as you get fewer and fewer people, if there's like two people rolling and, you know, it's round five, round six, round seven, round. I reckon they just got rid of those rounds. they just edited them out and down, I should say. Yes, yes.

And so then you start to get more, because at the beginning we don't get many snake eyes and then it gets. They suddenly cascade. Yeah. I have to admit, you watch the edit. The pacing is good. If you didn't understand the probability, you'd watch it and go, that was a fun game. Even I was bored.

In the first couple rounds, I was like, something better happen fast. Yes. Now, to be fair, I have. I haven't been watching this show the whole way through. You don't care about these people. Yeah, blah, blah, yeah, yeah. It's an interesting choice of game for a final episode. Yes, just pure random probability.

Because I'm assuming they don't do this in every episode? No, no, this is it. Because normally your final episode would have games that are really fun to watch. Yeah, yeah, it's the finale. Watching people roll up paradise. Now, I'm a big fan, but I get it. Yeah. I think the people reacted in a very genuine, excited way.

Yes. I don't think they were actors pretending it just... No, no. I think they were legit roles and people responding. I could be wrong. So I think that adds weight to the... They did lots of roles and just didn't show many of them. Yeah.

Because they could have just said, look, everyone, roll it five times in a row each time. Like you get five goes. Yeah. And then you pass it on, and then you get five goes. I'm still trying to find a way where it's fair. I don't think they would have done that. By the time it gets to you, everyone's had a lot of chances. You haven't had any chances yet.

So I do think they've done it one person at a time each time. I think they would have done that for a while and have been so boring. I, with makeaway takeaway, we made a big make at the end of an episode. It involved having an archer shoot at balloon. full of paint that were hanging over a picture. And it was a professional archer, but also quite a lot of space. Yes. And very windy on the day.

Yep. So the archer would get at where the balloons were, but the balloons would float out of the way. Yeah, yeah, yeah. And so it took a really long time. But eventually we got it, but it took a really long time. Yeah. I am aware that these sorts of things do end up. They just go, well, we haven't.

of a plan B. Let's just keep going. Yeah. Yeah. I think they took turns rolling and then just some of the rounds where nothing happened were taken out. That's my theory. Yeah.

And then maybe they just renamed the rounds. Oh, yeah, 100%. Yeah. Because each time they roll, it'll say like round four, round five, round. I think it actually makes the show look worse if they were being truthful and saying round 17. Yeah, exactly. Yeah, yeah, yeah.

Well, they never said every round does anyone wrong. roll. I mean, there are ways to wave this away, yeah. Because you can discount those ones when they both get nothing. You want to show that there's a round or two where no one got anything or not close or whatever. But if you'll notice pretty much after that, there's nothing for ages. Almost every round has. There's one quite early. Maybe they just got lucky. Yeah. And then they just cascade. So I think what we can say is it wasn't just good luck. Like that. so exceedingly unlikely. They've done something. Yeah. But I suspect you're right that they just realized that it was going to take forever and they fixed it in the edit. It doesn't make for good

TV. And the thing is, they might have known it might take a while. Yeah. They might not have known exactly how long it would take. But all reality shows essentially are a case of keep rolling. And then we'll happen eventually. Exactly. Yeah. So they're not new to filming a lot and then getting out the good bits. Okay. Well, if anyone here worked on the show. Let us know. I'd love to find out. So, Andrew, don't know if that counts or not, but we're going to go with, it's plausible, they just kept rolling and they edited it. Literally. Yeah. Yeah. On both counts, they kept rolling and rolling. And if anyone listening is a TV producer and would like to make Beck Hills version of the snake. Yes. Hit me up.

I've got many other ideas. Does it also involve people getting in a crate at the end of the... No, but I'm telling you about my, I can't believe it's not Celebrity Big Brother idea. It's Big Brother, but made entirely out of celebrity lookalikes. And I think some of them have to be the same celebrity, like multiples of the same. Multiple copies are the same celebrity. Yes, yes, yes. Either one. Make it happen.

We'll commission them. Next problem was sent in by Daniel, who went to the problem posing page at a problemsquare.com and said, I am able to juggle seven balls. Wow. And sometimes qualify it. That's where Daniel says you do twice as many catches as there are balls. Their problem is how many can flash, oh, that's one catch per ball or qualify, that's two catches per ball, seven or even higher numbers and how long would it take to learn it from scratch? Beck, you looked into this. I did. And what do you find? Well, fortunately, I know a lot of jugglers.

Yep. I know you do too. Yeah. We're both in juggler-adjacent industries. It's very true. Yours are math. Mass jugglers, yes. Yes, and mine is circus folk.

So to answer this, I went to Daryl J. Carrington. Yep. Who's a fantastic clown, comedian, performer, but also used to be the head of juggling. Head of juggling. At Serco Media. Oh, not avoid juggling. Just avoid juggling. Yeah, just a juggling, yeah.

Straight to the head. Maybe. Maybe. Maybe. That could be the highest ranking juggling position for all, I know. Yeah. Anyway, he's incredible. I saw his show in Edinburgh Fringe, and it was really good.

He does do some very impressive juggling in that. More than that as well. Yes. As you said, he explained to me what qualify and what Flash means. Yes, yes. So the Flash is just how many times you can. Throw them all once, catch them all. Yeah. And then to qualify, it's almost like saying prove it. Yeah, do it again. Prove it wasn't a mistake. Keep going. At least one more time. Yeah. So that explains that. What I found interesting is he talks about how to train someone to juggle seven balls and how long that could take.

I came up with a technique to be able to teach anyone to juggle really quickly. When we're juggling, basically the definition of juggling is having more objects than you do. hands. So if you're juggling two balls with two hands, that's not juggling, but if you're juggling two balls, throwing and catching with one hand, that'll be cast as juggling. Now, how many people can juggle seven balls? It's getting more and more because that amazing thing. So when I learned to juggle over 20 years ago, five balls was like, or five clubs was like, well, that was kind of a big deal. But nowadays, it's a lot more common to see people doing five, six, seven, So I think in the relative number of how many folks can do it, I believe seven has become more of a sort of a norm.

And you'll see that now that more and more people are performing seven balls and even with tricks. And in terms of how hard it is to learn seven balls, so I actually have a program where I get people from zero to juggling five balls. And I can get people usually to get up to five balls in about six weeks with a very specific training in very similar way. to learning to drive is that you learn the basics and essentially all juggling is is throwing one ball accurately so one of the reasons why I say a lot of people don't get up to seven

balls is because just the amount of time it takes to learn to throw a ball really accurately at the height to be able to fit six other balls in that same pattern does take a long time now we'd argue that sometimes someone without any because a lot of people that discover juggling or discover circus stuff, inherently quite creative folks. So, for example, when I learned to juggle three balls, you then start learning all the different tricks and throwing them around your body or bouncing on your head and all these different things.

So it can take quite a while to develop, like, say, seven balls because you're going on a really wiggledy path, do you know what I mean, through sort of expiration and kind of think, oh, I could do this, or I could do that. Whereas I think if you actually were really focused on the right my mission is to be able to juggle seven balls and essentially what you do is you start with one ball you throw it to the height of seven and a good way to understand what that height is

if you throw a ball up and you can do six claps underneath it so you've got six beats underneath it that would be the height so you're throwing from one hand's right hand across your left hand up one two three four five six catch that's going to be the height of your seven balls and basically what you'd do is you'd throw that one ball repeatedly and the way I get people to train is that you do 10 throws and catches and if you haven't had to make any adjustments haven't had to like reach out to catch the ball or shuffle your feet to be able to do it then how you kind of progress then you bring it up to then throwing two balls at that height then three in a sort of a fountain pattern and you can basically build these up so with my kind of hypothesis I'd say that if I can get someone to

juggle five balls within six weeks. I'd say seven kind of is essentially every time you had a ball, it does become sort of exponentially more difficult. But I would say it would be possible to get someone from nought balls to seven balls within, I reckon 12 weeks. If they were really focused on it and really wanted to sort of achieve that, I reckon 12 weeks would be a reasonable challenge. There's less than I expected. Yeah. I would have years. Well, because I think we think in terms of the way that you and I might learn stuff, we pick it up as a hobby and kind of do it in our space of time. We're not doing eight hour days juggling. Yeah, yeah, or doing like a very specific training program. Yeah, it's a good point.

I think, I don't know about you. I know I would get bored. It does require very specific ability that I do not have. Can you juggle three balls? I can juggle three balls, but I have to really concentrate. Oh, right. Can I see that? I've got three juggling balls here. I found these actually Lucy's old juggling balls. I couldn't find mine. Something else that Daryl said to me, which we won't play, but he was saying that it's very common for drummers. To be into juggling because of the rhythm. The rhythm. And I think this is really interesting because I tried to do drum. You're not a drummer.

Drums were the instrument that I was learning. I had a pearl export. I saved up a lot of money for it. I desperately wanted to drum. I did lessons. I can't hold a rhythm. I get excited and fall out of rhythm Yep, that checks out It's the same with my, I love dancing I can't do a choreograph dance because I get excited So I have, I think it comes down to like

My sense of timing is not great Well, I'm really looking forward to seeing you juggle now Okay Is you're going to gradually get faster and faster Okay, Beck is still sitting in the chair Yeah, that's impressive Laura's going to film Oh, great, great, great, perfect

I don't think I've ever done it sitting down before Okay that's why i have to watch them because they're not accurate because darrell says it's a you know learning to juggle is about learning to throw one ball very accurately throw it yes and then catch it but but yeah i can't throw accurately okay right that could be the beginning of the problem and i think that's why i have to be really paying attention to where they're going you're catching bit of your juggle is doing a lot of work yeah no Okay, pass them over.

I think one's on the floor. Oh, one's on. I found. Okay, again, sitting down is a bit different. Your throws are much more. Oh, is that the Millman mess? I got distracted. Was that the Millman mess or were you just...

No, Mills Mess is a whole other. I can do that where they're all... I can do that where they're all going up in the middle and down on the outside. And then occasionally you can do one over the top. I get a little bit and then you can just do that same one back and forth over there That's impressive

Not perfect That was very good But you can do the reverse juggling So that's, I can't do this properly But normal juggling is up on the inside down on the outside That's how I do it yeah But you can do them all the other way around But it looks like it's harder to be accurate that way

Yeah but if you filmed it forwards And then reverse the footage It would look like that second one Huh Yeah But I'm way less coordinated on the outside. That does look harder as well because of the angle that you're throwing at changes. But I had to learn because it's a standard maths bit of nerd cred. Yes. It's being able to juggle.

Yeah, yeah. Actually, it was in Edinburgh Fringe. When I was up at the Edinburgh Fringe in 2015, I was like, while I'm here, I'm going to learn to juggle. That was it. Darrell mentioned briefly in his voice note to me about side swap notation. I struggled to understand it a little bit, so I'm going to get you to explain more. Well, I have the rolling advantage of a friend of mine invented it. What? Back in the 80s, yeah, Colin Wright, who... Oh, yes, who you've mentioned before.

You've mentioned before. And if you watch my tipping tetrahedron video, he's the guy I interviewed because he had the model. Colin, a very good juggler, him and a mate of his way back, came up with side-swap notation as a mathematical way to write down juggling tricks. And there's a whole separate conversation about this, which is where no one had really found a rigourable. notation for juggling before. And because they then learned the patterns behind different ways you can combine types of throws and juggling, they predicted the existence of new juggling patterns that no one had ever juggled before, but then they were able to juggle

them. Amazing. And they wouldn't have found them because you can't just do any old throws and juggle because you can't hold more than one ball at once. So when you're throwing them in the air, they had to come down in a catchable rhythm. Yes. Which one way of doing that It's just by always doing the same throw. Another way is by combining different types of throws such that they come back into alignment as they come down. And in the voice note, they mentioned the 531 juggling pattern. That's one of the ones that Colin discovered, where if you're constantly doing three throws, so three is in the number. You're throwing them such that if you were juggling three balls, that's what you'd have to do every single time.

A 531 is where you suddenly do a throw as if you were juggling. juggling five, and then you do one as if you were juggling three. So you're throwing it up higher or shorter. Higher. Depending on whether it's a five or a three or whatever. And then you do a cheeky one, and then you can go back into threes. So previously Darrell was saying how with the set, if you're training someone to do seven, you want them to throw the ball high enough to clap six times.

So that would be your seven. Yes, that's a seven. throw. And then got it. So to learn to juggle five balls, you have to learn to do a series of consistent five ball throws. Yeah. And back in the day, it used to take a very long time to learn that because all you

could do was get five, start throwing them in the air, hope for the best is a disaster. Yeah, that's how I go. Start again over and over and over again. When Colin and colleagues discovered the notation, these other combinations, they found there were ways to be juggling three and in the middle of it throw in a five and then do a couple to compensate and then carry on juggling three. So suddenly you could practice a five throw as part of an easier juggling trick, which dramatically sped up the process of learning to juggle five because it was easier to practice that throw. And now I can see more why drummers would be

into this because so often it's a, yeah, it's almost like musical. You combine it. different intervals. Yeah, yeah. And so it's less about you're not sort of, you don't need to look at where they're coming back. It's just the rhythm. It's all about the rhythm and ensuring that if you're an accurate thrower, then they're always coming down in the same place. Yeah, that's really cool. Also, I've seen drummers drum using juggling balls and that's very cool. Yeah. And I'll link to, there's a great video with Colin talking about side swap and all the mass behind that. If people want to check it out. I can't juggle five because I know how much effort it takes to learn and I'm like, I haven't got that kind of time in my life. I guess I realized the constraints were

my time to hone my coordination and ability versus the amount of gravity we're under. Because if there was less gravity, I reckon I could juggle five. Yeah. There's too much gravity. Now, I've been invited to go to space. Close. On one of one of the ESA training flights. No. Yeah. Where they fly the vomit comet. Yeah.

But they're not doing zero G. They're doing lunar G. Ah. So I will get multiple bursts of time under moon gravity. Okay. I've asked permission to take juggling balls because I reckon I could learn to juggle five on the moon. So this was a.

part of the problem that we're solving. No. But I'm looking forward to the update on this. It's part of the answer. One way to learn is go to the moon. That's true. Yeah, because then if you, yeah, so that might bring down the 12 weeks to. Yeah, way down.

Hope. I haven't got 12 weeks. Yeah. Well, if you do it too quickly, you could try seven. Yeah. No, yeah. So I want to see if I can learn five well enough on the ground. That I won't be out of joggle five, but I will be able to under one sixth gravity.

Let's find out. We'll find out. Until then, Daniel, hopefully Daryl, myself and Matt have answered your specific questions. Wow. If it does give us a juggled ding. Nice. We're now down to any other bedness. Bedness.

That mum's in my bed right now. And I'm on the couch bed. in the blanche. We heard from Ian, who went to the problem posing page, and selected solution. Because Ian wanted to add, first of all, blah, blah, blah. Thanks, Ian. Listened since blah, blah. Anyways, long story short.

You have a lot of these details here back. No, Ian, remember it. I've been thinking about the problem of naming a set of children as in episode 113, Mark Anna, names amid career change. And I like the idea of using a set of overlapping names. For example, Edgar, Garris. Oh, right. So the end of Edgar is the beginning of Garret.

Yeah. So if I was to read this, yeah, so it's Edgar, Gareth, Ethel, Eliza, Isabelle, Bella. You could call them Edgarath Elizabella, if you need to address them as a group. That's great. That's fun. I love that Ian. Love it. If anyone's accidentally done that with your children names, let us know.

Oh, yeah, yeah. That'd be a fun thing to realize later. On that subject, we also. heard from Jasper, who remembered a story from 2021 of an actual Belgian family who gave all their 11 children anagram names using the letters A-L-E-X. It's never been better to be the oldest in a family than this family. Yes, exactly. Yeah, yeah, totally. I can't believe I didn't come across this when I was researching. This is amazing.

So Jasper said this was covered by several newspapers websites at the time. but more surprising maybe is that after 11 children, they got two more. Of course, continuing the theme. So since 2021, they've had two more kids. And they're stuck with it. Yeah. These are names of their children. Alex, Axel, Zella, Lexa, Zale, Zeal, Xel, Exler, Leax, Leax, Elax,

Laxay Well they've now Was that now 13 kids? Yeah That's over Wait what is it Four times three times That's over half the 24 possible

arrangements Are they going to have 24 children Just so that they can do this? That's all of them You thought you were dedicated to The bit While the names individually may not be all the same quality We have to give them credit for choosing a theme

And sticking with it After your discussion I simply couldn't leave this family unmentioned And get this, Jasper has provided sources, both in Dutch and English. That's thorough. Good work. Producer Laura also wants to give credit to David, who also sent in a message about

this as well. So thank you both of you. We had three people get in touch about the card shuffling from episode 114. This was one of those things where you systematically take cards off the top and move them to the bottom and all that kind of stuff. Oh, yeah. Like juggling but slower and more fun. So, now, I'm going to mention them in decreasing levels of how verbose they were.

Tom gave us a whole write-up, how they were fascinated by the deck shuffling problem. They thought they'd have a crack up making a website to do some visualizations to see if any other interesting patterns emerge by tweaking various deck parameters and shuffling methods. Now, Tom can confirm that there's plenty of bangers to go around their quote, and as in like there's some really satisfying patterns that appear as you go through these different shuffles. So they've put a website together with a full visualization of all the cool patterns you can come across for different starting arrangements. We will link to that in the show notes. Excellent work, Tom. Oh my gosh.

And they end with Love the show, blah, blah, blah. Love you, Tom. Blah, blah, blah. Burnett did the same thing. It's a visualization of the card. shuffle we'll link to bernard's site as well and bernard says they're gradually adding more features to their visualization over time but it's a nice start so do people check that out see what berners done finally sean just typed visualize shuffle and then a link it's good it's good work sean i appreciate

how to the point you were and we will link to all of these three different visualizations for the card shuffle in the show notes. Thank you so much. All three of you. Now we've gone from zero visualizations to a ridiculous number of them. Good work. I want to give an extra shout out to Tom who called there's Riffle Me This. Okay, extra points to Tom for Riffle Me This. Oh, and I have some additional any other business. Very sadly, there will be no a peanut squared. Peanut lived to the ripe age of two and a half years, which is half a year longer than most dwarf hamsters. But unfortunately, Peanut passed away recently.

And as I'm living on my own, I'm not going to get another hamster because I'm away a lot. And I don't think it's fair on a pet. I now have an incredible hamster setup. It's a beautiful terrarium, all the toys. There's some leftover bedding and food and stuff. If any of our listeners are interested in a very decent dwarf hamster set up, I mean, you could put a different animal in there, but it made a dwarf hamster very happy. How much hamsters need more room than people expect?

Yes. And you've got that room. I've got that room. And I can prove that my hamsters, both pudding and peanut live to ripe old ages. Yes. So if you are interested in that, I'm afraid it is pick up only. I do have it listed on eBay. We'll put a link in the show notes.

And as listeners, I'm going to let you know that I've got it listed for 50 pounds, but there is a make me an offer thing. And basically, if you're willing to come and pick it up, I'm willing for you to take it for any amount. Yes. Enter any quantity of teeth. Yeah, any quality. Yeah. Anyway, if you go and check that link and it has been sold, then you know it has gone. But otherwise, if anyone is interested and wants to give a hamster a happy,

home, head on over to eBay. Once again, I find myself feeling very grateful to our listeners. You guys are amazing. I am constantly humbled by your existence, whether or not you are sending in stuff, the fact that you listen at all. I'm very grateful for, but I'm especially grateful for the Patreon supporters who make this podcast possible by ensuring that it is financially feasible and that old snake eyes, Laura Grimshaw, is able to come back for more.

We like to thank our Patreon supporters by giving them access to our bonus podcast. I'm a wizard and also thanking three of them at random at the end of each episode by mispronouncing their names. And on this episode, those names are Sim, Onla, or Rio Pezzio. Allsar, Rithi. Final offer. Anyway, thank you so much for supporting us. If you would like to be awesome like those guys and have your name potentially mispronounced by us at the end of an episode, go to patreon.com forward slash a problem squared, where you can look at some of the other wonderful benefits of being a supporter. Now, all that's left to thank is my wonderful co-host, Matt Parker.

Oh. Myself, Beck Hill, and the proverbial mother of the show, who has come to stay. and won't let us leave, no. If anything, we won't fly the coop is Mama Bear's old snake eyes, Laura Grimshaw. You know old snake eyes. Goodbye. Okay.

Yeah. Battleship stations. So, my last guess I missed, and that was C6. Yes. You flanked a previous hit. So I'm going to go for B7. You're going to go for B7. Hit.

Yes! And, not unrelated, you sunk my battleship. Now, I was also coming off a hit. I'm going to continue in the same direction with a G9. G9. Miss. What?