085 = Coin Collections and Pin Selections

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, 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's 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.

Wow.

And according to BuzzFeed, I am.

Moving on, 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 the Spoken Nerds.

So myself, Helen Arnie, and Steve Mold, 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.

But.

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 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 it.

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 London, which is an eight-hour time difference.

Yeah.

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

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 on paper got over jet lag.

I then flew another seven hours continuing the same direction,

resetting the clock

for a total of 15

hours of jet lag over 15 days.

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.

Two weeks of

alert, awake, good.

No idea what time it is, but

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.

This sounds like a great TV show.

Oh, well,

I've been living there 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 ha.

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 it 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 of 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 ester.

It's all sorted out.

The dates are in there.

I don't need to change anything.

And they're like, but what if

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 an 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.

You didn't hallucinate any of this.

Oh, absolutely not, right?

And I'm so confused.

And then he like knocks on his colleague's window and he's like, I'm going to put in 90 days.

And the guy's like, all right.

And then shrugs.

And then he's like, yeah, I've just got to check a few things 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 okay and he goes oh hang on

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 he was like

oh okay um yeah that'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 um 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.

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,

that kind of emoji,

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.

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 going to go off here.

And he walks off to where there's like a back 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, 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, you know, you don't want to cause any issues again.

You're 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

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 happening?

So I go up to the desk again of the security guard.

I'm like, hi.

Really sorry.

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 don't mind waiting.

I just, I don't know why I'm back here.

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 has 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 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 no have zero power in this situation You're already just pushing your luck with not sitting down the first time.

Right.

So I'm 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've been 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 bus.

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 it, getting me into the office.

I don't know, that's this guy totally showing off to his colleague, hey, look, I've got someone, they believing 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.

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 sexy call girl ads, which I found really inappropriate.

Wow.

But distracting, I'll say.

So then

eventually I get seen.

And the officer who was given by a 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 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 Esther, send me back to the UK, and if they cancel my Esther, I can never apply for one again.

Ultimately, I could never return to the States.

At which point, I 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 it.

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 can look after their house.

By the time I got in, it was like 2.30 in the morning,

3 a.m.

And so 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 time.

What I'm saying is, if you want to get over jet lag, get detained because you're so tired afterwards.

You're so tired.

No trouble getting to sleep.

And emotionally exhausted.

Well, I'm going to give you a ding.

Well, no, no, not even a problem.

It's just a ding for foo.

Well done 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 assumed 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 matte 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 matte 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.

Absolutely.

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

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 two 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, okay, 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 um i 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 I'm being 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're legal tender anywhere in the Eurozone.

They're off.

So they dump them in their country and then who knows where commerce will take them.

And

anything like this, you can imagine people trying to collect them.

So, I totally get what Tom's trying to do here.

They're trying to collect all of these coins.

So, and 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.

Oh, I had the full set.

And it's been

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, fun challenge.

So, now.

This initially reminded me of a problem in mathematics called the coupon collecting problem.

The coupon collecting problem is, is, you know, it's like when you're collecting like stickers when you're a kid to put in one of those books or

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 character card.

Exactly.

When am I going 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 god that's 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 um because 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.

It 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 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,

How many weeks of running park runs would I expect to end up getting all of these?

And the calculator, I won't go through the mathematics behind it.

I did a video on this, so if people go to my Sand Up Mask YouTube channel, you can see all the working out.

But the wonderful, delightful result is if 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 1 half plus 1 third plus 14 plus 5th plus 16th 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

only works if all of them are equally likely.

So

the

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 then 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 list of them all.

Oh, my 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 did you gotta 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 all the numbers had been confirmed.

Because there's some where it's like TBD.

they don't know how many they're gonna 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 two euro coins out in the mix, and I had all 522 of them

in a big old 44 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.

89,795,361.

They were done by the European Union itself to celebrate the 10th anniversary of the Euro golf 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.

Blows.

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?

Do they mean 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 billion 916,000 two Euro coins in circulation.

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 fitness.

Can I buy a memory of 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.

There are 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 lists of number of banknotes and coins returned from circulation in the Euro area

monthly.

But it gives you the value in Euros.

I couldn't find a breakdown of

are they taking out coin?

And then I was like, oh, I could work out

like 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 two 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 2,204,191,059 commemorative two Euro coins in circulation, which does make up 31.9% of all two Euro coins.

Eurozone listeners, 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 thing.

I mean, 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, Beck, all of 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

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 a plausible number to be checking?

Just some quick maths, guys.

That's almost 30 million Euro.

Well done.

Almost.

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,

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 queens.

Yeah, yeah.

Like, I think even when I worked in,

like.

I mean, mine was hospitality, but like working a cash register, you'd maybe see a couple of grand per night.

Yep.

You still need 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 let's be let's say i'm looking at five grand a night yeah and i'm doing it every night

15 years and that's that's working every night so actually that's a good tom tip top top tom tip you got to get a job that requires handling a lot of cash bank television probably you wouldn't be the most to see a lot of coins a day i think working at a bank to see a thousand coins, a thousand two Euro coins a day,

that's still 38 and a half years.

Yeah, that's a lot.

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.

But as long as 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.

Is to find that rare finished coin, buy it, and then sell it to Tom for a much higher price.

There you go.

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 a problemsquare.com, selecting solution in the drop-down box, and say, I have this coin.

I would like to get it.

2015 finished coin to celebrate the design of the Euro flag.

Yeah.

I will also say, I did keep track 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

all of them.

And I'll tell you what, I'm going to give your result a ding, Matt.

I feel like that has, and I, 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 PromSquare.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 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, Sabek,

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

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 as a pin, like an enamel pin or a button.

A button is probably closer to what the UK calls a badge.

The round one with a little pin on 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 comfortable.

I made, I didn't didn't realise 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.

I did.

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 a quite a large collection of pins because people assume that you 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 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 notice 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.

Very valid.

One 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

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

point the camera at it right now.

I think it's kind of cool.

That's a cool effect.

I like that.

Yeah, it's a nice way.

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 like 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 foam board or something uh yeah maybe not even foam board but that 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 the 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 enameled pin displays.

Off the shelf.

So you can buy specific frames for enameled pins, and they look really, really good.

Again, 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 colour or something.

So it's very, 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

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 connection.

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 Gottaming, the star that we go to often after if we're doing a local record.

Yes.

And they have a

ridiculous turnover of beers.

One of the reasons why it's my favourite 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, you know, 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, the enamel 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.

Oh, yeah.

Yeah, no good idea.

Oh, yeah.

Or to put the backs on.

And then you lock them in place.

Job.

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.

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.

Turn them into fridge magnets.

Why not display all your enamel pins in 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 to be able to use some of this advice.

I feel like it would look pretty cool.

Really like the fridge magnet idea.

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, 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 spend ding?

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 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 feed 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 someone named Yorni who's got some comments about

when you were trying to channel Future Beck 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

less and row art on I

Lil

Ianna oh nice

spocky

now that's 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 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.

I think it's okay.

Why?

Spoo, 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, Beck Hill.

And as previously mentioned, our wonderful producer, Lauren Armstrong Carter.

That's the show, everybody!

A waka-waka!

Now, Beck, neither you

nor I are in the Godaming office.

No.

But in that office is a jar of dice that you have been trying to guess the number of, for reasons I've 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, which

means that this has been going on probably far longer than it needed to, based on me not realising.

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

I

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 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 survey.

No, 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 miserable

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 goddamning office.

We will both close this,

maybe,

and we'll take a photo of the roof.

Sorry, I'm going to say the 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

that?