A Problem Squared - 071 = Snap Probability and Zombie Mobility

Episode Date: October 24, 2023

In this episode...  🃏 Is the probability in a game of snap changed if two packs of cards are used?  🧟 Can zombies ride bikes?  🥣 A commemorative plate-bowl update.  👻 And some Any Other BOoOoOosiness!  If YOU want this year's APS Christmas card be sure to sign up to the Wizard Level on Patreon by the END OF NOVEMBER.  You can do that here: https://www.patreon.com/aproblemsquared/membership  We'll be sharing a link to our new Discord soon. In the meantime, go talk on the APS Reddit: https://www.reddit.com/r/AProblemSquared/  As always, pease send your problems and solutions to our website: aproblemsquared.com.  And if you want more from A Problem Squared, find us on Twitter,  Instagram. and Patreon.

Hello and welcome to A Problem Squared, the podcast which is a bit like Halloween, except our listeners come to us with problems instead of wearing adorable costumes, and we provide solutions instead of candy. We don't know what costumes our listeners are wearing no but that's my point they're not coming to us oh that's true we don't see them good point yeah i mean they can if they want that's true i'm your host comedian and presenter beck hill and i'm a lot like a zombie and that i'm often lacking in brains oh that's not true and i'm joined by your other host mathematician and youtuber matt parker

who is a lot like a vampire because he sucks oh my goodness wow yeah as soon as you were being nice and you're like that's not true beck i was like oh just oh mate just you wait it's all right i'm gonna bring us both down dang you're consistent it was either that or you're like the other one was you're a werewolf and that you're quite hairy in places you wouldn't expect. That is true. Talk about a beard. Yep, that's the intro in this episode. I do some spooky card maths.

I'm going to be thinking more about zombies. And we have some terrifying A-O-Boozness. Stay tuned. Hello, Matt. Hello, new listeners. Yes, welcome. We don't often theme an episode around a holiday. No, we did do a spooky episode a few years ago.

A few years ago. Where people sent us their supernatural problems. That's it. And I did like the pumpkin, hole in a pumpkin solution. And I think mine was how to get rid of a ghost. Sounds like us. So, but yeah, we haven't done one for a while. No, I got lucky. problem that came in i just went oh that's a bit it's a bit weird i was like i'll just call it spooky halloween here we go i did threaten you i did you did you've got to make it

spooky related yeah so yeah yeah oh good i appreciate that you're welcome have you been i've been all right i'm now acutely aware That We're gonna blink And the year 2023 Is gonna be over It's been a fast year Yeah It's been real swift And yet slow

I don't know about you But every now and then I think I remember something That happened You know like Earlier this year Yeah yeah yeah

And I'm like Wait what That feels like It was ages ago Yeah So So I'm Also

I'm going back to Australia For Christmas Yes And we fly out late november very jealous so it's gonna be great and that just amplifies everything because i realize that's like what five six weeks away now i'm suddenly gonna have i'm gonna be in australia so i've actually got less uk time left than i expected and so i do we we need to discuss and i need to sort out separately christmas cards for the year yes because for new listeners uh we do a christmas card for our patreon supporters um so we will we send out an original yeah yep we send out an e-card

to our everyone gets an e-card everyone gets an e-card patreon supporters yes and the wizard level supporters get a hard copy signed card we both sign a card and we send it out yeah and i design the card design the card yes and i have a similar system for my uh youtube patreon supporters who support the sound up maths channel but i always try and do a ridiculous maths card that ties into a video that will be coming out at about the same time so when you asked how i've been i suddenly realized i haven't got that long left to come up with an interesting maths thing that can be both a video and a card and i've got a prototype here so i actually thought i might test it on you if that's

okay is this part of your problem or just part of your chat this is chat wow i know i'm i'm using chat to help solve your problem yeah base yeah yeah cool you know this the podcast is problems all the way down we've been through okay so inside the card there will be eight presents numbered two through nine that you can cut out they're like pictures of presents i'm putting these in front of back right now yeah and the design is is will make them look a lot nicer i was just trying to mock them up. And then on the front of the card is a picture of a Christmas tree. I don't know if you want to describe that for the listeners. So Matt's showing me a stock image of a Christmas tree.

He's still got the watermark. Yeah. It's covered in baubles. Correct. And they're all numbered. Yep. But I have noticed that it's not consequential. What would you say if it's just the numbers one, two, three, four?

Sequential. Sequential. There you go. Consequential. I was close. They are consequential. What would you say if it's just the numbers one, two, three, four? Sequential. Sequential. There you go. Consequential. I was close. They are consequential. They are. My brain went for sequential though.

I'm very excited. You put consecutive and sequential together. I did. And got consequential. Yeah. There you go. Also, thank you for seeing me. Which sadly this time made a wrong.

Yeah. Which is not mathematically correct we need a saying for that anyway yeah so the way this works is you pick two presents so do you want to pick two presents any of these numbers yeah because i will say that these yeah these numbers are um i wouldn't be able to count them all yeah i have no idea how many there are they are in very they're very specific numbers and very specific heights. So if you take two presents and put them under the tree. Okay. So I'm going to take this one, which is, you've put it this way, so I'm guessing it's a nine.

It's a nine. Yeah. Actually, I didn't think, I haven't labeled which way up there. These are things you need to write down for you. I need to make a note. Hang on. Let me make a note on that. Oh, what do you got there?

So nine is quite tall. And eight is super low. Nine is very tall. Eight is the tall, very small. Tell you what, put them, and you've put them on, there's a line at the bottom of the tree. Yes. Do it. Stack them one on top of the other.

Oh, okay. Yeah. So now slide that stack along and the presents should sit directly underneath one number on one bauble. Okay. Yeah. So. They'll be close to other ones because there's a lot of baubles.

They are close, but it perfectly lines up with bauble 36. So it lines up perfectly with the number on. I'm making a note. I've designed it to match the number location and your instinct was to get it on the bauble. Yeah. So to switch to bauble. Right, got it.

Okay. And so the number they line up with is 72. 72, yeah. Which is nine times eight. Oh. So if you take any two presents, they will line up with what we would call the product if you multiply them together.

So I'm leaving the eight, funzos. I'm swapping it out with a five. Five and two. So people at home. Yep, and that is lined up perfectly with bubble 40. Oh, five and eight. Yep, yeah, 40. There you go.

So every single. Let's go for. Here we go. Let's go for seven and nine. Oh, go for the. Yep. Yeah, 40. There you go. Yep. So every single. Let's go for. Here we go. Let's go for seven and nine. Oh, go for the big ones. Yeah. They're the two biggest presents here. That's going to reach a long way up the tree.

There's only one at the top, so I can only assume. Oh, no, it doesn't reach that. No, it reaches 63. It reaches seven times nine. But those are the two largest presents. How would you get all the way up to 49? Well, I'd have to add another present. You'd have to have two sevens.

Oh. So now this is one downside to the card. To square a number, you need two copies of it, which is why I printed out two sheets, but I've not cut out the other one. Ah. But if I was to cut out the other seven, and have seven and seven, it would line up with 49.

Nice. And working that out is a non-trivial task to work out what height each one needs to be because some of these you can get there in more than one way. So that 18, that could be a 9 present and a 2, or it could be a 6 and a 3. Wow. That have to hit the same height.

But then the heights also have to work with every other multiple of 6 and of 3. So it's a very complicated system of heights such that you can get every single product. And what would be the real world application of this? Famously, Charles Babbage designed a mechanical computer in the 1800s, never got built. The second person to do that was an irish mathematician who wanted to have a way to turn multiplication into addition so you're adding together the heights and it's giving you instead of giving you the sum even though you're adding the heights together

it's giving you the multiplication of the two and this this was designed originally to be able to mechanically do multiplication by just incrementing something across. Like you could be rotating a cog, you could be moving a stick. Like you can physically be incrementing a thing and it turns multiplication, which is normally like a two-dimensional thing into a one-dimensional offset, which you can then automate. Is that like how an abacus works? A bit like how an abacus works a bit like how an abacus works but an abacus you're doing addition because you're sliding extra beads across but it'd be if you would have it'd be like an abacus but you'd get the multiple you'd get the

product instead of the sum when you're sliding yeah you can do multiplication on an abacus but you're just using it to kind of keep track of what you're doing it's not actually doing the multiplication for you yeah you don't have to do anything other than pick the two things you want to multiply and put them next to each other. And I had the benefit of coming up with this. This is my set of numbers, but I was able to use a computer to find them. Whereas the original,

this was done to invent the computer. So the original time this was done, they didn't have the advantage of the computer. So I found far more efficient ways of doing it, which is why I was able to turn it into a Christmas tree. Thanks to technology. Thanks to technology. But before it was done using brain power. You had to sit down and try and find sizes of presents in my context that would work. Whereas I just wrote some code to find the best possible

you know but that's the difference between you and me is if if we both had to come up with this thing you'd write some code and I would sit there yes and just put things on top of each other and work out the long way yeah how to do it which is how it had to be done originally yeah but that's my style of working I like to know how it's all done because I can't fathom it otherwise. So anyway, I had a lot of fun with that, but I've been doing it for so long and it's kind of so close to me, I've lost track of how it would work. But I found two very useful bits of feedback from you trying it. Thanks.

That's really nice. It's been very useful. And that, Bec, is how I've been doing it. That's really nice. It's been very useful. And that, Bec, is how I've been doing. Well, I just want everyone to know who's already a Patreon supporter or considering becoming a Patreon supporter that my design won't be this. No, no, no.

This is for the mass Patreon people. Bec will do a wonderful artistic design. Look, it might be interactive and creative. I haven't thought. I haven't even thought about it yet. It's also a timely reminder if people want to support us on Patreon just to get the Christmas card that's fine. Yeah,

you can stop afterwards. It's everyone who's supporting us at the end of November. So you've got to get on board so on the 1st of December all everyone who's a supporter at the wizard level will get posted a card and everyone will get emailed a card. Yes. And how are you doing, Bec?

I'm doing very well. As of this episode coming out, in a week and a bit, just less than a week. A week and a smidge, yep. I'm going to be hosting Brussels Comic Con again. Oh, again? Yeah, they're doing two. That flies around. Oh, is that another one?

Yeah, because May was the last one. I honestly thought I've lost all sense of time passing. I know. I keep getting confused because I'm like, wait, wasn't I? Yeah, I've already done one this year. That's why I feel confused. The lineup is absolutely off the charts. I mentioned this before we started recording.

You did. But the biggest guest so far is Jean-Claude Van Damme, which I'm going to have to pronounce better. You better practice that. He's the muscles from Brussels and will be in actual Brussels. What? Wow. So I think we might be interviewing,

because we host the main stage, Matt Heighton and I. So I imagine if he's doing an interview, it'll be on our stage. You get to interview him. Yeah. But also there's a couple of times that we've had Belgian guests. And so the interview is conducted in English because everyone at Comic-Con can speak English. But what will happen is then when we go to the audience, we'll get quite a few people asking questions in French or Spanish. The mix.

And so then what happens is the guest will respond and matt and i sit there like we have no idea what's going on we can't we don't know if they've asked a question that's offensive or so what i'm saying is if you want to ask an offensive question and you can speak do it in flemish yeah yeah but no i'm very excited about that and i'm excited on your behalf it's happening on the weekend of my birthday so it's very possible that i will be interviewing john called van damme on my birthday. Wow. Which is very exciting.

But you know who else I'm excited about? Now, UK listeners might not be, and some European, I don't know. I don't think it had as big a reach here as it did, definitely didn't in America, but in Australia. You know who one of the other guests is. I can't believe you've opened with john claude van damme macgyver richard dean anderson who's also in stargate i think stargate that's a big thing but like i was a huge macgyver fan as a kid like i mean i don't can you tell that i was somewhat influenced by macgyver i think you've macgyvered several things yeah today yeah so yeah that's I'm very very excited

But also we've got James Masters James Masters A.K.A. Spike from Buffy Oh my goodness And the spin-off series Angel I know Very excited

Robert Patrick What is this? Who's the second Terminator The very late 90s I mean yeah It's all the big hits I mean yes A lot of people will be excited about this

Jenna Coleman Who was one of the companions In Doctor Who Okay I'm gonna need The name of the actor Cohen What they did Yeah

Oh that's what I've been doing Yeah You leave a beat To see if I have A flicker of recognition On my face Joseph Marcel Who played the butler

In Fresh Prince of Bel-Air See that's how you do it Yeah Jack Gleeson Who's Joffrey In Game of Thrones Oh I haven't seen it Neither have I But I mean Matt has prince of bel-air see that's how you do it yeah jack gleason who's joffrey in game of thrones oh i haven't seen it so for me neither have i game of unknowns matt has thank you that's why matt and i host together between us you've seen it all we've seen the stuff yeah there's a lot of

incredible uh incredible guests and there's like as of the time of recording there's i think still five or six guests left to be announced oh my, my goodness. Which means when this comes out. There'll be even more guests. There'll be even more guests. I'm very excited. Can people still get tickets to go to Brussels Comic Con? Yes. Oh.

Yeah, they can. Well, they can't because they're going to use their money to subscribe to our Patreon. Yeah, that's right. To get the Christmas card. Some people do both. Yeah. Both? Yeah. Shout out to Denver, who I've talked about before.

I showed up and the first thing he said was, this is your card. Yeah, well played. Everyone who's going to Comic-Con, ask Beck if this is her card. Yeah. So I realize that that's not me saying what I've been up to. Well, you've been anticipating it. But I am looking forward to it.

And do you know what? I thought I'll mention it now because there might be people that want to go. They can go along, they can say hi. Because we've got listeners in Brussels. I don't think I've gone anywhere and done a show for a while without a listener showing up. Yeah. That reminds me.

A listener came to a talk I did in North Carolina. Oh, yeah. And they brought a gift that I left at home. Oh. I will give it to you after the recording. Because you mentioned this in a previous episode. Yeah, tell you what. The post-credit sequence on this video.

This audio, this podcast. The post-credit sequence on this audio content will not be you guessing how many dice are in the jar. Oh. But we'll record at home, just on phone gift me responding to yeah yeah okay deal and then next episode back to the dice nice our first problem is spooky problem our first problem look the problem itself is not that innately spooky. So I really got to dial up the dressing. Okay. So it's for you, Matt.

It's from Maddie. Maddie. From one Maddie to another. Sent this into the problem posing page. At a problemsquared.com. That's the one. And they said, dear Beck and Matt, love the podcast and have a hopefully interesting problem for you. Thank you for saying you love the podcast, by the way.

Imagine if you started out, I hate the podcast, but here's a problem. You're my last resort, you jerk. I want to punish you. It's a terrible problem. They said, the scene, a mathematical problem posed by a colleague being discussed in the staff room. I like this. I think all problems should be sent as scripts.

They should be like, oh, yeah, opening shot, exterior. Yeah. Karen, 46, short hair. That's how they describe sent as scripts. They should be like, oh, yeah, opening shot, exterior. Yeah. Karen, 46, short hair. That's how they describe them in scripts. Right, yeah, yeah, yeah. G'day, Karen, if you're listening. The problem. Two people playing Snap.

Is the probability of getting Snap, you know, playing Snap in the card game, is the probability of getting snap the same or different if played with two whole packs of cards. They put in brackets 52. Yeah. In case they were using score per card, which is 40. So they said our thoughts, just in case you want a little flavor.

Our initial thoughts were the probabilities had to be the same for both, but started doubting ourselves after some crude mental calculations. I like that. For me, crude mental calculations is 69. None of us were completely convinced one way or the other. Then the bell went for two to time. I mean, there has to be a school. There's got to be a school.

Then the bell went for two to time, so we haven't found the answer. Our plea. It's driving a few of us crazy, so please could you do the maths to show what the probabilities would be in each case and therefore whether they are the same or different. Thank you so much. Binge listened to this podcast over the summer and sad that I now have to wait two weeks for new episodes.

You should have been here in the one-month release schedule. I mean, they did have to wait three weeks for the last one. Three weeks for the last one, one week for this one. There you week for this one. Or one week. I've stuffed that up already. There you go. So I'm going to recap the problem. And I have brought cards. I know they're not great props for the radio, but bear with me. And you've got the classic bicycle standard cards, which magicians tend to. I do. And I just realized that I haven't used these cards before. I thought they were a used pack. You know, if you'd done this with tarot cards,

you could have made it a spooky Halloween one. Ah, that's true. But instead you've done zero effort to make this spooky. No, through the power of audio only, now they are tarot cards. Hang on. I don't know if we got that foley work. Hang on, hang on. Matt just tried to do some fancy shuffling. I did, and if we got that foley work. Hang on, hang on. Matt just tried to do some fancy shuffling.

I did, and they're brand new and they're almost. Yeah, yeah, blame it on the cards, Matt. I'm going to use the phrase stiffer than I'm used to. We're all going to be adults about it. A magician, a bad magician always blames the cards. Yeah, sorry. Let me just warm these up. Oh, there we go.

Imagine that Matt is doing some incredible shuffling. Oh, cards are flying. If he was doing this at a table you'd be like, this guy's cheating. It was card shop. So, one deck of cards. Did you say card shop?

Shop. Shop. What's a card shop? It's like a card shark, but pointier. Oh, okay. I think sharp's the original phrase. A card shop. Card shop. Yeah, what's a card shop?

I imagine it's like a loan shark. I can't stop playing as a card shark. Oh, yeah, because otherwise you die. So while that's happening, I've got two more decks of cards. So you've got three decks out now. I've now got three decks out. Okay, so on Beck's right, I have a single deck of cards I've just shuffled expertly. Here, I now have a double deck of cards.

I've put two decks of cards together, and I'm shuffling them together. Yes. So the question that's been posed by Maddie is, if we're playing snap with the single deck of cards, is that any different to playing with a double deck of cards? Okay. So there's a deck of cards. I want to get your initial impression. In fact, listeners, don't start working it out.

I just want to know everyone's initial impression. So on one side, you've got a regular deck of shuffled cards. On the other side, you've got two decks shuffled together. And we're going to play snap. Okay. Does that make a difference to the game? And I've simplified this down to like a single kind of snap event, which is where I'm going to turn over one card to start with.

How does snap remind me of the rules of snap. Oh, they vary. Because I think that makes a difference. They do vary, but at its heart, you're turning over a card and you're saying snap if it matches. But sometimes you'll have multiple piles or one pile or, yep. Yeah, okay, yeah. So what I've done done and sometimes you turn them

simultaneously sometimes people take turns turning them over so what i've done is i've just reduced it down to the turning event you've got a card already out you're turning another card do they match or not because i feel like when i used to play it you would you would deal the cards all right yeah evenly so both people would not would end up with half the deck. And then you would both at the same time put out your cards. And if those two match, then you have snap. But that is then different, isn't it? Because it means you can't snap to the previous card or the card after it.

It has to be the card that lines up with it. Yeah, but mathematically, there's one card and another card if it matches or not. So I'm pretty confident, and people correct me if I'm wrong, I'm sure people will write in if I am, that almost all versions of Snap can be reduced down to do two cards match or not.

Okay, yeah. And I'm doing it slowly so we can think about it easily by saying there's the first card, there's a six. Yeah, and we're just doing it on numbers. Just on numbers. Yeah. Otherwise, there would be no matches at all. We can't do it on six. It would is a six. Yeah. And we're just doing it on numbers. Just on numbers.

Yeah. Otherwise there would be no matches at all. We can't do it on six. It'd be a real boring game. But you could do it numbers and colors. You could do numbers and colors. Correct. But again, you could read the same logic would apply to numbers and colors. I'm just doing numbers.

There's a six. The question is when I turn the next card over, what's the probability there being a snap? And so I turn it over. Let's play it for the hell of it. Here we go. Turn it over. It's a seven. No snap. Okay. But what if over. Here we go. Turn it over. It's a seven. No snap.

Okay. But what if we did that with two decks of cards? I'm also going to point out that it's a different suit. So they know that Matt has shuffled them properly. Okay. That's a nine. That's from the double pack. What's the probability the next card's going to match? Turn it over. Oh, snap! That was an accident.

Yeah. Wow. And that that actually happened that's not just through the magic of audio only no that happened live in the room so what's your initial impression is it the same game playing with two decks shuffled together or is it a different game because the probabilities will be different i my initial thought and just the context a room full of math teachers and i'm assuming they're math teachers by the context. I mean, they'd asked you to do the math. But probability is famously difficult. And our intuition as a human is terrible at probability.

That's true. So this is why there's no right or wrong answer here because they couldn't decide. And I will reveal what my initial impression was in a moment. People at home, decide yours, people driving as well. Bec, what would you say? My initial thought is that the probability is the same. If you could hear that, that is Matt. My dog falling off the sofa.

Dog falling off the sofa. You okay? She's okay. We really need to start filming these sessions. Or not. My initial thought is that the probability is the same because while you've got more cards that are correct, you've also got more cards that won't be correct.

Yeah, the same cards. I thought they should be the same. Like if I had one short straw and 49 long straws. Yep. The chances of you pulling out the short straw are one in 50. Correct. If I had two short straws. Yep.

And 98 long ones. They're still one in 50. Then I. Two from 100, one in 50. Yeah. Yeah. I do it like. You're 100% spot on.

Yeah. It's not the same. Huh. They're different. Spooky as if you were. You're 100% spot on. Yeah. It's not the same. Huh. They're different. Spooky. There you go. So, and what I find particularly weird is I've got the whole double deck here. I could have then shuffled two together.

Got some big deck energy happening there. I got big deck energy. And I could have taken half off down to a regular deck size again. And so now it's still a different game. Because I shuffled two decks together and then yeah half the probability on this side is different because you might end up with loads more of the same card in one half due to the shuffling doesn't make a difference on average because as often you will have fewer right So actually that all averages out. Okay. It's not because, and you're right, because depending on where they clump, the actual probability is different. Because if you knew what the cards are, obviously they might all be at the bottom or be at the top.

It could be in this half or that half. But if we don't know, it's all equal. This could be any of the remaining, in this case, 103 cards before you turn it over. Yep. And so I was like, that's interesting. And I can see why they got into an argument because it feels like it should be the same. But then obviously they had an inkling that it wasn't.

And so I wrote some terrible Python code to play Snap. I mean, I feel like that eventually is going to be some merch, isn't it? Yeah, yeah, yeah. And so I wrote some terrible Python code. If we ever do a live tour of a Problem Squared, that's going to be a call and response thing. And so I wrote some terrible Python code. Everybody drink.

So I did. And I wrote it to play Snap, this version, and keep track of the probabilities as it goes. So I can tell you the actual probabilities. So if you've got a single deck and you put the first card out, the probability of another card matching with it is 5.88%. Okay. If you've got the two decks, the probability of two cards matching is more than 5.88%.

It's 6.8%. Why? It's more likely. Why? That's a great question. why would that be so i wrote the code to play snap with progressively more and more suits of cards so it started with a with a half deck only two suits so you can see if they match or not and then it started with a deck with three suits and then four suits and then five and then all the way up and so along the way it did a

whole deck and two decks and everything else and the matching rate increases as the deck gets bigger until it approaches a one in 13 chance which makes sense because if you had infinitely many cards and let's say you want a six one out of every 13 cards is oh because there's 13 cards in a suit cards in a suit ah and then you're like well hang on well why isn't that the case here? And it's because. And Matt is pointing at the single deck. Or either of these in a finite deck. Yes.

It's because that first six, once you turn it over, the remaining 12 cards from its suit are getting in the way and they're diluting the chance of getting another matching one. It's a little bit like the Monty Hall problem, a little bit. In that it's confusing probability. Yes. Yeah, it's nothing like the Monty Hall problem, but in that it makes me go, oh.

Oh, yeah, yeah, yeah. For me it was that real, suddenly I went, it's the other 12 cards getting in the way. Yeah, you can't match with those. So now it's making it harder to get the matching card. It's one in 13 chance plus diluted a bit because of those 12 cards. And when you've got the double deck, the extra 12 cards have a smaller effect because they're across a much, they can blend in across a much bigger deck.

Does that mean there's only six cards in the way? Per deck, yes. Yeah. So they make less of an impact on average. Yeah. And the more decks you're playing with, the more space for those 12 cards to hide until you've got an infinitely big deck and then they don't make any difference at all.

And you're back to exactly a one in 13 chance. So what's the minimum size deck you would need for it to be? Oh, for it to be close enough, I'd have to run the numbers. It's, I've made a little plot here. So there's my little plot of the probability approaching one in 13, but not quite. But once I realized what it was, once I had the logic behind it, I didn't need to run the code anymore because I played 100 million games per size of deck and then took the average match to get this.

But then once I did that, I was like, well, hang on a second. I could have worked that out because I flipped that first card over. The next card has a three because there's three sixes left out of 51 chance of matching. Because there's 51 cards, so I've turned one over. Yeah. And on the double deck, it's a seven in 103 chance. And that is a bigger fraction. Yeah.

It's more likely to happen. And that gives me exactly the same percentage as I said a moment ago that I got from the code. I could have just thought, if I'd spent a moment thinking about it. Yeah. I could have worked that out. Of course.

Yeah. Yeah. So what if you've got a pack made of 14 decks? Because you'll have 14 times 52 minus one. Yeah. That'll be the total number of cards left. And you're going to have 14 times four minus one that will match. So it doesn't work that way, does it?

Is it? Oh, no. Still the same problem. No, no, no, no, no. You can see where my brain was going. It's not correct. Yeah. It's still the same problem. No, no, no, no, no. You can see where my brain was going. I can see where your brain's going. Your brain is trying to think,

is there like a point at which you've covered all the bases and it works because you've got enough that you've done everything. But in this case, it just gets closer and closer but never quite. Yeah, yeah. Because you're still those extra 12 cards are still in there. Yeah. You're just, they've got more and more places to hide as you have a bigger and bigger deck. Yeah yeah so they have less of an impact on any and i see now why it's spooky it's spooky because it's 13. ah yeah there you are i hadn't thought of that don't tell me

i genuinely was like oh now i see where you're getting it turns out it is unlucky 13 spooky yeah wow i'm more on brand than I expected. Yeah. But that proved me because my instinct was wrong. We all had the same instinct, humans. And a bunch of teachers argued about it. But also what I love about probability is my instinct is write some terrible Python code, simulate it. But then I get the answer and I'm like, oh, that now makes, I can kind of reverse engineer the logic.

Yeah. But once I realized it's those 12 cards getting in the way, I was like, got it. See Matt, this is my favorite kind of problem that you do. Cause I come away from it. Like that's really interesting.

Oh good. I ended up telling other people about it. They won't listen to the podcast still, but I'll tell them. Oh well, tell them about it. We have one last bit of business on this. Yeah.

Producer Lauren, is it card sharp or card shark? Sharp came before shark. Wow. What's the etymology? The original sharp. Oh, I see. Yeah. So apparently the root word originated in Europe, taken from the German word scharfen. What? Which translates to sharpen in English and means swindler. Swindler? A sharp swindler. Scharfen. Card swindler. Card swindler sharpen card swindler cow swindler matt i think that deserves a ding oh thanks but i feel like we need to hear from the teachers no i want my working out mark yeah yeah yeah and i'm not gonna mark it no yeah uh teachers love extra marking yeah they do

let us know up next in our spooky Halloween a problem squared episode we have a problem for Beck sent in by Jenny on the problem posing page and Beck your problems is on theme as mine that's impressive arguably more I don't know

just because yours is about zombies so Jenny's problem is about zombies. So Jenny's problem is, can zombies ride bikes? I hope it's not a practical, a pressing practical problem. Yeah, you can imagine if. Oh, no, they've got bikes. Is this going to be an issue? Jenny's seen some zombies near a bike shop. She's like, get on the problem posing page.

She's got several sub questions surrounding this problem great now that i guess this is getting into the details jenny wants to know specifically can they bend their knees as in like if they can't ride bikes can they canoe yeah do they have enough energy to pedal would they be able to get their leg over if it wasn't a step through frame? So there you go. So if you're worried about zombie apocalypse, get a bike with a top bar. And they can't steer it. Because a zombie can't nick it and cycle up.

You wouldn't have to lock it up. No. It'd just bounce right off it. So they're thinking, so Jenny's discussed this with her friends, that the answer will depend if you consider the traditional film version of zombies with all their slow walking or the modern day modern day fast running variation yeah what does jenny know well you know like 28 days later i think was the the fast where i remember they that's the first one i remember with right okay so that it will depend on the additional model of zombie. Yes.

I thought this was an interesting one because, yeah, there are very, very different types of zombies. And so my first step was to see if I could find any reference to zombies riding bikes in media. And I couldn't. Now, as we know from my Autobahn thing, I'm not always correct. And so someone might be like, actually, I think you'll find. Actually, in this Victorian era novel.

Yeah. Yeah, sure. There was a zombie riding a bike. But all I could find was there was a zombie bike ride, you know, like a flash mob type thing. You know, because there used to be zombie shuffles in melbourne once a year they would do the zombie shuffle mid-2000s very mid-2000s very mid-2000s and so you'd have hundreds of people meeting up on one corner of the city and they were shuffling and you would shuffle through diagonally to the other corner of the city at the same yeah as zombies just for fun why not yeah it was the mid-2000s yeah

though i remember there being a a ninja one as well there for fun why not yeah it was the mid-2000s yeah though i remember there being a a ninja one as well there was a fellow i knew who was part of like a parkour group at adelaide and they had a ninja their way across where they needed but they're all parkour people so they're just as ninja and stuff yeah and i ended up using them in a video for my first solo show um because i was like hey can i borrow them for like 20 minutes and he was like, hey, can I borrow them for like 20 minutes? And he was like, yeah. And so there's a scene where I get chased by like 100 ninjas because I just happened to get it in on the right time. I'm going way off subject though.

Bicycles. Bicycles. So there's a zombie bike ride where people dress as zombies riding bicycles, but they're not actual zombies. Not real zombies. But I couldn't find any reference to zombies riding bikes. So I thought I will reach out to some people who I know who might know more about zombies. Now I'm wondering, bike experts or zombie experts?

Zombie experts. Of course it was bike experts. I come to you, Matt. You'd be the first person I'd ask. Funnily enough, I thought I'll start at the most, I think at the moment, if you Google zombie, annoyingly, the most sort of popular type of zombie is Minecraft. Of course. Yeah.

Because there's zombies in Minecraft. So I reached out to Peter Sutton from Fox Dog Studios, who is a huge Minecraft nerd, got really into it during lockdown and can now answer pretty much any question about Minecraft. Including the zombie one. So I reached out. I said, are there any zombies riding bikes in Minecraft? Yeah. Are there bikes in Minecraft?

Do they do it? No. Okay. Well, I don't think so. I don't think so. I said, can the zombies in Minecraft ride bicycles? And Peter said, sort of. Sort of?

Now, I think this has made all the funnier when they continue. Baby zombies can spawn riding chickens. Now, I would argue that that is not sort of like riding a bike. But I feel like if you can ride a chicken, you can ride a bike. No, no, I disagree. Really? Because riding an animal, you have to sit on it and hold it. But a bike involves sitting and coordination.

I feel like the balance required to stay on a chicken. No, but hand and eye coordination, as in your legs. You have to know to pump the legs on the pedals. There's a reason that people can't just ride bikes. You get that for free. Like people have to learn how to ride a bike. The balance is the issue. No, you need to be able to pedal as well.

I don't think riding a bike is the same as riding a chicken, Matt. And I don't think I'm like. Everyone. I don't think riding a bike is the same as riding a chicken, Matt. And I don't think I'm like. Everyone. I don't think I'm ruffling any feathers. Vote below. Was this going to be a Twitter poll? Twitter poll. Is riding a bike like riding a chicken?

No, no, no. If you can ride a chicken, does that mean you can also ride a bike? Yeah. Please show you're working out. Apparently the baby zombies that are spawned riding chickens in Minecraft are known known as chicken jockeys they could have called them jock chicken come on but peter also says despite their name the zombie has no control of the chicken see it's a skilled activity and so the chicken often walks into one into one high gap and kills the zombie that's good to know. Yeah.

Practical information. Yeah. So essentially, no. The zombies in Minecraft can't. Can't ride bikes. Can't ride bikes. You know one of my favorite moments when we record this podcast is we will have this discussion and we're like, right, vote. Is riding a chicken.

Is riding a bike. Yeah. I can just hear a sigh and then typing in the corner. Which is Lauren being like, now i have to remember to make a poll it's not funny if we don't make the poll i think it's an do you know what i love about this poll is i really hope that our listeners retweet it because void of all context without any context and i don't want any context no context on that question make a note she's writing that down she's deleting a bunch of context. I want there to be just people being like, why would you ask this question?

On Minecraft people will be like, that reminds me of those chicken jockeys. So I did say, so they would probably struggle with pedaling. And Peter said, almost certainly. There's nothing in the law that implies any sort of wheels or chain drive vehicles have even existed. Okay. So that was my first border call. So I was like, right, Minecraft zombies out. So then I was like, what about like classic horror?

Yep. And so I reached out to Stephen Kostansky, who is a director and writer. Excellent. Canadian director and writer who wrote a film that I'm going to make you watch tonight. Oh, is that? Oh, right. And directed a film as well. Yeah.

It's called Psycho Gorman. Oh my goodness. Matt Hyten, the other Matt I work with. The other Matt. You know a lot of Matt. Put me onto it. Right. And it is an incredible film.

It's great. So for listeners, we're recording in Godalming this time and near where I live. And so we're going to have a little film night. Yeah. Now, it's not a zombie film, but there is some reanimation that sort of goes on, kind of. And so I was like, you know what? I reckon Stephen's got a pretty good grasp of classic horror. So I reached out and Stephen replied.

Excellent. And I said, in your professional opinion, would a zombie be able to ride a bike? And Stephen said, I think if the zombie had a history of bike riding when they were alive, then they might be able to. Like they were a professional cyclist or something. Yep. But I don't know if you could teach a zombie to ride a bike. That's a good take. It'd need to be something they could do purely by instinct.

So when, in the classic zombification process in media, They retain some muscle memory ability. Exactly. Yeah. Because they can walk. They can walk. And when we're born, we can't walk. You've got to learn. That's a learned skill.

So, and in some cases you see zombies sort of vaguely doing. Doing. Things that they did in, you know, there might be some. Like repairive tasks. Yeah. Yeah. I did say I love this theory. Thank you.

And they said happy to field any more questions like that excellent um our collection of experts grows ever bigger they said i think a zombie rides a horse in survival of the dead and then they said that's kind of like a bike yeah see a bike is between a chicken and a horse i did say i mean what are horses if not fleshy bmxs yeah so that was uh that was the answer from steven yep potentially yeah i'm getting i'm getting more and more convinced and then i thought do you know what i need at least one more one more one more opinion so i reached out i sent into the dms of someone who i only slide into the dms of occasionally because i don't want to overstep my okay i don't want to oh is this like a contact where you you kind of feel like you've only got

so many asks yeah but yeah yeah so i ask edgar wright the same question oh that's amazing oh well done good use of an Edgar Wright ask. Yeah, yeah. You're never going to get a better moment to deploy it. In your genie three wishes thing, and I've used one to ask this question. Hope you're happy, Jenny. For context, for listeners unfamiliar, this moment would be useful. At the beginning when they mentioned zombies riding bikes,

I just imagined Shaun of the Dead like that. Yeah, because I think there's one where someone's like doing something in shauna the dead like that's yeah because there's some i think there's one where someone's like doing something in the supermarket or something like that and of course at the end nick frost is playing a video game yeah poorly poorly oh yeah sorry spoiler alert yeah so uh yeah i asked the same question your professional opinion could a zombie ride a bicycle and a great says muscle memory perhaps oh yeah like you said yeah and so i said so do you think if they turned into a zombie while riding the bike oh they might just keep pedaling automatically and they said i think so that's pretty definitive yeah so a zombie could potentially ride a bike

should the conditions be correct right they would need to already know how to ride a bike and potentially already be on the bike. Yeah. That's amazing, Bec. I don't think there's a more definitive answer possible than asking Edgar Wright. Thank you. I feel like you've won the Problem Squared 2023 Research Award. So I would say the answer is yes.

A zombie potentially could ride a bike. Potentially could ride a bike. I think they can bend their knees to answer the sub questions. Do they have enough energy to pedal? I would say the same amount of energy that they have to move. Zombies can go upstairs, right? Oh, this was a whole thing that I found. Oh, really?

I didn't realize what i was stumbling into people were saying they can probably they can go upstairs again if it seems like a sort of automatic like the same as walking yep type thing but ladders probably not oh that's interesting yeah okay i was just saying from a knee bending point of view yes i can go upstairs yeah exactly and also when you talk about the fast running zombies yeah then then they have to their knees. Have you tried running fast without bending your knees? It's hilarious. They look like an egg beater. Yeah.

My brother and I used to have races like that. It was very funny. Of course you did. Yeah. A lot to do in Adelaide. Again, would they be able to get their leg over? I don't know if a zombie would walk over to a bike and get on it. Yeah.

I think they would sort of already have to be on the bike. But if you put a zombie on a bike. If they fell onto the bike. And they previously knew how to ride a it. Yeah. I think they would sort of already have to be on the bike. But if you put a zombie on a bike. If they fell onto the bike. And they previously knew how to ride a bike. Yeah. And you gave them a push. Yeah. Yes.

So. Because like some serious cyclists, which I think this would require, your feet are clipped into the pedals. Like you're attached. And so if you were zombified with your pleats locked in yeah you just keep going so i i think i'm with jenny i think it does depend on the type of zombie yep i think one of those slow moving there's a minimum speed to keep a bike yeah upright yeah so they probably wouldn't have the energy but i think some of the faster ones would this is i mean

you had a track stand oh what one final piece, though, is a lot of people have pointed out that if you wanted to get away from zombies, bikes would be the way. Bikes are the winner. Yeah, because they don't need fuel, which a lot of people run out of. It's silent. Silent. So you're not going to. Andy, you see in zombie films, everyone tries to drive down the nearest highway.

That gets cluttered with congestion and cars and crashes. Bicycle, you can just weave on through, pick it up, carry it over. Yeah. So I think bicycles are the winner, and they're less likely to be stolen by the zombies. They keep going, the zombie can't take it. And they probably won't chase after you unless they're already on the bike. So, yeah.

There's your answer. Obviously, we'll go back to Jenny to get the official. But I'm prepared to give you a ding. Thank you. First bit of any other business is that we had some commemorative plates slash bowls. Yep. Bowls slash plates. Yeah.

That people could order. When we had a million downloads. Very exciting. Yes. And we also sent them out to our Wizard Patreon supporters. We did. As a nice little bonus gift. Just to say thanks. People in Germany, not everyone is getting their stuff.

Not getting their plates or bowls. This is not a us specific problem. No, industry wide. It is industry wide. Sending anything international. We've done all the right things. All the right things. If you're thinking, but you didn't put that barcode on it, we did.

We've got all the barcodes, all the numbers, all the codes, all the categorizations, the CN22s, the works. Yeah. We've got everything. I think it's because, I mean, basically people in Germany are sending back anything that they can find even the slightest fault with, even when there's no fault. And I think the fact that it's an ambiguous plate or bowl and they're like, well, you can't import something that's of unknown type. And so they're sending it back. Yeah. That's my theory. Sure. Is it a plate or a bowl ah send it back yeah let's say work it out then send it in let's i don't think we put that on the forms i think we just post them yeah yeah so anyway my point is is that uh if you are a wizard level patreon supporter who didn't receive it we're

sorry we're very sorry. We've tried. We've tried resending them. It's not happening. Move. Yes. Or if you paid money for one, if you pre-ordered one very kindly, we've refunded everyone we couldn't get the plate slash bowl to.

If you're a German Patreon supporter who didn't receive your free plate slash bowl as a surprise gift, then... We're sorry you found out this way. Yeah. Because you wouldn't have known. Or they might have been too polite, not wanting to raise it. Oh, that's true. Yeah. But we'll make it up to you some way.

Someday, somehow, somewhere. We'll find a way. Yeah. Also in a little bit of any other business, just a quick question from someone on the problem posing page. Nibble. Nibble. Nibble?

Nibble. N-Y-B-B-L-E says, do you use a cryptographically secure random number generator for picking the three Patreon supporters at the end of each episode? So each episode, we thank three Patreon supporters at random, not by posting them a bowl, but just by saying their names. And I pick them at random using an Excel spreadsheet. There's a built-in random function. There's a built-in random number generator in Excel, which is not cryptographically secure, that I use to pick those three people.

So the answer is I don't. I don't. It's not. It's not truly random. It's pseudo random. Yeah. I apologize for not being clear about that. And for anyone curious,

random numbers are an important part of keeping online information secure. But if there's any patterns to those random numbers, if they could be any way predicted or or understood that could be used as a way to break encryption and so if you want to go all out you can buy quantum random number generators as like a usb device that use quantum uncertainty oh inside the device, photons probably, to then generate proper apps. It's like rolling millions of tiny quantum dice. Proper randomness.

Whereas Excel uses a pseudo random number generator, but they're not actually random, but they're randomish enough. Does that mean that someone could hack it? Someone could hack it. Well, if we start, I mean, we have thanked at least one Patreon supporter twice ah so if we start thanking the same person again and again and again then we know we know we need to invest in a better random number a better source of randomness which reminds me what i have learned from the cards thing is that the more patreon supporters we get that's a great segue the betterness. Yeah. Only we had more patrons.

But also the lesser chance that people would get. Individually, yes. I mean, maybe one day we have to increase from three. Yeah, maybe we should do that. Maybe if we hit a certain number, we will thank more people per episode. And without any further ado, we should thank. We should thank three. Thank three people.

Yeah. So this episode we would like to thank. And Tony Carter. I just split it up into smaller syllables. Did you? We should say it did start off as a joke that occasionally we couldn't pronounce someone's name. And so to make no one feel left out. Make it fair.

We will now try and mispronounce everybody's name. Like I did for Ant on Waikata. Nicholas Owens. Nailed it. No second take. Nicholas Owens. And you, Schwartz. You, you,

we, Schwartz. Squartz. Yeah. Squartz. That works. I do realize this has been a very heavy mentioning the Patreon podcast. That's true. But they do make this enterprise possible.

Yes. Yeah, we actually cannot, we can't afford to have this show edited, produced or put out without you. So thank you very much. We really appreciate it. Of course, we thank everybody for listening, regardless of your ability to support us. No pressure. And if you want to be able to help us out, but you're unable to support us on Patreon, hey, just tell someone to listen to the show.

Word of mouth is the scarce resource in the podcast business. You know, whatever you want. Get it out there. out but but you're unable to support us on patreon hey just tell someone to listen to the show word of mouth is the scarce resource in the podcast business whatever you know whatever you want get it out there get it out there we appreciate that and don't forget if you support us on patreon no matter what level you support us on you automatically get access to our bonus podcast i'm a wizard not just the christmas card. Yeah, not just a Christmas card. You get an episode every month. Imagine this, but less slick. Less professional.

Imagine this show, but without the problems that we're solving. Oh, yeah, yeah. It is. It's just the packaging. Yeah, more magic. It's very magic. I also want to thank my co-host, Matt Parker. Spooky Matt.

Spooky. Matt, we should do the Simpsons names. We should. Matt Arrk Parker. I'm just going to do that. Matt Parker. And I thank myself. Beck chills down the spine.

Oh, well done. Thank you. And finally, our wonderful and patient producer, Lauren Armstrong Carter. You just said it with more vowels. That's all I'm doing. Okay, it's now 10 o'clock at night. Put your trousers back on. It's funny because I'm wearing my Trekkie Dex now.

So, we're about to watch our film. Yeah. So, we're about to watch our film. Yeah. And the gift that a very kind couple in North Carolina gave me is underneath this cloth. Would you like to unveil it? Yeah. I'm worried something's going to jump out of it.

No, it's perfectly benign. What? It's the illicit. As to and yet untasted Trader Joe's baked cheese crunchies. Oh, because this is like. This is the one. They're like the Wenzel's ones. The one we didn't get. Wenzel's, a wannabe Trader Joe's.

So we've been trying to find a snack which tastes like the Aussie one, Twisties. And this is the one that everyone said try, and we never found. So a listener found it for us and brought it to a talk I was doing in North Carolina. Do you wanna open it? Num, num, num, num. That's how it works, bro.

They're good. That's good. They're really good. That's how it works. They're good. They're really good. Now I want to try them versus the Wenzels. The texture is there. The flavour is a little hollow. It's a little too subtle. Twisty's really punch you in the face. But they're good.

The texture is spot on. Thank you very much to the listener do you remember thank you no i forgot i forgot your names you were wonderful people thank you for these tell us who you are yes