A Problem Squared - 114 = Delectable Dips and Dealable Decks

Episode Date: July 21, 2025

🃏 What’s the deal with cards?🫕 What is the perfect ratio of chips to dips?🍔 And there’s some Any Other B-B-Q-B-nessHead to our socials to see the card shuffle and patterns, Bec’s starstruck selfie, and our chips ‘n’ dips experiment!For all your homemade snacking needs:https://www.bbcgoodfood.com/recipes/tortillashttps://www.bbcgoodfood.com/recipes/homemade-tortilla-chips-guacamole-charred-tomato-salsaIt’s 5 o’chop Somewhere! (Really excellent work from Eve)https://www.instagram.com/p/DKZSlCGIdCZ/?utm_source=ig_web_copy_link&igsh=MzRlODBiNWFlZA== And some info about Aphantasia as mentioned by Keith…https://en.wikipedia.org/wiki/AphantasiaAnd synaesthesia…https://en.wikipedia.org/wiki/SynesthesiaIf you’re heading to the Edinburgh Fringe, you can get tickets to see Bec here:https://tickets.gildedballoon.co.uk/event/14:5884/And you can get tickets see to Matt here:https://www.pleasance.co.uk/event/getting-triggy-it-matt-parker-does-mathsHere’s how to get involved with Matt’s Moon Pi Kickstarterhttps://www.kickstarter.com/profile/standupmaths 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 our Problem Squared, the problem solving podcast, which is a lot like a barbecue. But instead of raw meats and or meat substitutes, you bring us problems and instead of cooking them, we solve them. Unless your problem is, what do I do with all these raw meats and or meat substitutes, in which case this podcast is exactly like a barbecue. Your grill masters are Matt Parker, a mathematician and YouTuber who enjoys repurposing old code to solve new problems.

Like a cook who might fashion a spatula from an old fly swatter. And me, Beck Hill, a comedian and writer who will often stray from the problem and fall down a rabbit hole. Like a cook who perpetually steps away from the grill to wander aimlessly through the sight of a large, densely built Warren. I view my code like people view leftovers. Oh, so you're like eating people's- To be reheated back up again. I'm like, ah, I can chuck in a few new bits, reheat it back up again.

And then serve it to the customers. Yeah, exactly. And listeners, you are those customers. Yeah, exactly. On this episode. I worked out what's the deal with cards. I see what you did there. I thought the deal pun was so strong, I didn't bother writing the rest of the sentence. But you really gave up on it towards the end. Yeah, I know. If you said, what's the deal with cards? I could have, you're right. I could have sold it. But it's in the delivery, Matt.

Yeah. I find out what the deal with dips is. And there'll be any other barbecue-ness. How are you, Matt? I'm good. I'm tired. Yeah, I can tell. You're a little bit grumpy.

That's true. I got more sass than normal. I do apologize. You're like a toddler that's just woken up after a nap. Bit bleary eyed. You know that when toddlers still have the little tears in their eyes, but they've just stopped crying. So they're kind of-

Yeah, that's me. Yeah, that's you right now. No, I just got lost on the moment. Cause you and I are both still honing our Edinburgh Festival friend shows. Yes. Which we will bring up every episode until it's too late for anyone to buy any tickets. After which I'm on tour, standupmass.com slash shows

for all your C-MAC inner show needs. And my book came out in paperback. Love triangle paperback came out. Ah, so it's more affordable now. Way more affordable. Price has plummeted. So it's now it's bendable. That's fun. A book about angles, you can actually bend it now. So that's nice. You know something there. I did the Joe Marla podcast. I'm just looking for a sense of recognition. People are sitting there going, oh, what's happened to my podcast app?

It's just stopped. Nope. That was me. That was you buffering. Staring at Matt in silence. You told me what the podcast was about. You said it's a rugby podcast. Correct.

It was not a rugby podcast. Joe Marla is a rugby player. Right. Well, he retired last year, I think. And so he did play for England, like played at an international level, like a very good famous rugby player. Obviously that level of competitive sport, particularly something with that much, you know, getting knocked around. You got to retire at some point. So he's like, mid thirties. He's like, I'm too old for this. Yeah, does a podcast nice And it was fun for two reasons The the second reason is just it was very friendly

The fantastic PR people at Penguin were like would you want to do the Joe Marla podcast? I was like, yeah, why not? I was timing out but no idea what it was gonna be like. Lovely. Just really good fun. Really nice Now him and a guy called Tom, chatting away. Very funny folks. Very slick, very professional. A lot of fun to be around. I had a great time. Slightly, actually, you know, one of the knock-on effects of me doing a rugby podcast is I get a bunch of credit with people I don't normally get credit with. So the pub that we often go to after recording the star here in Goddaming, the

people who run it are all big rugby fans. And I have never had more respect from the people who run the pub than when they found out I did the Joe Marla podcast. Nothing else I've done has even made a tiny dent. Well, they wouldn't have noticed. Like one time I walked in and Mike, one of the guys is like, was this you? And it was the Donald Trump tariff video I made. He just popped up on his YouTube feed. Up until then they had no idea. I was just that guy who came in with the Labrador. That was very friendly. He's like, what are you doing on YouTube? And like, that's the thing I do. But now Joe Myler podcast has also broken through the noise because he played for localish team called the Harlequins. When we were leaving, we were just chatting

and he, when he was younger, lived not far from Goddaming. He was in this area. And he mentioned, he's like one memory he had because he was a kid at the time. He remembered going to a pub called The Refactory. It's one of our favorite local pubs. And I'm like, oh, I know The Refactory. I love it.

He's like, yeah, it was always great because they had those tubes that your order would go up in. Like a pneumatic tube. Like a pneumatic tube. Nice. And I was like, you saw the tubes? Because they were removed long before my time. Oh, they were a thing of legend. Oh, I'd heard rumors of the tubes. I never fully believed they definitely existed and was true. Ah, but doing a podcast with a rugby player

played with England team and he just casually drops into conversation confirmation that the pneumatic tubes, because they used to take your order apparently behind the bar, and then like thump, and Oh, that's so cool. Pneumatic tube it to the kitchen. He's like, yeah, I saw the tubes. They've got one of those at the Postal Museum, so I got to try one. All of the messages came from some small children on the other side of the museum.

Now you and I are pretty good at not being starstruck by famous people. We work with famous people. We're very chill. Yes. I don't have to try that hard with sports personalities because I already don't know who they are and I'm in no way in awe. I appreciate, I think it takes a phenomenal amount of work, more work than being a comedian to be that level of sport.

Like that, that competition is phenomenal and the dedication and training and everything. So I'm very impressed when I meet professional athletes. Sure, yeah. So the whole time I'd been real chill. But at the end I just went, wow. As we were saying goodbye, I'm like, wow. I can't believe I met someone who saw the tubes.

Ha ha ha ha. He thought it was the funniest thing. We weren't recording. It was like the funniest thing he'd ever heard. And I guess he's sick, like rugby people are like, wow, I can't believe I made it. I'm like, wow, the guy who saw the tubes. And that's who he'll always be to me now. Yeah, weirdly, I gigged in Brighton recently and I caught up with our friend, Sebley Delisle,

who's a fantastic laserist. All my lasers. And he said, oh, there's this new brunch place that's just opened called The Canopy. It's really nice. They do really good brunch, very affordable. So we went there. We're sitting there chatting. I like to sit with my back to the window, otherwise I get distracted by what's happening outside.

As we're talking, the chef comes out and is chatting to the people behind the bar. I'm like, that's chef Michael Bremner from Great British Menu. Some years ago as well, I think it was during lockdown maybe, but I was like, oh my gosh. And then Seb turned around and was like, oh yeah, yeah, I think I remember them saying like it was a good chef. And I was like, and I kept getting so distracted. He could see me looking over his shoulder as like Seb could see that I wasn't paying attention.

And I was like, I'm just going to ask for a selfie. And he was like, okay. So I went up and I was like, are you Michael? And he was like, yes. And I was like, can I have a selfie with you? I saw you in Great British Mania and I think you're amazing. And it was like, oh sure. So we got a picture.

Like I have interviewed John Cleese. I have interviewed like Christina Ricci. I regularly spend time with quite like well known people in my job. Is that a selfie we could put out on the- Yes, we can put it on socials. Great, great. Yeah, yeah, yeah. I want to see, because someone who's been on both sides of those selfies, I want to do a little reading of the facial expressions.

I was so happy. I'm so, so happy. Yeah. And he's holding his spatula. It's a fly spotter. Yeah, yeah, yeah. So how are you, Be Beck? I'm good. Great. It's been warm, the weather. It's been real warm. So last week I went to a Lido.

British listeners, I have a bone to pick with you. So the pool that I used to, I grew up going to, firstly had like quite a little grass area around it. You put your towel out there. There's some trees. Yeah. So you can lie under the trees when you're not swimming. It's hot It's shade. Okay, this lighter and I've been to other lighters

I know it's not distinct to this lighter, but it was a hot day. Right? It's first time I've been to a lighter on a hot day firstly Did no grass? Concrete. Oh nothing but concrete or concrete or concrete More not much space. It was hot so much concrete. No shade. No shade. Well, not much space either. Famously good when it's hot. So much concrete. No shade. No shade. No, no, no.

Literally no shade. No where to sit. Get that heat right into the concrete. Big high brick walls. Yep. Concrete. It was like a prison. I'm not joking.

It was like being in a prison. Wreck time. At the light out. It was like a prison, but worse because, and I say that loosely, I've never been to prison so I realised that I can't. I suspect people would disagree with you. Yeah, sure. Carry on.

I would say it's worse because at least in prison you're not trying to sunbathe by a soup of children. They're all screaming and everything. It was so busy. It was so full. There was no space to like properly swim or splash about or whatever. Wow. There's nothing like that. It's like one pool.

It's not like they've got a big one and then a small one. Cause normally there's like one that people can splash about in and be stupid and then there's another for laps and stuff. Laps and everything. I understand Australia, we have more space, I get it, I get it. But there was a park next door. There is this land. That's where the grass was. Yeah, but it was outside of the big tall brick walls because it wasn't in trouble. You had to go over the razor wire.

Right. It was so close. I would not be surprised if there was razor wire at the top. It was so... and we had to pay £12 for one hour. £12 an hour. A pound every five minutes. I couldn't believe I was... And I went with another Australian and she and I were like, this is hilarious and frustrating. I only went because it was my friend's birthday. Oh, that's very nice of you. But then afterwards, also for my friend's birthday,

we went to see the band Sparks playing at Hammersmith Apollo. And I was familiar with some of their songs, but seeing them live, I was like, Oh, I get it now. Oh, right. They've been going forever. They've got like 28 albums. They're like, it's like you, Matt. They're the most famous band you've never heard of. Yeah.

I would say we might've been the youngest people in the, in the crowd. Yep. It was, but they're fantastic. They're really good. But the thing that I got distracted by was the stage in the crowd. It was, but they're fantastic. They're really good. But the thing that I got distracted by was the stage lighting. Now it was like sort of, uh, rods of light, maybe like a meter or so. Oh, like a fluorescent tube. And they were sort of, it was set in almost a grid type pattern.

Right. So then they could make different patterns and stuff like this. And there was no real, like there were patterns, but they didn't like represent anything in particular or whatever. Sometimes they made it look a bit like it was raining. Other times it was all very random, but I felt very nervous because I kept thinking at any point this could accidentally make like when you've got a grid and you're like you could make some pretty offensive patterns.

Now, those offensive patterns pop up occasionally in maths when you're doing things with symmetry and whatnot. And they're commonly referred to as the unfortunate fourfold rotational symmetry. I love this. That was what I was worried about. And then my friends and I were talking about this and saying, and because it made me think of segmented displays. Oh, yeah. Yeah. And how you you could create segmented displays. They could have done numbers, letters or something.

And that made me wonder, do you reckon that they have some sort of program that if they are sort of doing a random pattern type thing, to make sure that it never shows anything offensive or accidentally spells out like bomb or something? I've been looking into things like that because I've been putting the lights for my show. Ah. So the stuff I've seen there probably, you get LED strips now that you basically put inside a plastic tube with a frosting to make it look like those. Yeah, and I'm sure that's what it was.

Yeah, and then you get all the, you can have DMX controllers that are doing all this stuff. Very interesting. I haven't got the time. I wish I could throw myself into it fully because it looks so amazing. I haven't got the time. I wish I could throw myself into it fully because it looks so amazing. I haven't got time for another hobby at the moment. But I will say, your friends and mine, Foxlog Studios,

Pete and Lloyd, they were hired many years ago by the BBC to run an interactive stall for school kids at the Big Bang Fair. The BBF. The BBF, the Big Bang Fair for the BBC. And I've done stuff there as well. I happened to be there the year they were there. So I hung out with them for a bit and chatted about the system, but it

involved allowing thousands of teenagers loose, who are in about, without significant adult supervision, free entry text boxes that will then automatically appear on screens around the game zone or whatever it was. Foxtalk were running. Now it takes less than a second of thought to realize how that's going to go wrong. Yep. Because they don't want to sit there and manually check every single word. So they had to come up with a system to stop that from happening.

So they basically had to come up with all the words or fragments of words. They wouldn't want to appear on the screen and then run everything through the check before it goes anywhere near the screen. So I imagine some people were likewise tasked with, here are all the symbols, but you've got to then convert the light signal into what it's going to look like as a readable signal, because just two contrasting colours could do it. Three contrasting colours with the right arrangements could do it. I think it'll be an interesting challenge how you'd code up that filter, but I almost

guarantee it exists. LORRAINE I suspect what is more realistic is it wasn't random and they just programmed it to do very specific patterns that weren't bad or rude. I think that was a substantial chat. I suppose we should answer some problems. Get to these burgers before they burn. Problem burgers. Our first problem comes from the problem posing page on a problem squared dot com.

This is Mark who said, take a sorted deck of cards, i.e. a deck sorted from ace to king of spades, then ace to king of diamonds, then clubs and hearts. Shuffle the deck in the following way. One, hold the deck face up in your right hand. Shall we do this at the same time as you reading out the steps? Yes. I sorted a deck into the four suits. They're all in order.

What order did they want the suits in? They've suggested spades, diamonds, clubs, hearts. Okay. So what do I do now? I'm holding the deck of cards. They're in the order that Mark has requested. Okay. So you're holding the deck face up in your right hand.

Face up in my right hand. So that's like, I can see the King of Hearts now. Yeah. Take the top card from the deck and hold face up in your left hand. Done. Take the top card from the deck in your right hand, and place it on top of the deck in your left. Done.

Take the top card from the deck in your right hand, and place it on the bottom of the deck in your left hand. Oh, there it goes. Then repeat steps three to four until the entire deck has moved to your left hand. So I'm taking the cards off the top of the deck on the right. Okay. So I'm now working my way through the deck, taking cards off the top and I'm putting them alternately on the top and the bottom of the other deck. Oh, oh my goodness.

This is going to take a while. Okay. Well, Matt does that. I'll read the rest of the question. Great. Now repeat this again and again. What? I've not even done it once.

They said after 12 reshuffles, you will get back to the original deck order. However, the curious pattern emerges at nine. Oh. The cards will now be grouped by rank rather than suit. And those groups will be ordered like so. One king, two queen, three jack, four, 10, five, nine, six, eight, seven. Notice how the numbers climb from one end towards the other end. And then at seven reverse back through the deck into leaving.

Yeah. Also notice that within each group, the order of the suits will be the same order of as the original deck, but this also reverses when the cards go back through the deck, i.e. the order of ones is spades diamonds Clubs hearts then the order of Kings is hearts clubs diamond spades. I Hope you can explain both why it repeats and why you get this curious pattern. Why why why mark? Well, I can do one half of that Okay, each of these shuffles, which is not a great name because they're going to the same place

every time. But let's just call it a shuffle. Each of these specific shuffles, because they're always identical, have to repeat. At some point, they have to go back to where they started. Yeah, it's like when you do a Rubik's Cube, you do the certain... Exactly. There's only a finite number's Cube, you do the certain. Exactly. There's only a finite number of arrangements the deck can be in.

And so if you're doing the same thing every time, you're eventually gonna come back to a state you've been in before. I know we've discussed this for other problems. Cause either you'll do every single one of them and you finally get to the last one and then you come back to the beginning. Or more likely you will hit the starting state and then loop back. Or it might be that you

go for a while and then you hit one that you did halfway through and then you go into the loop. You got that loop with a little tail it took to get in there. So any set shuffle you do, if you do it long enough, you'll get back exactly where you started. It can just take a different amount of time. This one takes 12 rounds. You know, at the very beginning, when we started taking the cards off, we put the first card in my left hand, and the next card, we started with it going on top, and then went under, then on top, then on under. If you accidentally do it the other way around, if you did under first, then on top, then repeat all the way down, you would still get back to where you started, it would take 51 shuffles.

Wow. So it's 12 is the one that Mark mentioned, the quick one, that seemingly trivial change over four times longer. Wow. 51. Hmm. And I know that because I did it using terrible Python code. 51. And I know that because I did it using terrible Python code. So to answer the second question for Mark, it will always repeat. Doesn't matter what shuffle you do if you do it consistently or any consistent

series of shuffles, as long as you repeat that series over and over again, you'll come back to where you started. So if the number of cards in a suit is 13, but it ends up being one less than that number of cards in a pack is 52, but it's one less than that. Is there another move we can do to test to see if it's one less than that number of cards in a pack is 52, but it's one less than that. Yeah. Is there another move we can do to test to see if it's one less than that? What would that test be? I have no idea. That was for you to answer.

I'm not a mathematician. We're looking at number of cards, numbers in a suit. The only other thing you have there really is the number of suits, which is four. Yeah. So it needs to be something that takes three. Yeah, I think it'd be reverse engineering. It would be very difficult. Unless it was a really contrived shuffle.

Yeah. That just like moves the middle to the top to the bottom of back. Done! We've proved it. I've done. Yeah. So I put together some code and I just wrote a little algorithm, which takes the deck as just a list, 52 values, and a long list. And then takes them out of one list and puts them into another list, according to the algorithm.

So it takes them all off the bottom, because you're dealing from the face. And then alternately adds them to the beginning or the end of the other list until they're all done. So, coding-wise, it was pretty straightforward. the face and they'll turn it into the beginning or the end of the other list until they're all done. So coding wise, it was pretty straightforward. Then I had to set up different decks, put it in, see what comes out and then feed it back in again until it to stop when it hits something it had seen before. So that's how I got it to, it can tell me how many it takes before it goes all the way through.

Now I was just kind of doing that to make sure my code was working and I understood and I got the 12 that Mark mentioned. I not only have that it ends up back where it started and it's that interesting one nine in, but I've got every other single state it goes through along the way. So I thought I'd show you that and we'll have a little look and see if there are any other fun patterns. Yeah. And we can verify what Mark said, that that definitely is the thing that happens part way through. Would you like to see the output? I can do this either way. It can either be all the cards numbered one to 52,

or it can be the face values. It'll be like ace, one, two, three, four, 10, Jack Queen King. Face values. Face values it is, okay. To see a whole deck at once, you got to make the type quite small. Oh, I don't like it. So, well, tough.

It's like looking in a magic eye. It's not looking like looking in a magic eye. I reckon if I- It's a sailboat. Yeah, exactly. Dolphin. Okay, so we'll put these in the show notes, but there's your 12 states, and the first one is just Ace, two, three, four, then up to King and then repeats Ace all the way up. The lead card is interesting. The top card in the deck goes Ace, two, four, eight, so it's doubling.

But then it goes three and then doubles to six and then two and then ten and then seven then King King King right at the end I don't like that. No, it's not pretty. That's not a nice pattern When I scanning through the in-between states There's no other ones that really stood out to me as being like, oh, that's interesting Other than because that's all of it for me. Oh really? Yeah, here's the one that Mark got excited about and you see this one here starts It goes King King King and then Ace Ace Ace and then Queen Queen Queen, two two two. So this is the one that Mark was talking about, nine in where they're all, they're in batches of four.

Yeah. After that, they're in pairs. It goes King King Ace Ace Queen Queen and then all the pairs repeat. And then you have another one that looks like mess. And then the last one is right back where it started. So I stared at that much like you and thought I can't see anything particularly interesting in that. I then had a look at the one I did where you start under instead of on top, which takes 51. And the ninth one in, totally different. I was like, well, hang on.

It's both the ninth one in and it's the third one in totally different. I was like well hang on that. It's both the ninth one in and It's the third one from the end So I went and looked at the third one from the end of the other system, and it's the same It's the same setup Huh, I was like it's curious and then I tried it with smaller suits So I took out all the Kings around the simulation again It takes a different number of times to repeat so if we get rid of all the kings from the deck, and then run the code again, it now takes 24 deals before you're back where you started.

But one, two, three before the end. Yeah, Queen, Queen, Queen, Ace, Ace, Ace, Jack, Jack, Jack. You'd have an even number of suits for it to work. So if you just took out all the spades, wouldn't work. Right. If you took out the spades and the diamonds, it would work. So if you just took out all the spades, wouldn't work. Right. If you took out the spades and the diamonds, it would work again. Huh. And if you take cards out of a suit, it still works.

Okay. So I'm just, I use the code so I could rapidly try a bunch of variations because if something breaks it, then that must be important. Or it persists despite a change. That's giving us an insight into where the pattern's coming from. And so what we've learnt is, it's not the ninth one in that special, it's the third one from the end. Huh. Has to be an even number of suits. Doesn't matter how many cards are in a suit. So there are constraints now on when it works. So for me, this is like the beginning of the problem solving process. Here's a pattern, and it's something like it's algorithmic or involves a situation.

I'm like, well, what happens if I take or remove things from the situation? And that doesn't mean it's important. So the key for me was realizing, oh, it's not how far from the beginning, it's how far from the end. And I was like, okay, yeah, because if the deck has to end up back the way it started, you could think of a shuffle, which is the exact reverse, where you start with a deck and then you take the bottom one off, then the top one, then the bottom, then the top, then the bottom, then the top, and you're putting them into a new pile in order, which

is just the exact reverse. If you do that three times times that's what goes from. Having them in the perfect order to this interesting order and that's the actual journey that matters that's the one that's the same every time and so then I wrote out a simplified version of. A deck of cards in it. So I've numbered the cards one to four and then one to four, one to four, one to four. And then I reversed the pattern back and it works. Yeah. And so the reason it works is partly what we spotted before and partly something I didn't really notice about the second last one. That's why I actually reversed it from the middle out, so I did the cards in the same order. So I took the middle one out and put it back on the bottom,

and then the one that would have been above that back on the next one from the bottom, and then reversed all the way back. And you're kind of going from the middle of the deck and then bouncing backwards and forwards as you go out, which is reversing when you started in the middle and you were adding backwards and forwards on both sides. And it means you're going forward through some suits and backwards through other suits. Right. Because the ones where you're going like further into the deck are in order, but the ones where

you're going back in the deck from the middle up are the extreme ones. So your fours all end up being paired together because they're the same distance away from the middle. All the other ones are in different orders apart from the middle one, because you're once you're halfway in from one end, it's the same as being halfway in from the other. You reach the same card. in from one end is the same as being halfway in from the other, you reach the same card. And so you end up pairing up the extreme values and the middle values and the other ones, you flip half of them and the next time you do it, they get paired up. And so then you've actually got a whole bunch of pairs and then those pairs get paired up and that becomes the four groups of four afterwards.

That was a very hand wavy explanation. Yep. I've convinced myself why it works. Okay. And it's because you're starting in the middle and you're going in different directions. There's no really neat reason other than it happens to happen because of the way the cards are. There's not like some beautiful explanation behind it. It's not some sort of Fibonacci.

No, no, it's not like, yeah, oh, it turns out because the golden ratio or sometimes it's really pleasing where you're like, oh, it's the explanation of this because if you think of the deck upside down, it's a triangle. Like those things I love, it's not one of them. Right. It's just, it's what happens and will always happen I love it's not one of them right it's just it's what happens and will always happen if there's an even number of suits you know what

I'd really like to do what would you really like to do attach a different colored piece of wool yep to each card yep long long bit of wool baby. I hear you saying yep and Then do this technique and see what braid you end up with yeah, you would see the pattern you that would make it a lot more visual a friend of mine Henry Sagan man Who's a mathematician who juggles Henry and I got bored one time when he was staying over and so we got some juggling Balls and tied ribbons to them great so as you're juggling you and tied ribbons to them. Great. So as you're juggling, you braid the ribbons like a three ball cascade. And then we realized one of us could do a three ball cascade and one of us could do the opposite of that facing each other and the balls are tied in pairs. And so as you're both juggling, they never get tangled.

Cute. And then we looked up braid identities. So we could be doing different juggling patterns, but still the ribbons would never get tangled. And we had some good nerdy fun. I should make a video out of that. It was so much fun. Yeah, that would be really interesting. It would be really good fun.

I would be really interested to see you pair that with a hairstylist. Right. Because you can get really intricate hair braids. Yeah. Done. I mean, braid theory is a whole area of maths. So I imagine braid theorists have talked to hair braid people and compared notes. But I'd always heard that a juggling cascade is equivalent to a braid.

And we want to do it with ribbons, but you're right. Well, it is because when you're braiding, cause I use, when I had long hair, I used to braid my hair, the normal braid, the most common ones, the outside in. Yep. So that's if you were juggling, you'd be sort of throwing inwards. Throwing inwards. And then the reverse is the normal juggle where you're throwing up in the middle. You're throwing in the middle.

Yeah. And that's when you're braiding outwards. That's the one that gets you the French braid, the one that's sort of on top that I think is prettier. But anyway, I'm biased. So you're right. This shuffle feels a lot like that. You could maybe do it with a reduced deck like I did on paper and see it.

That would probably be one of my next steps if I felt like there was something else interesting in here, would be to draw that diagram, like have arrows, this goes here, this goes there. And see if any patterns come out, but the wool idea is even better. I also want to point out that this was not the problem you were going to solve originally on this episode. No, not when we met this morning. Yeah, you needed an item which we went on a hunt for and could not find. We went out for lunch and it wasn't in Sainsbury's where it was meant to be.

Yes. So I was like, I'll do it next time. So you've knocked this together in quite a fast amount of time. Yeah, I don't know if that reflects on me in a good light or a bad light. I think it's very impressive, but I also think it should be mentioned in case anyone points out glaring errors. Oh yeah, that's more like it. Yes, yes.

Yeah, there's any, and waviness. I did this over lunch, so go easy. And I know that there's gonna be hundreds of you listening going, but I sent it a problem. Why would you choose that one? Because I was looking for one I could do over lunch. I looked around the room. You know, you gotta make up a fake name.

You literally dropped a bunch of like, packs of cards this morning. So I think that was fresh in your mind. You were Darren Browning me, weren't you? I was, yeah, that's right. I was planting all of the problems. Yeah, it was me. I sent you this one. I was getting out the podcasting kit this morning and knocked some cards off a shelf.

I was like, I've got cards. I was like, how do I trick Matt into making me a friendship bracelet? A little long game. Anyway, in conclusion, it is because it is, it's neat. It's a fun pattern. I don't think it's a particularly nice is because it is. It's not as neat. It's a fun pattern. Hmm. I don't think it's a particularly nice reason why it appears. It's kind of fun, I guess. The big thing is Mark saw something interesting, thought, huh, and then investigated it and we had a play and it was a lot of fun and it doesn't always go anywhere and this time it just turns

out it is and I convinced myself it's true. They can't all be bangers. The end. Next problem is from Higgins who went to the problem posing page at a problemsquared.com and they opened by saying Beck and Matt, very polite. I have a problem. Good. I mean, I'm sorry to hear that, but also good. Yeah, that's why we're here. Yeah. I thoroughly enjoy bringing in snacks for my teammates at work. That's not the problem. They specify that.

Imagine if it was though. That's the problem. Yeah. I enjoy it too much. Yeah. Often, this isn't the form of a dippable thing. That's the problem. Yeah. I enjoy it too much. Often this isn't the form of a dippable thing and the dip the dippable is dipped into. While I bring the food in for my teammates, I also partake of the food items. And this is where the problem starts. For example, if I bring in tortilla chips and salsa,

I will likely end up with leftover chips or exclusive or leftover salsa. I will then go refill the Dippable or the dip so as to use up my leftovers and most of the time I create the inverse situation and repeat the cycle until I get lucky enough to correctly estimate the right amount of dip and dippable needed to have no leftovers. It is important to note that I do not like wasting food. Well, that much is very obvious at this point, Higgins. How can I solve this problem and avoid eating the bulk of the food I bring in for my teammates?

Love the show, blah blah blah. Okay, Higgins, you want me back. Thank you for the help. Can we name this, by the way, this- because I feel like this is a highly relatable problem. I think we've all been in the situation where we've ended up with leftover dip or leftover- Dippable. Yeah, some kind of food that requires the other. Yeah. And if they're not eaten in the correct ratio, you've got a useless

portion of one. Yeah. Thus creating- is it the Higgins problem or the Higgins paradox? Yeah. And I guess what Higgins trying to say here is they bring in a reasonable amount of chips and dips. A few chips and dips are consumed by their colleagues and themselves until one, the limiting reactant runs out.

From what I'm reading between the many lines, Higgins then goes home and goes, I better get more chips, because I've only got dip. He's like, oh, no, I've only got chips, but I get some dip. And they eat multiple times the original office food before they've depleted and eventually they've come into phase. Now I'm going to argue that my favourite part about, because I love going to a picnic, love a barbecue, love a, you know, bring some stuff along. Theme of the episode.

My favourite part about it is leftover- Oh yeah. Dip or dippables. Gotcha. Because then I'm like, oh cool, I can go get the thing that it needs. And then I've got something to eat as I go that is half the price. Or you know- Because you're half way there.

I'm half way there already, right? The meal's meeting you in the middle. And I feel like that's kind of the plus side of this scenario. Yeah, but Higgins is a finisher completer. So am I. But then it is half price until you buy too much of what's missing, and then you've got to buy the original one again. At this point, you've just paid for the whole meal.

But then you got to buy the other one again. Then you end up paying two or three times before they come into phase. then you end up paying two or three times before they come into phase. What you don't want is the amount, the unit purchase of dip and dipable to be close, but not quite. It's going to take longer. It could take longer to come back into phase. Just like if two frequencies are slightly off, the beats are super long. Yep.

Whereas if you just like the dips was twice the Dippable. Boom, you got it in one extra purchase. Yeah. Yeah. Now, I can't help but feel that this is a trick. Oh. By I think it's very smart. OK. This is my theory. Well, not theory. This is a hypothesis.

OK. Because I haven't tested it yet. My hypothesis is the brands or whatever, because often they'll create- they'll put out both the chips and the salsa. Yeah. And they make it so that it's not the right amount. Yep. So that you're forced to keep purchasing. Love it. It's like how- The hot dog is not in my bag.

I think we've talked about Tim Tams. Yeah, hot dog, same thing. They're like, quite often you'll end up with an uneven, like Magnum ice creams now come in packs of three. Three. Who does that? Masochists. If you never have a prime number of things

in a food packet that's designed to be shared. Yeah. The only time that that would work is right now. There are three of us in the room. You've either got the prime number of people or one very hungry person are the only solutions to that problem. Yeah. Now in the case of the three ice creams, both would work.

Yeah. But in bigger situations, no. Yeah. So that case you're going to, you're blaming big dip. Blaming big dip and big dippable. They don't like the constellations. Yeah. Yeah.

So I've made this my dinglet because- That's a short problem for- That's a short problem for new listeners, yeah. Because I think it really matters. There's so many variables. So many. So for me to do this is like a proper big main problem. I would have to go back to you Higgins and be like, right, how many teammates do you have? Is it the same amount of teammates each time? Yeah. I'm going to guess that Higgins likes to switch it up because otherwise you're going to be known as Tortilla and Salsa person. You don't want to be Tortilla and Salsa person. No. You want to be Snacks person. I'm going to guess that that's the case. I'm also going to guess that occasionally someone might

stay home. There also might be people with specific food. Somebody's like, I can't have Tatsuki. I can't have it because I can't spell it. Is that the rule in your house? You can't eat it unless you can spell it. I can barely have guacamole. It's still not every time. That's all French cuisine out there. You haven't had a croissant for years. No, I dream of a croissant.

Baguette, baguette about it. I'm here eating things like ham, soup. Oh, we've reached silly o'clock again. I'm gonna do a quick test. We couldn't get what you needed from Sainsbury's. No. But we could get what I needed. One that was there.

So you've gone for some brand name tortilla chips, not the faux Ritos, which is- Oh, who do we call them? Yeah. I came up with that name when I was doing a questing time in Manchester. I'm sticking with it. Great. I feel like there's a crossover from people who went to questing time and who listened to this.

So about two people just got very excited. So I'm going to open them up. So this is my very specific scientific theory. What I wanted to do originally was to weigh the chips and the dip and then weigh them after we've eaten to see what was left. But we don't have weights. So I'm just going to get us all to maybe unobserved that by all I'm including producer Laura, we're going to dip a whole tortilla chip into the dip. But then I think on the count of three, we'll compare our chips to

see if we tend to go for the same amount of dip each. So because we don't have scales, what I think I'm going to do is count how many tortilla chips in this packet. And then I'm going to see, first of all, we'll do the blind thing to see how much we load onto a chip. Yep. Just out of interest. Then we can kind of guess. Yep. Like how many am I take? Then we will work our way through this salsa, the three of us. Right. We will work out how many, then we're going to work out how many tortilla chips we get through, because we've got a significant amount of tortilla chips in this pack. Yeah, and a lot of dip.

Yeah. We'll count how many tortilla chips it takes us, and then we will see how many are left. Right, okay. All right. So everybody take a tortilla chip and dip it without looking. And then hold it. Just to start with. Oh my goodness. Okay. And then, and then we will- Do you want to go first? I'll close my eyes.

Okay. Okay. This is so ridiculous. Okay. I'm holding it under the table. Okay. I'm going in. I'm going in. You slow? Okay. Everyone in the middle. What do we got? I've gone for quite a lot. I'm, I'm a big dip guy.

You are the big dipper. Laura goes for very little dip I've noticed. This is interesting. I'm a big dip guy. Mm. You are the big dipper. Mm. Laura goes for very little dip, I've noticed. This is interesting. But I think it's good. This is why I couldn't just test it on my own. I love the fact that we could just hang out as humans, but no, we're having a simulated hypothetical party right now. Technically at work, you've brought these in for your colleagues too, so this is very realistic. Have very- just call me Beck Higgins. Beck Higgins. Beck Higgins.

I'm going to keep track of how many I've eaten, by the way. Are we allowed to take these down the pub until we finish them? If we keep counting. Of course we'll keep counting. This is number seven. So, because we don't have time to casually wait to see how long we get through these. No. We'll continue to do this.

Cause we're finisher completers. We are going to finish either the dip or the chips. Yep. And then we'll record a voice note. Once we have a solution. Yep. Great. Once we have a result.

Oh, did our post-recording drinks just get tax deductible? Yeah, they did. All right. So the result of that will appear here. Okay here it is now. Thanks Judy and Matt, it's On Location Matt here in the pub and we have just finished snacking. Yes, here is On Location Beck to say that we got through 82% of the dippable chips in the pack because we were left with an amount that were far too small to dip.

We got through 82% of the pack before we ran out of dip, which was 86 chips that we counted. Yes. Out of 105 for anyone who's curious. The dip itself is 300 grams of salsa. So we worked out that each chip carried 3.5 grams of salsa. That might be interesting to know should you have shop bought tortilla sized chips

that you're working with. And in terms of conspiracy theories involving Big Dip, 80 to 20 ratio is about as far as I would push it to make people have to buy more. Like that's right on the cusp of recurring purchases for as long as possible. Yeah, because we were looking at the packer going, ah, probably wouldn't buy a whole new salsa for that. It was close. But it was, yeah, it was very close. It was very close. And to be fair, we went for a hot salsa, which meant that we probably didn't

eat through it as fast as people would have if it was a mild salsa. Yeah, maybe. I think the 80-20 ratio stands. Back to you, studio Matt and back. Well, we'll let those guys get back to the pub, shall we? Yes, yes. Now my solution for you Higgins, my solution to the Higgins paradox, is that you should do a similar experiment and then just make your own salsa. Make your own dip. Oh! Work dip. Oh! Work out. Oh, I love it.

How much it takes you to get through a packet of tortilla chips or make your own tortilla chips. I love making tortilla chips. Do you do it with pita bread? No, flour. Oh, you make it properly. Well, when I do burritos, like to do my own tortillas anyway. And again, I didn't make the right amount.

So then I just hang them out in the oven to get real crispy. Cut them up into little triangles, a little bit of olive oil, bit of salt, wang them back in the oven. Ooh, that's a tasty, they're really good. All right. Well, do you know what? Let's stick some links to some tortilla chip and dip recipes. I would just encourage everyone to go for less pre-packaged stuff. Get the exact amount you want.

That's my advice. Good advice. Yeah, thanks. Take down Big Dip from the inside. And for any other BBQ Venus. Wow. Matt, you've got a plug. I do. I like to promote Beck's

Edinburgh show. It's called, um, oh hang on. Guess who's Beck? Beck again. Beck Hill's back. Tell your friends. Beck Hill's back. Beck Hill's back. Yeah. Tell your friends. Yeah. Great back. Beckhill's back. Yeah. Tell your friends.

Yeah. Great. I've seen a lot of places get it wrong, because clearly they've decided to type it out instead of copy paste. Copy and paste. Yeah. Shout out to listener Sunny, who did the photos. Oh, listener Sunny. Yep. And then the lovely William Andrees who put it into a nice poster. But yeah, check out my Instagram, BeckelComedian. If you want to see, see my Edinburgh Fringe poster.

Or indeed, if you're in Edinburgh, you might get, I'm going to do limited edition of flyers again this year. Oh, interesting. Yeah. Hand numbered. Mm-hmm. I'm doing all flyers different as well. But I'm doing it using TurboPython code. Yes, I'm very excited about this.

Yeah, each flyer has 102 different symbols on it. Or not all different. Any two flies will have one and only one symbol in common. So it's a Edinburgh wide game of double. The printers are not happy with this game. No. And I think they can play with the posters too. Yeah, yeah. We're not happy about that. the posters too. Yeah. Yeah. We're not happy about that.

It's great. Yeah. It better happened. I love that. See you all there. Links to the shows in the show notes. You've got in touch on the problem posing page. Not the first time they've used it because they're the one who posed the problem where

they had chopped karate chopped a board in half. Like a total badass, their words, but they are correct. And this is way back in episode 106. They wanted some ideas on what to do with their karate chopped board to commemorate the achievement. We had a couple ideas. They picked one and they've sent us a link to it on their Instagram. So I'm just going to open that and have a look at what they did. Oh, that's great. So I'm just going to open that and have a look at what they did.

Oh, that's great. Okay, Bec, I'm going to hand over to you to, uh, to describe what we're looking at here. Yeah. Cause I suggested that maybe because you get so much art, I'm using that term loosely where it's like engraved or burnt into it with a fun phrase. Quirky expression. You don't have to be crazy to have work here, but it helps. That kind of thing. And then I suggested a bunch of very dumb affirmations and Eve has chosen one of them.

A really good one. Which is, it's five a chop somewhere. It's five of the chop. Somewhere. Eve has posted of the chop. Somewhere. Eve has posted it saying, it's definitely not perfect, but I'm really pleased with how this turned out. Eve, you should be. It looks fantastic. I wouldn't change a thing.

It was great to use my wood burning tool a bit more. Well, there you go. Look at that. Even if my lettering is a bit wobbly. Eve, I think your lettering is better than my handwriting. It's now hanging above the desk in my spare room slash office, office for those work from home days. I am absolutely thrilled.

Good work, Eve. This makes me very happy. It is indeed five o' chop somewhere. Eve's shown how they put the board back together again with paint and glue and a bit of, do a bit of sanding. Oh, there's a little guide. I missed the guide. A little finish. And there's also a picture of Eve chopping the block. No. Oh, look at that. In the first place.

Mid chop. So this is great. That's really good. We'll pop this link in the show notes as you did tag us as well. Very impressive. We've also heard from Keith. Great name. Who's listening through episode 111. And Beck mentioned she's a very visual thinker.

That sounds like you. And they've commented on, Beck, thinking about how a lot of people evoke mental images. They just wanted to give a shout out to all the sufferers of aphantasia, like Keith, who are unable to create a mental image. And they've given us the Wikipedia entry to aphantasia, which Keith, who are unable to create a mental image. And they've given us the Wikipedia entry to Aphantasia, which we will put in the show notes. They discovered a couple of years ago that they and other people can't literally see pictures in their mind's eye. They always assumed that when people talk about a mental image, it was a turn of phrase and not literally an image in your head. So thanks, Keith.

Shout out to everyone who doesn't have mental images like that. It's very interesting because Keith explains a bit more about it and how, once they realized this was something that they were doing differently to how other people are imagining things, it made sense why people would complain about seeing a film of a book they'd read and say they didn't enjoy it because the film looked different to how they imagined the book. And they've just realized, oh, that's why, because other people when they read books have mental images of what's happening and Keith doesn't.

That's great. Yeah. They also said that it's why they've never really been into reading books, which makes sense. Yeah, makes sense. But have's why they've never really been into reading books, which makes sense. But have been interested in photography because it's the creating of the images and helping recall things. Keith also goes on to say, I think I'm at a disadvantage when trying to recall things, particularly when trying to describe detail like a person or a location.

It's not that I don't know what they look like or can't describe them, but it's more of a feeling and list of descriptors than a photo. Do you have any advice on improving memory and recall for non-visual people? I don't because it's not something that I have, so I have not had to, but I'd be interested to know if any of our other listeners have aphantasia and what they've done. If you've got any advice for Keith on and what they've done. If you've got any advice for Keith on ways to help memorise things. I'd be curious to know, because a common way of like memory trick

is to use a journey you do frequently. Yes. We're very good at remembering those. Mm. It'd be curious to know if you've got a Fantasia, how you recall the journey. And depending on how that's done. got a Fantasia, how you recall a journey. And depending on how that's done. Yeah. Cause I used to do one, which was the walk from my house to this office, because I can picture several key points along the way and they're surprisingly little discrete locations.

But depends how, if you think about a journey, a walk that you do frequently, what that's like, maybe there's an equivalent way to then attach concepts to each of however you've split that up in your memory already. Yeah. Well, we also found out after that episode that producer Laura Grimshaw has synesthesia. So Laura has certain colours that are evoked by words and sounds and letters. Yeah. Aren't we all different? Yeah, it's great.

I love this. It's very cool. Keith also says thanks for your hard work on the excellent podcast. Thanks Keith. No blurs. And as we near the end of the podcast, all that's left is for us to thank, obviously, all of you. We really appreciate all of you, but we also specifically want to thank our lovely Patreon supporters who go to patreon.com forward slash a problem squared.

They also get access to our bonus podcast. I'm a wizard and early episodes. And there's I'm a wizard. Is that like the kind of real like raw experience of us at the beginning of a recording session before we're it is exactly warmed up. Oh, if you think this is slick, you're like polished. Yeah. I want to know what these guys, what's it like to be their friends?

That's surprisingly accurate. Yeah. Hop on over to patreon.com. Yeah. Hop on over to patreon.com. So we're going to randomly choose three of those supporters to thank by mispronouncing their names. And on this episode, those supporters are. Yeah.

Why, son? Ha. Ah. Shabarge. Ah. Wow. Joe Shu. Hooray! are. Wow. Joe Shu. Array!

By armoring. Do do do do do. By armoring. Do do do do. By armoring. Do do do do do. Do do do do do do. And finally, thank you Matt.

Oh, thanks Bec. For helping me at the grill. You're too kind. Flipping these burgers. I'm the sous chef. They're all very well done. Yeah, we, like a lot of the podcast, overcooked it. Yes, but nobody's getting food poisoning.

You'll be chewing on it for a while and you probably all reckon you could have cooked it better and you might be right. But it got cooked and that's what matters. So thank you for helping me, Matt. I've been Beck Hill. And as always, we want to thank our wonderful producer and editor, Laura Grimshaw, who is like the main host of the barbecue. Oh, right. Loro sends out the invites. Yeah. Yeah.

Make sure that all the dips have been topped up as well as the dippables. Grimshaw. Grimkoshlaw. Nah. Leave the word jokes to me. I'm demonstrating exactly why that's our policy. Loro Grillshaw. Right there. Bye.

Biki. I didn't sink your battleship, did I last time? You did not. It's unsinkable. Or, or is it? Yeah, pretty sure. Because I'm gonna choose C, no, can you imagine? I'm gonna choose F.

Yep. Eight. Oh no! Fate. I swore it was on single all, but fate has sunk my battleship. Weeeeeee. Direct hit, well done. Do do do do do do. I'm catching up! Now, I'm almost a hundred percent certain... that I've got all the ships in the cluster you had.

But, just in case I've made a mistake in my logic, I'm gonna fire just a celebratory shot at H5. H5. H5. Miss. Okay, okay, I'm okay with that.