A Problem Squared - 085 = Coin Collections and Pin Selections

Episode Date: May 21, 2024

🪙 How many coins would you need to sort through to collect all commemorative €2 coins in circulation?  📍How do you display enamel pins?!  💼 The Any Other Business briefcase is…mostly open.  Here’s the Coupon Collector’s problem video: https://www.youtube.com/watch?v=BstloCx8KDk You can see more on the “Number of banknotes/coins returned from circulation in Euro Area, Euro area (changing composition), Monthly” here: https://data.ecb.europa.eu/data/datasets/BKN/BKN.M.U2.RE10.C.20P0.AS.F.E And, Wiki Sources: “2 euro commemorative coins” on good old Wikipedia: https://en.wikipedia.org/wiki/2_euro_commemorative_coins As always, send your problems and solutions to our website: www.aproblemsquared.com. And, if you want more from A Problem Squared, you can also find us on Twitter, Instagram, Discord and on Patreon.

Hello and welcome to A Problem Squared, the problem-solving podcast which is a bit like The Muppets in that it is equally educational and entertaining and the real talent is behind the scenes. Shout out to our producer Lauren who is the metaphorical hand up our bums. Your hosts are myself, Beck Hill and Matt Parker. Out of the gate strong there, Beck Hill. Thanks. According to a BuzzFeed quiz we did over several episodes, Matt is most like the Muppet Scooter, which rings true if you base it off

his role in the 2011 film where he is a massive tech nerd on his way to a TED conference. However, I would say Matt is most like Dr. Bunsen Honeydew in that he is very clever, funny, and powers on despite his many disastrous mistakes. And according to BuzzFeed, I am... Well, then I'm sticking the landing there. And according to BuzzFeed, I am most like Gonzo, which tracks considering my love of stunts and affinity for chickens. However, most would probably argue I am most like Fozzie Bear because I make a lot of bad jokes and look good in a hat. You do look good in a hat.

Yeah, I suit hats. I did do a not a TED talk but Festival of the Spoken Nerds and myself, Helen Arley and Steve Mould were the entertainment at a TED conference in maybe 2011 and it was quite the journey to get there

so I think you may have been you know, surprisingly accurate with that I heard they based Scooter's role in the film on seeing you there. Well, I've got very little residuals to indicate that. On this episode. I found the numbers on trying to find coins.

I look at where to pin pins when you're not pinning them on yourself. And we have any other business. Or animal Oscar Big Bird. Well done. Is that like the phonetic alphabet, but Muppets? Yes. Yeah, that's right. Matt.

Beck. How are you? I'm good. I'm in the Southern Hemisphere. Continuing our trend of recording from countries, separate countries, same countries, just being on the road. Yes. I thought I'd mix it up, head to Western Australia. Now, from memory, weren't you in Australia before you came out to the States?

No, no. I was in Australia for Christmas. Oh, that's it. Then I did go to the States immediately after that, but that was my January US trip. That's right. I've just come back from my April USA trip and then come straight back to Australia. It's a bit much. I'm suffering from...

So I went from California to Londonon which is an eight hour time difference yes i believe you know i've never fact checked this i just always accepted the conventional wisdom that it takes you know you adjust to jet lag one hour per day so yeah i've heard that as well eight hours of jet lag is eight days i don't know how scientific that is but i was only in the uk for eight days so i landed the day i of 15 hours of jet lag over 15 days i've i i forced my body to do it the long way around so and today day of record is technically this is the 15th day of my 15 days of jet lag how are you feeling? two weeks of alert awake good no idea what time it is yeah sure I feel I feel I think there's a

tv show where you get someone and every eight days you move them a third of the way around the planet and just keep going till one day they burst I don't know it sounds like a great tv show oh well i've i've been i've been living that for two weeks yeah so how about yourself did i tell you what happened to me when i went to the states i don't think i mentioned this in the previous episodes i got detained no you did not tell me that. Yeah. So I'd been in the, you know, the queues in the States take forever to get to the front of. If you don't have an American passport.

So I was in the queue for two hours this time, which I think is the longest time I've been so far. And I'd landed around sort of eight o'clock at night. So I get to the front of the queue at about like 10. Yep. And Sam, my co-host on the other show, was coming to collect me from the airport. And the whole time he's been waiting for me and I've been texting him going really, he's waiting like two hours while I'm in this queue. And I'm like, really sorry. You know, I'll be out soon.

And then I sort of said, oh, can you imagine if I get to the front of the queue and they send me back? Ha, ha, ha, ha, ha. Ha, ha, ha. And I get to the front. And they do the usual, you know, I've got all my Esther and like my tourist visa sorted and everything. And they ask me the usual questions. And they're like, what are you going to do here? And I'm like, oh, you know, I'm going to visit some friends.

And I've got another friend who's going on holiday. So I'll house sit for them while they're away. And, you know, just general going to visit some friends and got another friend who's going on holiday, so I'll house-sit for them while they're away. And, you know, just general stuff. Go to Disneyland and everything. And they're like, oh, okay. They're like, oh, I've just got to put some stuff into the system. How long did you want to stay for? And I was like, well, I've got a flight leaving.

And this time they're like, you're here for a while. And I was like, well, originally I was going to come for three weeks. All my work is remote, so I can do it while I'm here. You know, I just prefer the weather. And they're like, oh, okay, yeah. But, you know, you can stay up to 90 days. And I was like, sure, but I don't need 90 days. I only need however many days I've got, 60 days or whatever.

And they're like, okay, but do you want me to put in that you might be here for 90 days? And I was like, well, I don't understand the question. I've got the estimate. It's all sorted out. also the dates are in there i don't need to change anything and i'm like but but what if what if something happens and you need to change it right and then and of course like i'm like not wanting to be difficult and i'm like well they know the system better than i do and they're like what if something changes and you have to stay for longer like you know and i was like okay fine yeah sure put in

90 days I don't know right like at this stage I'm like trying to remember what the process is so I'd been awake for 23 hours at this stage yeah I was very very very tired so then I'm just sort of getting really confused and then he's like sorry I don't have any entertainment for you while I do this and he puts up a speaker on the thing and starts playing the new remix of eiffel 65's blue and i'm like i don't understand what's going on here so i'm just kind of like no this is fine nodding my head like just waiting are you sure you didn't you didn't hallucinate any of this oh absolutely not right and i'm so confused and then and then he like knocks on his colleague's window and he's like i'm gonna put in 90 days and and the guy's like all right and then shrugs and then he's like yeah i've just got to check if you think okay all right it's in the system now we just need

your fingerprint now which is the final step and i'm like cool and that's normal that's the normal part of the procedure yeah and then he's like does the reader have a green light or a red light and i was like it's a red light and And he was like, oh, okay. Yeah, it's been playing up on me all evening. Maybe that's why there's such a long queue because they're having issues with the tech or whatever. Like this is where my brain's going. And he's like, it's all good.

We'll just have to use the fingerprint reader in the office. So if you just come with me and we can do that. And I'm kind of getting that feeling in the pit of my stomach where I'm like, ah, this doesn't feel right. And we go past his colleague and he knocks on his colleague's window and he's like, points at me. And then he says to me, give him a wave. That's my boss.

He's the reason I was able to get the software all working, the computer working. So give him a wave. Tell him thanks. So I was like, okay, thanks. And then the guy just like shrugs again. And then I'm like that's again weird and then he takes me to and i text sam saying i'm being taken to the back office

like oh that kind of emoji oh that face and then i walk in and he he's still got my passport and then he goes and i it's a waiting room with all of these like booths and stuff uh but i'm like and i can see it's obviously a waiting room they use for like other questioning and everything but at this stage i still think he just wants me to give him my fingerprint and then he's like i'm just gonna go off here and he walks off to where there's like a back behind the office and there's also a bathroom sign and i was like oh well can i have my passport back because i don't really want you taking into the bathroom with you and he's like oh no no i need to hold on to it but you know you'll get it back and i was like okay and as soon as he

disappears this armed security guard is like ma'am take a seat and i was like oh no no it's fine he's just going to the bathroom i'm just waiting for him she's like it doesn't matter you have to take a seat and i was like no he'll be out in a second she's like no you have to take a seat and i was like no he'll be out in a second she's like no you have to take a seat and i was like you know you don't want to cause any issues again no like oh yeah the moment they ask you to do a thing you do a thing yeah so i was like okay all right so i went and sat down and i took my phone out to text sam and be like it's really weird ma'am ma'am no phones in here and i was like oh okay i was just i i okay and so they come over they take my phone off me so I now don't have my passport or my phone and I was like okay so then I'm waiting and then I see him just slip out like he just leaves and I was like maybe he'll come back and I wait a few minutes he's not

coming back and I'm like okay what the heck is? So I go up to the desk again and the security guard, I'm like, hi, really sorry. I, I don't know why I'm here. And they're like, you just have to take a seat. And I was like, no, no, no. I, I don't mind waiting, but I just, I don't know why I'm back here. He, he, that guy told me he needed my fingerprint but now he's disappeared I think he's so I don't know what's going on I thought this was just going to be a quick thing and they're like we don't know why you're here either we're just security you have to take a seat and wait

for an officer who's been and they're like you have to wait for an officer who's been assigned to your case and I'm like what case and they're like well we don't know they would have brought you back here because they have a reason to but we don't know what the reasons are and I'm like what case and they're like well we don't know they would have brought you back here because they have a reason to but we don't know what the reasons are and I'm like okay how long is it until an officer sees my case and they're like four hours and of course you don't want to overreact because you have zero power in this situation you're already just pushing your luck with not sitting down the first time right so I like, can I just text my friend to tell him he can go home and maybe come back later when I come out? Because he's already been waiting for two hours. And they're like, no, no, you can't.

And I was like, well, can one of you guys tell him not to wait for me? And they're like, no, no, there's no contact with anyone outside. And I was like, it feels like you're being arrested. Like I was just like, okay. You're being detained. Yeah. Yeah. But at no point did they tell me I was being detained. feels like you're being arrested. Like, I was just like, okay. You're being detained. Yeah. Yeah. But at no point did they tell me I was being detained.

I had to guess that. I had to ascertain that I had been detained from the limited clues that they gave me. And so eventually. I feel like if you don't want people to make a fuss, but you need to detain them. And these are not, you know, American citizens. These are just, you know, people coming into the country. Saying they need to go out the back to get their fingers scanned separately

is the easiest way to move someone off the floor. I am fully aware that they did this as a way of making sure that I did not cause a scene. That it would be as simple and as quick as possible.

Now, him making me wave to his colleague and say thank you is just a douchebag move. That has nothing to do with me getting me into the office. Yeah, I don't know. That's this guy totally showing off to his colleague.

Hey, look, I've got someone. They believe in everything I say. Like that was a total jerk move. So I'm in this room. I've never been more aware of my privilege, by the way, because I'm surrounded by people who don't speak English and they've got translators coming in and they're trying to, you know, talk to them and explain what's going on. And I suddenly realize what it must be like for just anyone in any sort of minority in this situation when they're being profiled,

any sort of minority in this situation when they're being profiled how scary it is it's really scary and so anyway I had to wait there and I was so tired but I couldn't go to sleep because if they called out my name and I missed it I didn't know what would happen so I'm sort of like in a half awake half asleep state for this whole time with nothing to do like I don't there's no magazines or anything they have a tv on a sci-fi channel which was weird which had a lot of uh sexy call girl ads which I found really inappropriate wow but distracting I will I'll say so then then eventually I get seen and the officer who was given by case was actually he was really good he was obviously stern and, you know, unbiased and everything. But he could also tell that I was just so tired.

Like I was like, like leaning against the desk because I was like, I'm sorry, I'm so tired. I don't know what's going on. And basically the reason I was detained is because I said that I would be house sitting for a friend for a few weeks. And that can be counted as a job. In most cases, they would cancel the ESTA, send me back to the UK, and if they cancel my ESTA, I can never apply for one again. Ultimately, I could never return to the States, at which point I started to cry.

I ended up having to show them my bank statements to show that I'm not like desperate for cash. To show them that I could afford to get a hotel if I needed. Basically, don't house sit. If you're on a tourist visa, don't house sit is my advice. Wow. I would have done the same thing. I wouldn't have gone house sitting.

Oh, that's a paid gig. I'd be like, oh yeah, friends out of town. I'm going to look after their house. Yeah. By the time i got in it was like 2 30 in the morning 3 a.m and so i i didn't really have any jet lag i fell straight asleep and then woke up at a reasonable time and then didn't have jet lag at all was pretty much on a normal so what i'm saying is if you want to get over jet lag get detained because you're so tired afterwards you You're so tired and stressed. You have no trouble getting to sleep. And emotionally exhausted. Well, I'm going to give you a ding. Well, no, not even a problem. It's just a ding for well done on surviving that. Yeah. Thank you. Our first problem is from Tom. This came into the problem posing page, which is a problemsquared.com.

And Tom says, hello, my friend loves your podcast. She was the one with the bathtub problem. Oh, there you go. That was, I assume the one with, if you have bubbles, does it keep the water hotter for longer? I believe so, yeah. So Tom says, I wanted to submit one too. More of a mat problem. I want to collect all commemorative two euro coins in circulation, but some are pretty rare.

How many coins would I need to sort through to find all of them, given how few of some are in circulation and how long would that take? And what to do with all these coins when I have them? One for Beck. Now, we should make it very clear, while people can describe something, just as an attribute as being a Matt problem or a Beck problem, that's independent of, like, which of us will solve it.

They can't request one of us to solve a specific problem. No, but that said, they have pretty much nailed it here. Oh, yeah, Tom was spot on. We're going to do it that way around. Yeah, yeah. So just to clarify the problem, in the Eurozone, or wherever you can use the Euro, classic currency, there are coins and notes, and of all the coins, I mean, the coins change a bit. You can tell which country minted a coin because one side of the euro coin will have something

to represent the country that was minting it. But the two euro coins, countries can not only, you know, say, we made this, although it's legal tender in any of the countries, they can have commemorative coins to celebrate some kind of special occasion. So originally, countries were only allowed to do that once a year. Once a year, they could release one special 2-euro coin.

That was up until 2011, I think. And then as of 2012, countries can release two different special two euro coins every year. So it's not a bad solution to a problem because countries like having commemorative coins and currency to celebrate things. And when you switch to everyone having the euro, they're like, OK, we get it. You're going to want your silly coins for fun occasions. But we're going to try and maintain the chaos just within the two euro coin.

Everything else is just standard. But when it comes to the two euros, you can go nuts twice a year. Interesting. So I actually had a quick look to see what had happened recently because there's a list obviously on wikipedia so this year in greece greece are using in 2024 the year we are recording this greece are going to use both of their slots one of them they're going to do a special two euro coin to celebrate the 100th anniversary of a children's book author penelope Delta.

And they're going to use their other two euro coin slot to have a special coin to celebrate the 50th anniversary of the restoration of democracy. So there you go. They both sound equally as important. Exactly. And that sounds like a big sarcastic, but as a children's author. Exactly. And that sounds like a big sarcastic, but as a children's author. Exactly. It's about time children's authors were celebrated on the same level as democracy. Well, you know, you've got to start somewhere.

It's so true. So true. So I like it as a concept because a country can decide what's important to that country to celebrate, which can be grand big things, or it can be children's book authors also very grand but you could argue maybe more local and then these coins travel they they're legal tender anywhere in the eurozone they're off so they they dump them in their country and then who knows where commerce will take them and anything like this you can imagine people try to collect them so i i totally get what tom's trying to do here they're trying to collect all of these coins so it's kind of fun i guess you just keep an eye on your change and you look at your two euros to see if you get one of

these special coins have you ever collected coins matt i have collected coins but only like specific things i once spent a while collecting a 20 pence coin from every year they'd been in production so i had the full set it's been it's been impressive maybe seven to ten years since i did that, so I've got to top it up. There's been some more, but it felt like a fun challenge. So, now, this initially reminded me of a problem in mathematics called the coupon collecting problem. The coupon collecting problem is, you know, it's like when you're collecting stickers when you're a kid to put in one of those books, you know it's like when you're collecting like stickers when you're a kid to put in one of those books or um you know you want to collect like all of some coupon but you get them at random yeah pokemon cards like pokemon cards like any kind of pack of trading cards you get the cards

at random and let's say there's like i don't know like you know 50 different cards you want to get and each time you open a pack, you get a bunch of random. And everyone wants a shiny Charizard. Exactly. When am I going to get my Black Lotus? And so you, initially, the first pack you open, or the first coupon you collect, or the first whatever you do, you're guaranteed a new one.

You're like, oh my goodness, new, because I currently have zero. But as you go along, most of the ones you're getting are new, but gradually you start getting doubles. You get repeats. And then eventually you're getting pretty much nothing but repeats as you're chasing those last few hard to get ones at the very, very end. I came across this because your friend of mine, Jeff Marshall, does park runs, which is where everyone runs around a park as a cult on Saturday mornings. And people compete to do all sorts of ridiculous things with their data because you get your time every single time you do that goes on your records. And so they have a version of this where people want to get every possible value for the number of seconds. So they don't care about how many minutes. They're like, oh, I want to get every possible value for the number of seconds. So they don't care about how many minutes.

They're like, oh, I want to get some number of minutes and zero seconds, some number of minutes and one second, and they want to get all 60 possible values of seconds, which is, assuming the seconds are random, is a coupon collecting problem. And so Jeff originally came to me and said, is is the coupon collecting problem and so jeff originally came to me and said how how many weeks of running park runs would i expect to to end up getting all of these and the the calculator i won't go through the mathematics behind i did a video on this so people go to my um sound up master youtube channel you can see all the working out but the wonderful delightful

result is if you want to work out you there's n some number n of coupons you want to work out, there's N, some number, N of coupons you want to collect. The amount of time it takes you is N times 1 plus a half, plus a third, plus a fourth, plus a fifth, plus a sixth, plus all the fractions up to 1 over N. So you add them all together, multiply by N. That's the number of coupons you're going to have to randomly check to see if you get the right one and that's a bit of mathematics called the harmonic series and i thought this was lovely because i wouldn't have expected the harmonic series to show up in that problem and it's always nice to find a fun new application of a seemingly unrelated bit of mathematics does that change depending on the availability of each thing?

So, for instance, the Pokemon, the shiny Charizard is rare, so you're far less likely to come across it. You are 100% correct. The coupon collecting problem and its wonderful, neat, tidy mathematics, that I already knew uh only works if all of them are equally likely so the the um pokemon problem or the two euro coin problem it's going to change because there are different amounts of each one so i then realized i had to know first of all well how many two euro coins

there are in circulation and i need to know how many special types there are and for each of the special types i need to know how many of those were originally made so thankfully wikipedia has got a pretty good pretty good list of them all oh goodness. Someone should give those guys a raise on the donations. Yeah, someone should double their salary. And this is the usual story. I have to do a bunch of data tidying. Because, of course, the table doesn't have all the numbers the same way. Some are all in digits.

And some will be like, you know, 12 million. And spell out the word million. I'm like, why do you got to do that and the dates are done differently anyway so i did all that i sat down i tidied up all the data as of the end of last year there had been 513 commemorative two euro coins made and i then found as many from this year for which uh all the numbers had been confirmed because there's some words like tbd they don't know how many they're going to make and i found an additional nine that have been made and we know how many they're making and

they've been released so i'm pretty confident at the time of recording, there are 522 commemorative 2 euro coins out in the mix. And I had all 522 of them in a big old spreadsheet. 4 euros worth of coin. Exactly. Well done on doing the calculation. Thanks. So you know what? I've got my spreadsheet in front of me here.

So how many coins were made and oh my goodness so the most common one you're going to come across was released in 2012 and they made over 89 million of them 89 million 795 361 they were done by the European Union itself to celebrate the 10th anniversary of the euro, of currency, of the euro currency being produced. So that's fine. The coin from a country that there's the most of

was Greece for the Summer Olympics in 2004. Wow, first ever commemorative two euro from 2004. They made 35 million of those. Wowzers. And then most of them are in the millions. Some are like hundreds of thousands. All the way down to the rarest one was 2015. Finland was celebrating the 30th anniversary of the EU flag being designed.

Wow. And Finland only made 500. 500. The second rarest was Monaco did 10,000 in 2015 to celebrate, and I quote, the 800th anniversary of the construction of the first fortress on the rock. Sure. What does that mean?

Yeah, why not? Do they mean Dwayne the Rock Johnson? I assume so. I guess Dwayne the Rock Johnson was alive in the year 1215 and had a fortress constructed on them. So anyway, but that's like 10,000. That's reasonable. Good job, Monaco. Finland.

So this is going to throw a spanner in the works. There's a single commemorative two-euro coin of which Finland only made 500. And I then looked up how many coins are there. Well, this gets mildly complicated. There are currently, or at least as of the end of 2021, 6,916,002 euro coins in circulation. Oof.

That's a big number. If we assume all 500 of the Finnish coins celebrating a flag being designed are still in circulation, you're looking for 500 out of roughly 7 billion. That's not good odds. That's worse than one in a million to get one of them.

So thanks a lot, Finland, for making that real difficult. And I take it that you're calculating this based on how likely it is to show up just in circulation in your change, not how likely you are to find it if you Google rare fish commemorative coin. 100%.

In fact, my one bit of advice, not to skip ahead, but Tom said any advice just find someone and buy that one coin and it dramatically speeds up the process of finding the other 521 randomly

that's the sticking coin so again not to skip to the punchline because there are different numbers of so many different coins. I was like, you know what? I'm just going to write some terrible Python code to do it a bunch of times. I did have the issue, though, of obviously not all those coins are still in circulation. So some of them have been decommissioned either through wear and tear.

Some will have been lost and some will have been put in collections are there other toms out there collecting these things so ones that are lost i don't know how we put a number on that ones in collections it's hard to guess in terms of ones that have been like actually removed like actively taken out of circulation the european central bank does have a pretty good database of these things but i couldn't find anywhere where they split them into types so they've got like they've got lists of number of bank notes and coins returned from circulation in the euro area uh monthly and it gives you the value in euros i couldn't find a breakdown of are they taking out coins. And then I was like I could work out the average distribution of value because I know how many notes there are of each type and how many coins

because that's publicly available. I could do a ratio of how many of them are 2 euro coins. But coins wear out slower than notes. i was like then i need like a half life because the longer a coin's been out the more chances had to lose numbers from its ranks and i was like oh that's also so complicated so what i ended up deciding to do is to work it out for a best case scenario just to see if it's plausible so i assumed every single commemorative coin was still in circulation which means i added them up there are two billion 204 million 191 059 commemorative two euro coins in circulation which does make up 31.9 percent of all two euro coins eurozone listeners if if you can just give me a sense check on that just look at your change

for a while is roughly a third of all two euro coins you see are they commemorative two euro coins maybe it's possible it's probably less than that but that's the best i mean i i'd also be interested to know like because i don't really have any change these days because everything's contactless oh great point so if i was to do this now the chances of me finding anything are very slim well that's a good point because in a moment back, all this is going to hinge on how many two euro coins you see per day to work out how long it's going to take. Because I've done it in terms of number of coins

you have to check, but then you've got to work out how long that's going to cover. But to give you your numbers on how long it's going to take, so we had our 100 Toms. They all, they were very dedicated, these Toms. They all collected every single coin.

To get all 522, it took them, on average, just over 14 million coins checked. The average was 14,053,009 coins. So how many coins a day do you reckon is is a plausible number to be checking just some quick maths guys that's almost 30 million euro well done almost that's wow with error bars and i don't know about you but i do not see that much money ever that's a really interesting way to do a sense check on the number because i was like well how many a day and i'll divide it by 365 uh which i all did but you're right it's just actually a case of that much money is unlikely to come through your hands in terms of yeah yeah like i think even when i worked in uh like i mean mine was hospitality but but working a cash register, you'd maybe see a couple of grand per night.

Yep. You still needed a lot of that, even just to get to a million. If I was to look... All right, let's say I'm looking at... Let's say I'm looking at five grand a night, and I'm doing it every night, 15 years. And that's working every night. So actually, that's a good top tip. Top, top, top tip.

You've got to get a job that requires handling a lot of cash. Bank teller, probably. You need to see a lot of coins a day. I think working at a bank to see 1,000 coins, 1,002 euro coins a day, That's still 38 and a half years. Yeah, that's a long time. Assuming you work every single day, no days off, no weekends, nothing. Now, interestingly, if you don't worry about that one ridiculous coin of which there are

only 500 and you just buy that separately you get the other 521 coins in under four years oh wow so what that process would actually look like is under four years of working in the bank you've got all but one coin and then the next 34 35 years of your life are waiting for that one specific coin to show up now that's always true of this problem because getting the last one is the difficult one because there's only one remaining one but you still got to check everywhere and that is just if you already had that one you were starting with it then you're in a good position to get all the others yeah you'd still have to wait a long time for the 521st one,

but nowhere near, you know, it's not like decades. It'll be months. So there's my top Tom tip is to just buy that particularly rare one somehow or convince yourself you don't need it.

Yeah, and my tip to the listeners is to find that rare Finnish coin, buy it, and then sell it to Tom for a much higher price. There you go. No, I wouldn't encourage that. I would say more likely, given the community of our listeners, if anyone happens to have this coin on them and isn't collecting them themselves, then let us know by going to aproblemsquared.com, selecting solution in solution in the drop down box and say, I have this coin. I would like to get a 2015 finished coin to celebrate the design of the euro flag.

Yeah. I will also say I did keep track of of the of the 100 virtual toms who got all the coins the fastest and who took the longest. So the average was 14 million. One Tom did it in 863,000 coins. So under a million. Some of the fastest ones came in under a million. The longest one is one poor Tom took 53.3 million coins. So over three times as long.

They spent 146 years working in that bank to get all of them. And I'll tell you what, I'm going to give your result a ding, Matt. I feel like that has, but you know, a sort of tentative ding, because I'm interested to hear from our listeners as to if they've managed to find any rare commemorative two euro coins. And for the part that Tom has asked me about and how to display them, I think there might be some crossover with my answer. Oh, you're going to roll it forward. Interesting. A crossover episode.

our next problem was sent in by someone named adam who also went to the problem posing page at a problem square.com and said how do i display my enamel pins they go on to elaborate that they have a small collection around 20 of enamel pins from various events they've attended and cities they've visited. And if they were commemorative two-euro coins, it would not be enough. That would be an embarrassing collection of commemorative two-euro coins. Now, Adam's current solution is to store them in a box.

Well done, Adam. They want to know a few, wow, demanding, of the best ways to display the pins so they can actually look at them and admire them on something approaching a daily basis. And their final point, well, they got one final point they actually wrote out, which is that they don't think they want to put them on something that goes outside. So I guess they're referring to like clothing or a hat or something. Out of fear they get lost.

So it needs to be quite a secure solution. And the unsaid bonus thing is it'd be really handy if it doubled up as a way to display commemorative two euro coins. So, so Beck, what have you, what have you got for us? Well, I have this exact same problem because I have accidentally started collecting enamel pins.

Basically. Before we go any further, can you define for me what an enamel pin is? So an enamel pin is, it's a badge, but it's those ones that has a pin with a little back that you sort of lock onto it. Almost like an earring, but for clothing. Okay. So it has a little graspy clasp on the back of it, and it's usually sort of in the shape of whatever the design is. They're usually quite heavy, metal. So it's just a type of badge, which is quite common.

We use badge quite vaguely, like as a word in Australia, but other places like the States would define that something is a pin, like an enamel pin or a button. A button is probably closer to what the UK call a badge. The round one with a little pin, like a safety pin on the back. But we're specifically referring to those ones that have got a bit more weight to them, a bit more collectible. I made, I didn't realize at the time I was contributing to this hobby.

I made a bunch of my say no to mathematically impossible street sign enamel pins as part of my campaign. You did. And in fact, I've got one on my bag, which you gave to me. And this is the thing. I started accidentally collecting them because I kept sort of being given pins

and then I would put them on my backpack and I wear a backpack almost always. And people started to notice them. And so then more people started to give me pins as presents and I would add them to the bag. And so I never intended to collect pins, but now I have quite a large collection of pins because people assume that I want them. My bag is probably twice as heavy as it needs to be purely because of the amount of pins on there. purely because of the amount of pins on there. And the issue I had while I was in the States is that I've lost several pins and I need to start taking photos of it because what would happen is I'd noticed there was a gap, but I had no memory of what was missing. There would just

be a gap left there. So Adam's requirement that the pins don't go outside is valid, valid concern. They will fall off. Or yes mini solution is to get these lockable backs and just really or spot weld them on the back yeah yeah yeah exactly i do actually have a few displayed in a i bought a uh deep photo frame a while back because I like to collect little things. I have a lot of tiny things and some of them are pins. And so I mounted them all almost like how you would a butterfly display in a museum. So I'll take a photo of that for socials and I'll also... Oh yeah, you're pointing the camera right now and I can see it. That's a cool effect. I like that. Yeah, it's a nice one. You can choose how to lay it out, make it look a little bit more official.

With that, I think the way that I mounted it was with, I think I just used a hot glue gun and hot glue gunned it to it. But you could, if you were just doing pins, you could get like a thick photo frame, sort of box frame, and then get some foam. Yeah, foam board or something yeah maybe not even foam board but that's sort of trying to think of an example of when you would see it it's almost the sort where if you were given a collector's item you would cut they would cut that shape out it's almost usually got a velvety covering on it, almost like what you'd have jewelry displayed in. So you'd get like a sheet of that, and then you could actually use it to put the pin through

and stick that in there. So I think that's one option. There are actually loads of options online for enamel pin displays. Oh, off the shelf. So you can buy specific frames for enamel pins and they look really really good again I'll I'll choose a couple of images to put on Instagram and Twitter I did a bit of searching as well to see how other people have done them and take to it the same way they do with books they'll do it by size or by color or something so it's very uh very enjoyable to look at but

another thought that I had is I have a lot of like t-shirts or things where I don't wear them anymore but I don't want to get rid of them because they're from an era that I that meant a lot to me. So they might not fit or they just might not be a style that I like anymore but it might be something I bought on holiday or something I was given or maybe it's a band that I really enjoyed or something. And so one idea I've been toying with is just putting all the pins on a specific T-shirt and then hanging that up on display somewhere on the walls and having it like that. Yeah.

So there's an option there. You could also cover a cushion, a couch cushion in them. I tend to, with old tote bags, with old canvas bags, I tend to turn them into cushion covers. You could very easily cover an old canvas bag in your pins, then put a cheap cushion inside it, pin it shut. I mean, it's not going to be a comfortable cushion, but hey, if you're just looking to have it sitting on a couch displaying everything, that could work as well. And so leading on from the last problem, I think you could do a very similar thing with the coins.

I think some more fun ways of displaying two euro coins would be a cheap Kinect 4 game. But the right size. You might have to get your own 3D printed or CNC'd or something. Yeah, yeah. You could do like an ant farm style, where it's just two bits of acrylic that are close enough together with a gap that you can just plonk them in the top and they just build up. Yeah.

For the pins, you're familiar with the pub in Goddoming, the star that we go to often if we're doing a local record. Yes. And they have a ridiculous turnover of beers. One of the reasons why it's my favorite pub, because every time you go in there, there's new wonderful beers to try. But it also means they have loads of those badges. I'm using the word badge again.

Those are the emblems that go on the pumps to indicate what beer it is. And so they've got a serious churn of those. And so it's a very similar problem. And their solution is just to stick them to the ceiling. So when you walk in and you look up, the ceiling is just covered with all the old beers that have ever been on in the pub. So that's my solution. You could just stick them into the ceiling. Start in one corner of a room.

Well, there are more pins. Take the back off. My worry with that is that they could be quite painful if they fall out. You need a friend up in the loft space with a welder. Or to put the backs on. Or to put the backs on. And then you lock them in place. Yeah, yeah. You to put the backs on. And then you lock them in place. Yeah, yeah.

You need a lot of magnets. I did actually. You fill your loft with magnets. Well, I was going to say, it's funny you say this, Matt. You can get magnetic backs for enamel pins. Here you go. Which means if you want to display them, you don't want it to go outside, but you've got a big fridge. Oh, that's great.

Dismantle fridge magnets. Why not display all your enamel pins on your fridge? Or your car if you want to want it to go outside but you've got a big fridge that's great to them into fridge magnets why not display all your enamel pins on your fridge or your car if you want to take it outside well beck i feel like you've given us a lot of options for both pins and coins i now am tempted to start collecting enamel pins to be able to use some of this advice i feel like it would look pretty cool really like the fridge magnet Yeah, I've now decided that the fridge magnet idea is a much better idea than locking them all to my bag. So, um... I feel like it's a ding because you've...

What Adam wanted was a range of options to choose from. So whether or not Adam picks any of them is, strictly speaking, above and beyond the original request to solve the problem. So you've solved it in terms of giving the options so you're going to get the ding now you can put that ding on the fridge you can put it in the box frame but i feel like we still want to know what option adam ultimately goes for and indeed tom with the coins yeah tom do you give us a spending whoa because it's a coin now we've reached

animal Oscar Big Bird any other business which by the way I did a Muppet theme for this because one of the things I did in LA was go to Puppet Up which is the improvised puppet show at Henson Studios where I was in the same room as Brian Henson

and merely feet from him because my friend was one of the puppeteers on the show. And I was going to talk about that in my opening chat, but instead told like a 20-minute story about being detained. So, yeah. Did we have any other business our headline any other business is uh someone named yoni who's got some comments about um when we were when you were trying to channel future back back in episode 082 oh yes they said I was trying to channel Future Beck. Future Beck transmitted stomach rumbling noises. And then the food poisoning episode happened afterwards. You should have listened to Future Beck.

Wow. I mean, if past Beck knew about this, she'd be stunned. Yeah. The problem is that I was going backwards anyway. So I couldn't have listened to Future Beck because Future Beck was in the past. I'll be honest, as I said that, I wasn't sure if that made sense, but it sounded cool. Wow.

That's future producer Lauren's problem. And speaking of future Lauren and people that we like to thank for helping us with the show, on every episode, we like to thank three of our Patreon supporters at random by mispronouncing their names. And on this episode, those three supporters are... Aless and Ro. Art on I.

Lil. Iana. Oh, nice. Spocky. Now that's funnier if you can see it because it's written spooky with like three O's. So I thought it was very funny to say Spocky solely because it would make Beck laugh

and I then realized it was not a good joke for people listening along. So that's why that was funny. Es poo. Okay. Why? Es poo. Yeah.

It's nice when they're a sentence. Yeah. That was basically a short play. I also want to thank my co-host, Matt Parker. My pleasure. Myself, by Kill. play i also want to thank my co-host matt parker my pleasure myself by kill and as previously mentioned our wonderful producer lauren armstrong carter that's the show everybody Now, Beck, neither you nor I are in the Goddaming office. No. But in that office is a jar of dice that you have been trying to guess the number of for reasons I have long forgotten.

I've been higher or lowering you. I have long forgotten. I've been higher or lowering you. I would just like to do a quick calibration check to make sure I've not given you a wrong steer. Well, I think... Do you know what bounds you think we're within? Yeah, because I think one mistake I've been making is looking at the previous guesses

and assuming it's between the last previous two guesses, but not thinking about whether you said higher or lower. Higher or lower at the time, yeah, yeah. This has been going on probably far longer than it needed to, based on me not realizing. It's just not the optimal search. No, because immediately I was like, oh, well, the last guess was 464. And the guess before that was 466. So therefore, this one should be 465 and we've got it.

But then I just realized you probably said it's lower, which means I've still got between 461 and 464, I believe. Which means I've still got between 461 and 464, I believe. I would have said lower on 461. Right. I think you saw 461 and 469 and went, it's between those. Yes. When actually they were both lowers as well. I'm undoing all my good work. I'll tell you what, though.

I'm sort of relieved because I was worried that I would guess this while neither of us were in the country. And I'd kind of like to be there for it. Right. So. I'd also say this is partly my fault because I've not been keeping an eye on the guesses. Because the guesses, we've got a record of them in like our notes here. But I just, every time you say a number and I just compare it to the actual number and say higher or lower, I've not really been tracking the search. It was only when I was like, wait a minute, these don't make sense.

I was like, oh, wait a minute. I think we've had a mistake. Okay. Okay. So. Can I ask, is it between 453 and 461? It is. Okay.

Can I now make a guess? I think we pick it up from there. It's between 453 and 461. Okay. So I'm going to guess 457. Higher. Okay. Now we know it's between 457 and 461.

Okay. And next episode, we're recording back from the Goddoming office. We will both close this, maybe. And we'll take a photo of the roof. So let me say that whole thing again. We'll both have the next installment in Guessing the Dice with the jar present. And we'll take a photo of the ceiling at the Star Pub. Perfect.

Let's do it. Can you do any Muppet impressions, Matt? Have you ever known me to do any impression of anything? No, that's true. Can you at least do hi