A Problem Squared - 090 = Washing Machine Lies and Lincoln Penny Highs

Episode Date: July 29, 2024

🧺 Why is the cycle time on my washing machines always wrong? 🪙 How long will it take to sell 400 Lincoln memorial pennies for $20,000?  🔔 We have DINGS!  🧳 And the business briefcase is open!  Disclaimer: You may hear a slight change in tone on Matt's audio at points throughout, that's back up audio which sounds different. If you want to find out more about the IMO, or International Mathematics Olympics, you can do that here: https://www.imo-official.org/  And if you’re in London and you want to experience the janky eclipse, why not visit Novelty Automation! You can find details about this gem of a place here: https://www.novelty-automation.com/10_current-machines.htm"       Finally, send your problems and solutions to our website: www.aproblemsquared.com. If you’re on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on the ‘Sup ‘Zards’ pinned post!  And if you like, leave us a review, pass the podcast onto a friend or give us a rating! Every little helps.  Finally, if you want even more from A Problem Squared, you can find us on Twitter, Instagram, and on Discord

Hello and welcome to a Problem Squared, a podcast which you could say is a bit like a recording of two people talking about solving problems. Um, you're joined by your host Beck Hill, who's a, she's a lot like the things that she's similar to a comedian, performer, and famously has, uh, performed many of her own jokes. And I'm Matt Parker, a mathematician who's a lot like analogies, which are not well explained. So, Beck. Wow.

Wow. And I thought I dialed it in with the dog references in the last episode. Maybe dialed it in. I feel like that had a lot of details. I also famously, a lot of my books were written by me. On this episode. Why do washing machines lie? I've calculated the value of 400 pennies.

And they'll be A-O-B, which stands for Any Other Business. See, it's not fun when you just fax, Matthew. Um, have you, have you, I mean, I think we've got a pretty good insight into how I'm doing at the moment, but how are you doing? I'm good. I've been busy. I already mentioned this on the I'm Wizard bonus podcast we put out for our Patreon this year. But I'm off to LA for a month as of next Wednesday.

I went to Berlin for a long weekend. Oh yeah you did. So my recently, that was very fun. Actually you know what, I was aware you were in Berlin because I think in some of your messages you used the phrase I'm in Berlin. I was like, you're doing work or something. I didn't realise that was just pure holiday. So these are my friends, Gilda and Mathieu, who are friends from Paris.

Oh, they're the ones that had the zeroth floor. There's a minus zero floor on their apartment block in Paris. Great. Great. Mathieu, when I arrived, brought a big box of Ferrero Rocher because I had complained on the podcast when you threw out all of the Ferrero Rocher. Yes, yes, you did. By your words, they had gone off. You still complain about that. Chocolate never goes off.

I'm still curious. I'm still human. It was years ago. Unbelievable. So, he got me a box of Frérochés, which is very kind and thoughtful of him. Did you have anything to report? Did you have any? I'm locked out of my house.

Why? That's happening right now. Lucy locked me out. I do think it looked a lot more outside than usual on your Zoom. No, no. You're in your office, I can see. That's a joke. I'm in the office. Yes. I was in Bath working yesterday and then staying over and coming back this morning for this record. And I forgot to tell Lucy that I didn't take any house keys with me. And by the time I remembered to say, I didn't bring my house keys. She'd already gone to work. So I'm in our normal gottaming and recording office, but she's coming back tonight, right?

She will be home before we finish recording quite safely. I imagine. When you said that you'd been working in bath, my brain initially misheard that as you've been working in the bath. In the bath. I'm so glad you got locked out with your clothes on. Yes, I was working in the bath and then Lucy locked me out. So that's the story. No, it's the International Mathematical Olympiad is on, which is like the big maths competition. And every country sends a team of their top young

people to compete in doing maths. I can't... you mean the Math Olympiad? Yes! The... Olympiad. That's the one. You know it. I know it. It is very very nerdy and so they bring in a lot of people like me because now they have to entertain all the young people. So they got all these students, they're like upper high school, like 16 to 18 year olds. And they've all done these incredibly difficult exams. And now they've got to mark them to work out who won. But they've got to entertain all the kids for a couple of days while they're frantically marking these very difficult math questions. And so they bring in a bunch of people like myself to do things with them. So I was, I gave,

I was doing a talk last night and then I hosted, they got the kids doing a talent show, which was a lot of fun. But I came out after the show and there was obviously unsurprisingly a big, big queue of young people who want to say hi. And my favorite moment, I, I, you know, occasionally you say something without thinking, and then you realize you've, you've now committed. Two people give up at once, two students. I was like, Oh, do you want to selfie together or individually?

And they're like, Oh, actually, could we do both? I'm like, yeah, that's fine. We'll do every combination. And then I realized we now had to do every combination. It doesn't speed up the queue. I will have, the organizers did come over to me and she's like, are you okay? I'm like, it's fine. It's a hundred percent fine. We will do this. Then the students realized the ceiling above us was reflective and so then

everyone wanted a selfie where it's a reflection selfie taken off the ceiling above us. It was a lot of fun. Our first problem is for Beck sent in by Naomi who went to our problem posing page at a problemsquared.com and said why do washing machines always lie about the amount of time it takes to do the wash slash dry. Naomi elaborates that they put their washing machine on and they expect it to be done by the time it says. And I will agree, Naomi, that is a very reasonable expectation. And they're going to say that the time always increases and it takes longer and longer and holds Naomi's clothes hostage,

particularly when they need to be somewhere. So Beck, have you got to the bottom of these, these lying washing machines? I have. So in a nutshell, this isn't really something that has occurred until sort of slightly more modern washing machines. So basically these days, there's a lot of senses in washing machines to ensure that everything is sort of used as optimally as possible, whether that's water or temperature or things like that. And also to make sure that you're not having

to wash your clothes like several times. For instance, if you put in too much detergent and it's really sudsy, it's handy to have a washing machine that's like, hmm, this is still pretty sudsy. To me, suds. Let's rinse it some more rather than I'm going to have to put on the load of washing all over again. Obviously, depending on the washing machine, there can be all sorts of different sensors.

But the ones that I thought were the most common in this, you've got a load size sensor that measures the size of the load of washing that you put on and it notes the resistance in the drum. Oh is that why when I put washing in my machine hit go the first thing it does is just like just rolls it around like it's like tasting a fine wine like it's just calibrating gently. Do you know what I think that might be the case I haven't seen anything to specifically say that's the case, but that would make sense because what it needs to do is obviously test the resistance to the turning drum. The number of spins the drum needs to take before it detects the resistance change is the key to

how to know how much water to put in. Got it. Yep. So then it puts in the water and then it's got a water level sensor as well. Once it knows how big the load of washing is that you're using, it'll obviously sense that there's enough water in there that all the clothes are fully saturated. You know, I don't know if I've got a cheaper washer and I sometimes find that I pull out my clothes and it's sure it's done a spin and stuff, but I might find that if I've overloaded it, some of the clothes are a little bit patchy with water. You're one of those cram in the clothes people.

Yeah. In fact, when we got a new washing machine, the instructions said that you should be able to, this is how Gav explained it to me, it's a front loading washer and the instructions on that one said you should be able to put your hand in above the clothes and hold it as if you're about to shake hands with someone. So you should have enough room to do a small handshake above the clothes. That's their unit of measurement. And I do this every time now.

Do you know what? It may have been that that was Gav translating for me, but I've remembered it. It's memorable. Yeah. It's a pleasure to wash you. Yeah. Yeah. So I think basically what happens is your washing machine is making an estimate about how long something will take. You might put something on a 45 minute wash. It will estimate as you're doing the dials. So if you do like a 90 degree wash for white sheets or something, it might suggest that it's going to take three hours or whatever. But that's not going to be down to the minute because it's not until it gauges how big that load is and how much water it needs that it knows just how long it's going to take to

saturate the clothes, to spin them all, to get the spin right. One of the other things that timing might change is that when you've got an uneven load or a light load, the washing machine will sometimes add more water to balance it out so that the drum will spin properly. Oh, because it's too light otherwise. Yeah, exactly. And if you've got a light load, then you'll end up with there's no even distribution. So it's going to go all over the shop. So what it will do is actually compensate by putting in enough water that that unevenness is spread out a bit more and

the weight is a bit more even across the board. And that's why if you're like chucking in like a pair of jeans, and then like some cotton undies or something like that, something that's a lot lighter. Even if it looks like a full load, because it's taking up more space, you're going to end up with an uneven distribution of that and it will need more water and it's going to take a lot more sort of effort for it to work out what it needs to do to wash efficiently and that will add more time to your wash. So if you want your washing machine to go closer to the time that it's estimating, it's better to go by the manufacturer's instructions, be more careful about the distribution of the weights of the clothing that you're washing,

not just the amount. Think about the mass, not just the volume. And don't overload it. Don't overload it. Don't overload it. They say you should be able to imagine putting a salt shaker in there and seasoning the washing before it starts. If you haven't got enough clearance for that, you've put too much in.

Yeah. I think the handshaking thing is nice because it suggests that what if your washing machine was a portal and you were meeting the other version of you on the other side. There's another reality where they have machines that dirty their clothes. Yes. They've just got, they've got a reverse portal onto the back of our machines that clean clothes. That's pretty cool.

So I hope that answers the question. May I tell you my concern with my complaint, let's say with all of this. And I get it. Cause I know you're right. Cause I was thinking that's annoying because it must have some program. It's going to do the steps. It knows how long they're going to take. Why can't it be accurate I know you're right. Because I was thinking that's annoying because it must have some program. It's going to do the steps. It knows how long they're going to take. Why can't it be accurate?

You're absolutely correct. I love the sensors. I'm very happy with it doing that. It's the user experience. Why is it still communicating a seemingly very precise amount of time if actually there are error bars on that time. It reminds me of like there's the cliche of when you copy files or do something on a PC it gives you a very precise amount of time remaining but then it

jumps all over the place because there's big error bars. This is exactly seven seconds. No wait three minutes and 12 seconds. No wait it's a week. No hang on 24 seconds. Whereas on a Mac it just says, three minutes and 12 seconds. No way. It's a week. No, hang on. 24 seconds. 12 days. Whereas on a Mac, it just says about three minutes and it, it bakes in the uncertainty. And I think you look at it and you're like, Oh, okay, I don't need to know you're up to date. Like second by second, very precise estimate. I just want to know roughly how long it's going to take. So I would be a lot happier if the washing machines had like an approximately symbol, like on the display. So it can be like to the rest five minutes or 10 minutes.

Oh, approximately. This is approximately a 45 minute wash. And then maybe it can fade out the approximately symbol as the certainty gets smaller and smaller. I think I should go the other way. I want washing machines to be like, okay, this is a 45 minute wash, two hours, three minutes. Wait, 10 seconds. Oh, hang on. Keep me on my toes. Why doesn't it just overestimate how long it's gonna take?

Overestimate. I don't know anyone who would complain that they're washing finished early. Expectation management, that's what washing machines have to learn. So I would say in conclusion, Bec, because I have been as frustrated as Naomi in the past and I feel like you've answered my questions. I'm still annoyed at washing machine manufacturers, but I feel like you have correctly broken down why it's so terrible.

I'm gonna give you a ding at an unknown amount of time in the future. Two weeks. One day. Ten seconds. Three years, final offer. Ding. This next problem is from Eli or Ellie. And they say, I have a beer bottle full of 400 Lincoln Memorial pennies.

One, how long do I have to wait until I can sell them all and make $200,000? Very specific amount. And two, what should I do with it for now? I mean, I would suggest they should get me to guess how many pennies are in there, but they've already told us. So to ruin that one, Eli slash Ellie. We could have dragged that out for months. Matt, do you have an answer?

Yes. Yes, I do. So they want 400 pennies to be worth $200,000, which means they want each penny to be worth $500. That's a 50,000 fold increase on the value of the penny, which is a pretty big return on an investment given we can assume the pennies cost one cent each to purchase originally. And now, now they want to have 50,000 times that value. So I'm just going to step in here as someone who I know I've been to the States a lot, but I've pretty much been to the States mostly since things were contactless. So I don't really use that much change. I use quarters for, because for some reason, most of my friends who live there have communal

washes and dryers, just to link this in. Yep. And they use quarters because of reasons. So the link at a Lincoln Memorial penny, this isn't just a normal penny. I'm guessing this was like a specific penny that was a limited edition penny. Nope, just a regular old penny. Okay, with slightly in the loosest possible sense, it was a limited edition penny because the original Lincoln penny, which is not the Lincoln Memorial penny,

there was a penny introduced in the year 1909 for the 100 year, the centenary anniversary of Lincoln's birth. And it was a big moment. It's the first time they put a president on coinage because it was a bit too monarchy for their land of the free to have a president on their coinage. That's what countries with kings and queens did. And they didn't want their presidents to become like a monarch. The flip side of the original Lincoln penny from 1909

had a picture of some wheat on the back. They had Lincoln on one side and wheat on the other for 50 years from 1909 through to 1958. And that's known as like the Lincoln Wheat Penny. So then on the 150th anniversary of Lincoln's birth, they thought that mix it up. They retired the wheat version, and they brought in one that had a picture

of the Lincoln Memorial on the back. And that ran for 50 years. And our friend, Ellie, has 400 of the more recent design. They've got 400 from the penny that was available from 59 through to 2008, which are currently not worth much because they're quite recent pennies. So quite conveniently, even though these are fairly modern pennies by all standards and they haven't really increased in value yet. We have a perfect test case of the older set of pennies that also ran for 50 years and

we can see how much they're worth and use that as a prediction for how much these ones might be worth in the future. So I went on to some kind of electronic bay auction site that I went to the US version to get some US numbers on these I excluded Special versions of the pennies like some are like they've got like mistakes when they were stamped or they're from a very specific Year like there's a bunch which have above average value for additional reasons And it seems like this is just a beer bottle full of 400 run-of-the-mill pennies. So I just got prices for like just nothing

special you know standard penny and I pretty much got the whole run. I've got one for sale that was minted in 1909 so that's right at the beginning and I got one that was minted in 1958. So that's it. And then a whole bunch in between 14 pennies altogether. And the average price of the wheat penny was $2.92. It's still got up in value by 292 times. And actually, if you had- Yeah, I mean, that's a decent amount of inflation. And actually, if you had a bad return, if you had 400 wheat pennies and you got the average of all those auctions, that's over a thousand dollars. So you know, it's not, it's not to be sniffed at.

It's some gain. I then looked at the average age of those pennies and on average they were 86.1 years old. So I could now try and work out the percentage increase per year. And this is just taking this as a very broad average that the pennies have gone up. Now, one caveat before I give you the amount they've gone up per year on average is that they don't seem to do that. So the age of these pennies doesn't correlate with their value. In fact there's a very very small correlation the wrong way around

and actually newer pennies being listed for slightly higher prices than older pennies. So that's to say the actual year of the penny, if it's not a special one, is not important. It's just that it is one of those pennies, as far as I can tell. So this percentage increase is less about, you know, which penny you've got from the 50 years they were available and more as a cohort from their average age, what had to happen for them to be worth almost $3 each now. Right. Is this that they're valuable because they're like, you know, there's fewer of them and people collect them, blah, blah, blah. Or is this just down to basic inflation? You know, like back when they're like, back in my day, you can buy a whole house for six shillings and still have some leftover sweets.

Yeah, exactly. Yeah. Well, that would, yes. So, I mean, they're still, their face value hasn't changed because inflation just means you can buy less with them, but they're still worth one cent each. Like they're still legal tender. So. Oh yeah. Inflation goes the other way. Yeah.

So you can buy less with them. But also inflation just changes the buying value. It doesn't change the face value. So they're still worth $4. So these 400 pennies are $4. $4 is $4. So now. But in today's money, it might be worth more if inflation was a thing, but it's not because

we're talking about the physical objects. Now inflation does play into this because Ellie wants to know when they can exchange their pennies for $200,000 and the amount of money they will get for, let's ignore that their currency for a second, they're an antique. The amount of money you get for an antique will go up over time as the antique gets older and rarer, which is what we've been kind of looking at so far. It also goes up in just absolute value because of inflation. So an antique that costs $10 this year will cost slightly more than $10 next year. Not because it's gone up in value, but because of inflation.

Now it takes more money to buy something of the same value. So I then had to combine both and they're both working in our favor. Every year, the pennies are worth more intrinsically because they were getting older and more antiquey but they're also worth more an absolute currency because of inflation and both of these things are increasing how much money you would get if you sold them. I then went and found the data for historic inflation in the US. There's very good records month by month for inflation between 1914 and the modern day. So I took it until the end of 2023, which means I had 110 years of inflation data.

And it does go all over the place. It lurches forward, it goes back, it's nuts. If you average it out, the average inflation in the US over the last 110 years, and I'm just assuming an average is an acceptable way to do this, even though there's different amounts of currency and different things happening in the economy, is 3.267%. 267 percent and Historic increase of pennies

using the wheat ones as our example is 6.812 percent so what I did Was start with the pennies in the year 2024 Assume right now. They're worth four dollars and to be fair, it is a little bit after when they were minted. So maybe I should have backdated that a bit, but I just take it that they're currently worth $4 and we're going to go forwards. And then, then you set those two things going. And so I increased their antique worth. I then increased what that would cost with inflation

and the point at which they would be exchanged for more than $200,000, assuming everything remains constant, is the year 2135. It's a mere... That's not a ridiculous amount of time away. No, it's 111 years. I mean, they won't be worth 200,000 in today's dollars. No. They'll actually be worth in today's dollars about $6,000 at the point in time.

So they will have gone from $4 to $6,000 of today's value because they're now old, assuming we can extrapolate from the other type of penny and assuming that holds for another century. But then the rest of that to get from the $6,000 to the $200,000 is just inflation. You're just waiting for your money to be worth more. So does this mean if you were to buy a $200,000 house today? No. That it would be worth $6,000 in the future.

The other way around. If you bought a $6,000 house. Oh yeah. That it would be worth, that makes sense because of how things are, because of the fact that my landlord. Because of the way things are, yes. Look, if we could just stay on task here, Bec, we're talking about pennies. If I'm not doing this podcast in order to work out how to get rich quick, then I don't

know what to do. Good point. I thought at first the secret would be people just give us money. The next option was, do I fill a beer bottle with pennies? Apparently I can't even do that either, unless I'm going to live for another 111 years. Can I also add that I did check how much collectible beer bottles are worth because I was like, wait a minute, what if the pennies are a distraction and the beer bottle is where the value is? It turns out no. Like I tried to look up old ones for sale and every now and then people

will list them for, you know, a couple hundred dollars. But there doesn't seem to be, I think that the people who collect old currency, that's a better market to invest in than people who collect old beer bottles. That's a shame. What I'm saying is put all your money in pennies, take it out of bottles, put it in pennies and then put those in bottles. Or give it to me. I'll give you six grand in 111 years. That's not how it works. I'm going to give that 400 dings. It'll be worth even more in the future.

Oh good. thank you. And now it's time for any other business, which is a bit like when you've got a bunch of business and nowhere else to put it. Nathan Kirby wrote in when we were talking about potential cheap ways to see an eclipse, a solar eclipse, without having to go somewhere where you'll be in the moon shadow and they say there is a solution for that and it's right in London. It's convenient, that's where we are. They say there's a place called novelty automation just around the corner from the British Museum that is just that an instant

eclipse. All right. I wonder if they can explain that. They say it's something it really needs to be experienced. Oh, okay. So you have to experience it. They warn us it's super janky but they claim it's worth it. The entire place is incredible, highly recommended. And then they've got a link to a novelty automation. So we'll put that in the show notes and at some point, one of us will go there and try it. Yeah. One of us already has.

What? I can't believe I didn't mention. I think I almost mentioned this on the episode, but I thought it's going to be too hard to explain what it is for something that is not really a realistic solar eclipse experience. That's the vibe I got from Nathan's comment here as well. Yeah. Cause you were talking, I think the conclusion we came to is to recreate the

experience. It's not just about the idea of something covering up something, you know, and then darkness. You were saying it's to do with being able to see the aurora of the sun and that sort of vibe. So I didn't bring it up, but I do want to say thank you for bringing it up as a place to visit, Nathan. I could not agree more. for bringing it up as a place to visit, Nathan. I could not agree more. It's a tiny little place. I took my friend Sam when he was visiting from the States. We spent an evening just putting coins into things, lots of automatons. It's very silly, very kooky and highly enjoyable. Thoroughly recommend. Amazing. We heard from Pietro, who's commenting on episode 88, Tied Tires and Curvy Cubes.

Pietro says, thanks Beck for solving my problem about where does the rubber go in episode 88 about, well, I'm guessing rubber from tires. They said, it seems like it's everyone's problem now. Yeah. Yep. Yep. That is true. De Quart famous song,

The answer my friend is blowing in the wind and sinking in sewage water. It's definitely a ding for my part. PS. I love the pie troll version of my name and we'll cherish it always, but in actual fact it's pronounced Pietro with a resounding Italian R. Ah, Pietro. Is that right? I hope so. I choose to respectfully disagree. And finally we have another ding from, well, not from Tim, but from Tim's wife,

who we can now reveal is named Viv. Tim wrote in when Tim and their wife were arguing about, do dogs have four legs or do they have two legs and two arms? And we had quite, quite the discussion and an overwhelming number of listeners also had opinions about this. But the person who poses the problem gets to adjudicate the ding. And Tim has reported that his wife has said, yes, ding. And they also want to reassure us.

They didn't feel like we gave them a particularly hard time. In fact, they were delighted. Oh, thank goodness. Cause I felt like we were kind of raining on Tim's leg parade. Tim now gives us a bit more information. Like they hadn't really paid attention to what was happening. They were just catching up with the podcast at work and their problem came up, which was great.

And if you want to experience that giddy rush, head on over to the problem posing page at a problemsquared.com. Uh, no promises will get to your problem, but we will try. Uh, they are now a little concerned that as they write back to us to give us the ding, they are writing or typing rather with their wings instead of their front legs. So they do say thanks for the brilliant podcast. I do not think we have completely won over Tim to be team arms, but at least we have settled their spousal argument. Yeah, thanks, Tim.

Thank you so much to everyone who listens to this podcast. You make it a meaningful experience for us and a huge amount of thanks to our Patreon supporters who are the people who give us money to make the podcast. And every episode we like to thank three of our Patreon supporters picked entirely at random from my magical randomizing spreadsheet. And this episode that includes... I swear people are just now giving us names that we definitely wouldn't be able to pronounce even if we tried. I agree that names are definitely

getting, I don't use the word ridiculous because that may come across insulting. Elaborate. They're definitely becoming more elaborate. Stigeric. Blomkvist. No notes. Cor. I din. Oh, goodness. I wasn't ready for this. Fitzy G. R Rald Hoode. Same Sund and Zyga.

We appreciate you all very, very much. If you want to join the spreadsheet of people who might have their names mispronounced every episode, you can go to patreon.com slash problem squared. But that is it for us. Huge thanks to Beck Hill for being Beck Hill. I'm Matt Parker, consistently being Matt Parker and of course our producer, who fun fact, in a spare time, produces podcasts, is Lauren Armstrong Carter. Bye. Music Wrapped and slapped.