A Problem Squared - 057 = Factorial Calculations and Optimal Celebrations

Episode Date: April 10, 2023

In THIS episode... * Matt has found the last number. * How do you determine which day of the week a given date falls on if you know the day of another date? * And some other international business. If you'd like to see Bec and Matt at An Evening of Unnecessary Detail IN NEW YORK, get tickets here: https://festivalofthespokennerd.com/show/an-evening-of-unnecessary-detail/ This is your 10 day call, this link closes on the 20th of April! -- Roll up! roll up! The limited edition Millionth Download Commemorative Plates and / or Bowls are here. You can ORDER them here: Plate: https://achievefulfilment.onwarehouse.app/preorders/new?campaign_id=y696c5w Bowl: https://achievefulfilment.onwarehouse.app/preorders/new?campaign_id=wzv5cew If you want to find out more about the Solar Eclipse Matt's going to see in Aus, do that here: https://www.australiascoralcoast.com/products/ningaloo-eclipse#:~:text=On%20April%2020%2C%202023%20visitors,a%20total%20solar%20eclipse%20occurs. Matt explains this tweet to Bec in our first problem: https://twitter.com/standupmaths/status/1354919418300657669 And here is the offending, and very funny, website they reference - Visual Fractions: https://visualfractions.com/calculator/factorial/what-is-the-factorial-of-170/ If you'd like to find out which Muppet YOU are, just speed ahead of Matt and Bec and find that out here: https://www.buzzfeed.com/jenlewis/which-muppet-are-you. Send your problems and solutions to our website: aproblemsquared.com. And, finally, if you want even more from A Problem Squared, find us on Twitter and Instagram.

Hello and welcome to A Problem Squared, the podcast equivalent to horoscopes, in that only a very small proportion of you will actually find our answers useful, but you will all keep coming back to us again and again, even when we're vague and or wrong. I'm Bec Hill, a comedian, writer, and Scorpio, which means I'm curious, obsessive, and controlling. And I'm joined by my co-host, Matt Parker, a mathematician, YouTuber, and Capricorn. Oh yeah, correct. Yep, I know, because I control that. He's our Scorpio, yeah. Yeah, and I'm obsessed. Which means he is relentless, a workaholic, and pessimistic. I do most of my problem solving via cold reading too. That is true.

It all lines up. Yeah, yeah, yeah. I wouldn't call you pessimistic. I ramble until I get a hit and then I just double down on it. Yeah, yeah. We try and be vague enough that everybody can find use in our answers. Everyone feels like we've solved their problems yeah yeah yeah what was the rest of my um uh workaholic i would agree with that yeah but it's true yeah but you enjoy your work we wouldn't be recording a podcast if we weren't

workaholics i know that's the only reason we were able to find to meet up as friends uh relentless i would agree with that. Relentless? Relentless. You'll get an idea for something and then go for it. That's true, but I also prune ideas. But is that, I don't think that's what relentless means. Okay, that's true.

Just to make room for more relenting. So carry on. And pessimistic, which I disagree with. I think you're quite optimistic. Oh, there you go. Well, that's enough hits for me to, I'm you're convinced yeah sign me up yeah i had to uh i had to double uh check your birthday yeah right on the cusp yeah which i is now in my diary oh good yeah because my my two friends called matt Matt are both in December. It's a good month.

I don't want to get you guys confused. For Matt production. On this episode. I have found the last number. Cool. Yeah. And speaking of birthdays, we're going to find out what day of the week your birthday might fall on. Oh, yes.

And got another Problem Squared international announcement. With any other business, stick around. So Matt. Yes. How are you? I'm good. I'm good. Excellent. We'll move on. Done? That's the whole thing? No! Oh my goodness, I'm doing so many things at once at the moment. Actually, I'm also, I'm going to be back in Australia again. Oh yeah, you are. One of the many things I'm doing is planning kind of my trip back to Australia to make

sure that's all lined up. That's quite soon, isn't it? Yeah. So actually I will be flying two days after this episode comes out. So there's not a lot of time and we're not recording with that much lead time either. No. So it's within two weeks i'm flying um yeah and was it six weeks i'm back for oh yeah five to six weeks in there

somewhere lucy's back for like three or four weeks she comes back sooner than i do yeah he's got a real job and you know physics to physics but we will both be out there for the total solar eclipse i'm so just which is what's prompted this trip I'm always saying to you that I've never seen a solar eclipse and I'd like to. And now there's one in Australia and I didn't find out until it was far too late. And also. It's real hard to get to. Yeah. And also at a time where my work is not paying enough.

Oh, no. And you can't just zip around the world on a whim? No. Wow. That's the annoying thing. When I can't just zip around the world on a whim? No. Wow. That's the annoying thing. When I can't afford to, I'm far too busy. Well, any other business. That's true.

You're making money and you can't travel. Yeah. And you've already got your whim travel locked in for this year. I do. Any other business. Yeah, we'll talk about that. No, but I'm very excited going out. The drive from Perth to the Eclipse is happening in a place called Exmouth, which is like way up, way up the coast.

It's 1.5 megameters drive to get up there. But we're not going the most direct route possible within the journey back is one and a quarter megameters. So we're doing a total of 2.75 million meters. And I love megameters because Lucy's work on the sun wouldn't she doesn't work on the sun she works studying the sun and when you're talking about the sun sun's big yeah they measure their distances in mega meters oh wow i didn't know that and a mega meter like a million meters it's a thousand kilometers yeah and a thousand kilometers is not like a scale at which it's easy to have a human intuition about.

And so we once drove from Perth to Melbourne. I was going out for the Melbourne Comedy Festival and we drove all the way across and we stopped every megameter. Nice. And Lucy was doing some research at the time, which was roughly on the scale of Perth to Melbourne. Just to confirm, you did stop between those points as well. No, only on the Megameter Purist. No, yes, we did. Yes, yes, yes.

We stopped more than once every thousand kilometers. So the trip I'm going to do up to the Eclipse and back, I'm going to set the little odometer thing and we're going to stop and celebrate every megameter. Although we only get to do two because we'll get back on 2.75 megameters. And what's the point of the detour on the way back oh on the way up we're going via shark bay just because there's it shark bay is pretty cool and there's not a lot of places to stay oh fair all right so question solved and it

was real oh my goodness getting accommodation is there's not normally a lot of people in that part of wa and a lot of people are showing up for this eclipse. Probably because they call it things like Shark Bay. Shark Bay. Yeah, exactly. X mouth. What happened to the mouth? Yeah. By a shark.

So we've got to basically take enough fuel for the round trip with us. Yeah. So we leave Perth without needing to stop at a fuel station. Oh, yeah. We're in like a hybrid Rev4, like to maximize maximize fuel efficiency to be able to do the whole thing. We've got to take all our own water with us, all this jazz. We've got to take jazz as well? We've got to take our own jazz.

Oh, my gosh. And we are like camping some nights, staying in hotels other nights. Depends when and how we can get accommodation. So I'm very excited. But I love a good solar eclipse. Yeah. So that will be on the 20th of april if people are curious and if you're in perth or other i mean comparatively more populated areas of western

australia you'll get a partial eclipse so it's still a sight to behold if you're in western australia and it goes through bits of indonesia as well so um yeah anyone who's going to be nearby check it out and say hi anyone who's there i mean nearby, check it out. And say hi, anyone who's there. I hope that the weather is better than it was when you're at the North Pole. Yeah. No, the South Pole. South Pole. I'm now two from three on a clip success.

Yo. Lucy's two from four. So this is going to see if we can do better this time. Yeah, good luck. Yeah. How about you? What have you been up to? I got to talk about Spider-Man for about three hours. Oh, you mentioned.

You said that when you arrived today. And I said there's a lot of the wide range of scenarios in which that is. Yes. I was like, were you trapped by a child or were you doing like a radio interview or anything in between? Yeah. Sky Cinema are celebrating the release of spider-man across the spider-verse so they did a talking head show and they got us to talk about all the spider-man films that have been on since toby toby guayas won in 20 is this one of the talking head shows where they basically

sit you in a chair yeah was it green screen or do you have a real background no real background no no it was cool they've done a little set to make it look like the sort of lair that he has in the animated. All my talking head stuff was in like a green cavern. Well, when we, the executive producer on the show was also the exec producer behind DC Fan Cast, which for listeners was a show that I did about seven years ago on Sky, which was a companion show for the DC comic book shows.

And they built this beautiful set for us that like combined all of the sort of elements of Flash and Legends of Tomorrow and Green Arrow and stuff. It was awesome. So, yeah, I wasn't that surprised, but I was very excited by the set and everything. Physical set. Yeah. But they've got to get it down to like a half hour show and there's like loads of other guests on there. So I'm not sure how much of me will actually turn up on there. Were they doing that thing where they're pitching you a bunch

of like questions just constantly? Yeah. Or was it just like off you go, talk about Spider-Man? No, it was like constant. But a lot of it was also like can you describe what happens in this film? Okay. So they had a vision for what they're going to do.

Yeah, yeah, yeah. It was fun. I like it. It's not a bad way to make a living. They're good films. Mostly. Our first problem is for you, Matt. Oh, okay.

Yep. And it comes from me! Oh, wow. Exclamation mark. We've already closed the loop on this podcast, haven't we? I know, I know. I'm sorry, listeners. I did Q jump on this one.

It was because you tweeted in response to a tweet that you'd done a couple of years ago. Yes, yeah. You said, two years later, I thought I'd update that they totally fixed this page. There you go. A little update. It's a link with a question that says, what is the factorial of 170? And I started to read it and look at the replies to you and was very confused. The replies were all very funny.

Yeah. And I could tell that I don't like being left out of in-jokes. Yep. Whole lot of computing in-jokes. Well, no, in-jokes. Computing jokes. Yeah. And I don't like being told that something can't be done because then i

want to know why yeah and i noticed that that seemed to be a theme in this so will you explain your tweet to me because you replied on twitter and said can you explain this to me in the podcast yes and then i and then i uh yes i can did a little a little a jokey troll thing by saying it'll be on episode 57 exclamation, Factorial. Yeah, exactly. Here we are in episode 57. Yes. Exclamation mark. So that's funny, listeners,

because Factorial is traditionally written as exclamation mark. So you write a number, you put an exclamation mark after it. But what it actually means is you multiply the number. So if you were doing, let's say, 5! You're multiplying it by all the numbers

smaller than it so five times four times three times two and you can do times one doesn't make a difference don't do times zero though because that ruins everything so and for five factorial it's uh 120 from memory so if i wanted to work out the factorial of 4, so the factorial of 1 is 1. Yep. Factorial of 2 is 2 times 1 is 2. Got it. And then factorial of 3 is 3 times 1. So 3, 3 times 2.

Yep. 3 times 2. It's always you multiply the number by the factorial before it. I'm not adding them together though, am I? No. I'm just timesing and timesing. Oh, yeah. So 3 times 2 times 1.

Which is 3 times 2 factorial. What? So instead of doing, if you do 5 factorial, that's 5 times 4 times 3 times 2 times 1. But 4 factorial is already 4 times 3 times 2 times 1. So 5 factorial is actually just 5 times 4 factorial. And so people often talk about factorials in terms of you multiply it by all the numbers smaller counting down. It's actually easy to think about going up.

Yes. Because then each time you want to go up to the next factorial, you just multiply by the one more number and you're there. And what's particularly fascinating about factorials is they get very big very quickly. Yeah. Because you're always adding a bigger and bigger number each time. Yeah. And so they're very big very quickly. Yeah. Because you're always adding a bigger and bigger number each time. Yeah. And so they're very large numbers.

And this website was funny because the website said, did you know the number 170 is the highest possible number you can calculate a factorial for? Any higher than 170 and the mathematical answer is infinity. And that's very funny because there's no largest number yeah for that to be true we'd have to run out of numbers yeah and i saw that and i was like yes that sounds wrong that sounds wrong because there should be another one because you can take if you know the factorial for 170 you just multiply that answer by 171 and you'll get the factorial for 171 and you could And you could do it by hand.

Yeah. You could sit down and just work that out. Yeah. Which is why it's particularly funny. Yeah. Like there's lots of things in maths where they might have said, this is where it ends. But factorials is particularly hilarious because if you know one of them,

getting the next one's trivial. Yeah, got it. It's so easy. And 171, it's got a bunch of ones in it. That's a real easy number to multiply by. I can't do it in my head, but you could do it without too much hassle. Shall we have a look at what it is? Yes. So I've got a spreadsheet here.

And in this column here, I'm going to put the numbers. One, two, three, four, right? And then over here, I'm going to put equals fact, which is short for factorial of whatever the number next to it is. So it's going to give us the factorial of 1 is 1. Oh, nice. Which you did yourself. Down to 4.

We can go down 5. 120. I was right. There we go. Yay. Let's go to 20. It's already had to switch into scientific notation. The numbers are getting so big.

Yeah. Trillions is 12. Quadrillions is 15. Quintillion. So that's 2.4 quintillionillion and we're only up to the factorial of 20 yeah stupidly big numbers okay just ridiculous okay let's go to 200 whoa okay so 200 is so uh felicity's um excel has just done uh i'm gonna say hashtag hashtag num with an exclamation mark i guess it's saying that it's so big it's delicious exactly that and so it's broken excel can't work it out yeah and if

you scroll back you're like when did it break at 170 170 so 170 it worked it out uh-huh and 171 it's like no deal you're on your own. We should try it on some other devices. Yeah. Do you have a scientific calculator on your phone? I mean, I do, but I very much doubt it's a scientific one. I mean, I've got a number of them. Well, actually, it's a bit different on the Android. All right.

So the 170, and then there's my X exclamation mark. Oh, yeah. Calculation outside of accepted range. Yours breaks exactly on 171 as well. Now the iPhone, I don't know if this, if people try this, my iPhone will do the factorial of 101, but it won't do the factorial of 102. Look at that, 102 factorial error.

Yeah. What we learned from this is that computers, and I guess whatever the website was using, stop calculating factorials at 170. That's the last one they do. And then after that, you're on your own. At 170, that's when you skip between 1,020 digits and a number that's bigger than 1,024. Than what binary can do. Yeah.

Now they have updated the website. So they've given a reason now. It no longer says that the numbers run out. It no longer says that 171 factorial is infinity. Instead of saying this is the biggest number, it now says, did you know the number 170 is the highest number we can calculate with basic PHP? What's PHP? Is that right up, doesn't it?

Not at all. I didn't think so. That's the programming language that a lot of websites use to do calculations. Oh, okay. So they then go on to say, any higher than 170, we would need a much more powerful 64-bit computer. Older computers used to use 32-digit binary numbers. Yeah. And newer ones use 64-digit binary numbers. Whenever I think of hearing bits, I think of like 8-bit gaming. Yeah. And then you'd have like, I think there were 32-bit. That was the Mega Drive. Yeah. And

the SNES. Yeah. Yeah. And then nintendo 64 i'm imagining four bits you've cracked the code all right there you go so we would need something stronger than a nintendo 64 yeah it's what i'm thinking so their explanation is still wrong yeah they're close though they're close which direction are they wrong like do we need something is it that you need something stronger than that or less than that or has it got nothing to do with that? It's got something to do with that. So what's happened is they have said it's the size of the number stored by PHP. Got it. But 64-bit, they're probably already using 64-bit.

64-bit is not enough. Because if you have a look at my spreadsheet of values here, they're saying they need to go up to 64 digits to get the answer in. But if you look at when the answers go past 64 binary digits, it happens at 21 factorial. So by 21 factorial, you can't even fit it into a 64-bit computer. So it's not that the numbers don't fit in the space available for each number. They're represented by something called floating point numbers,

which is a fancy way of saying scientific notation but for computers which is which is what we already have here so excel already switched to representing the numbers as one as you know something point whatever times 10 to the 17 times 10 to the 18 times 10 to the etc computers do the same thing they can flip it in binary to be something point something times two to the whatever. So they have the binary version of scientific notation. Wow. And if you've got a 64-bit computer using standard binary floating point,

there are 11 bits used for the power, which means that the biggest number you can write down is something times two to an 11-bit number, but they actually go from positive to negative. So actually it goes from two to the negative 1023 to two to the positive 1023. And that actually doesn't make a difference if you're on a 32-bit machine or a 64-bit machine that's just how much precision you can have in the thing times two to the whatever yeah but what's limiting the factorial is the whatever in times two to whatever and you don't get you don't get a bigger exponent you can have a bigger exponent in a 32-bit it just depends how much of the number you assign

to the bit you're multiplying and how much you assign to the power of two. Got it. And so they're blaming the wrong thing. Yeah. It's not the fact that they're using a wrong bit computer. It's the fact that they're using floating point arithmetic. And the standard for that doesn't accommodate numbers that big. And that's why all these things are breaking because like the international standard for writing big numbers in binary says you only use 11 of the digits for the power and if you want to represent a bigger

number than that you'd have to use more digits for your exponent okay now the question remains yeah how would you calculate oh how would i calculate more than one i would i would do this i would go to wolf from, which we've discussed on. We really should see if they can. We should get a membership. I'm using the free one. Yeah. Ready?

171 factorial and answer. Yay. Because you can use like infinite precision or you can have systems that deal with much, much bigger numbers. You can't just use the out of the box way that computers handle numbers. You've got to be clever and kind of do that yourself as such. Does this mean that Wolfram Alpha isn't using PHP? I feel like that's a dumb question.

Correct. It's not. It'll be using, well, it'll be using the mathematical language on a server somewhere. So the person on that website is correct in that. PHP is the wrong choice i reckon you could fudge php to do to do it properly but it wouldn't be pretty okay php people may disagree with me but there's fewer and fewer of them these days so basically will from alpha because it's all about the maths they've got their own solution for dealing with big numbers right and. And so they make it work.

The one thing I just wanted to say is that website, I don't understand this website. So they've obviously, in the two years since I tweeted that, they've, I think they might have read the replies and then cobbled together what sounds like a plausible explanation. But it's just missed the subtleties of why that's gone wrong. But if you look at the URLl it's what is the factorial of 170 that's baked into the url and you can you can change the url so what is the factorial of let's do let's do 102 that my phone couldn't do there we go and it generates exactly the same page oh but it swaps everything over to be 102 oh isn't that weird so this isn't a page where someone's done like a special thing about 170 no it's like a generator yeah it's dynamic it's taking the url and then generating

a fun factorial page about whatever number yeah they obviously weren't expecting such big numbers because if you it says here in this case the number of whole numbers in 102 is more than five yep breaking news 102 is bigger than five um you can see how this quickly gets out of hand with larger numbers and then and then and then the text is always the same it just swaps out a few of those bits and it breaks in two kind of fun ways you can first of all you can ask it what the factorial of zero is uh zero times nothing equals one. When describing a factorial, you would usually say zero. I'm pronouncing the exclamation mark there.

Yeah. Like zero factorial, zero shriek or zero bang. Personally, I prefer shriek. Is that true? I've never heard anyone say shriek or bang. Or bang. No.

Oh, okay. There is a joke on there though. Yes, there is. Yeah. I don't want to get the hopes up. Same joke on every four or four page. Oh, okay. Well, what did the evil fraction say?

You will never stop my plans for world denomination. Oh, it's quite cute. I like it. It's got a denominator, right? Yeah. Yeah, it's cute. It sounds like something I would write, to be honest. That's true. That's true. It's got a denominator right Yeah it's cute It sounds like something I would write to be honest That's true, I can't be disparaging about it

Because it's not bad I would say factorially and factorially This is the sort of website I would make Yeah Both it's level of jokes And it's maths precision Yep Well thank you for explaining that to me.

So that's why it was very funny. Yes. Me updating that on Twitter. Yeah. Because they fixed it, but they fixed it wrong. I also appreciate no one pointing out to me the joke I'd made about 57 exclamation mark. They just sort of went, oh, like, oh, you got me. And I was like, oh, good.

No one mathsplained it to you. No, and I appreciated that a lot. Because everyone went, that's a joke. Like, oh, you got me. Yeah, exactly. And I was like, oh, good. No one math-splained it to you. No, and I appreciated that a lot. Because everyone went there. It's a good joke. Because they would be within their rights, to be fair. That's because you and I, Bec, have the best people online to follow us. Yeah. Next problem, Bec, came through on the Problem Posing page

at a problemsquared.com, and they say up front it's a two-part question they think it would divide nicely between your skill sets okay and it was inspired by a recent string of questions from their four-year-old they say for beck which day of the week is the best day for your birthday to fall on not that you can really change that but good problem they then say for Matt, just to keep me involved, is there a shortcut to determine which day of the week a given date falls on? If you know the day of another date. So apparently the four-year-old is wondering what day of the week their birthday will be on this year and if they can look it up or if they can work it out. Well, I'll answer mine first then.

Yeah. I think it does depend on your age because I think when you're in school, you want your birthday to be on a school day. Oh, really? Yeah. I mean, depending on the sort of kid you are as well. Special day at school. Exactly.

And then, like, you know, kids have to wish you a happy birthday. Sometimes your class might sing it to you. I don't know what they do now. We're different people, Bec. Yeah, I was going gonna say it depends some of the listeners might be like no i don't want any sort of i would i want that and in fact when i did have a day job i quite enjoyed having my birthday on because if your birthday was on when you were at work you they would be cake there'd be a cake at the office you and i are very different people you get cake you get cake you get cake yeah free cake you know once you've got a job you can just buy cake i guess free cake free cake yeah is it free cake also i think we've had very different day jobs that's true

very true i mean free cake was worth a lot more to me at the rate i was being paid right i think i was a teacher i mean yeah to fair, probably not that different. That's it. All of my, yeah, all of my, because my birthday is very close to Christmas. Yeah. And so my birthday, I'm saying all this, my birthday has never fallen on a plausible school day, which for much of my career was also my work days. Yeah. So I have always had a holiday birthday.

You've never experienced this. This is why you don't know it's better. That's one plausible explanation. Oh, I know what we're doing listeners let us know what you're gonna make me go to a school no who's this guy it's his birthday we said we'll bring him to a primary school we have to record on the day so we'll work on my birthday yeah then I get free cake. And I bring in a cake for you. I'm on board. That's how it works. 100% I'm there.

Deal. What sort of cake do you want? Birthday cake. Well, duh. What's your favorite? If I got to pick the cake, I feel like I'm doing the work. You don't. Oh, I mean, is it work?

I don't know. Because you don't really have much of a sweet tooth I haven't got a sweet tooth That was the other problem When I was a kid Other people would have strong opinions About their birthday cakes Whereas I had no real

Because a confectionary Doesn't particularly do it for me I'll occasionally have a craving For something sweet But it's like Ones of times a year Yeah You want a birthday soup?

Exactly I do I have a Party birthday meatloaf so yeah i'm more of a savory i'm a savory human so yeah so i would argue that a friday would be the best day right in general yeah because friday if you're at school or at work you get your free cake free cake get a bit of attention free attention and then and then it's weekend so you could there you go you could then do a party or something in the evening

yeah and you've still got two days to sleep in there you are yeah to recover i think the worst day to have your birthday on would probably be a month oh maybe monday would like would make maybe a wednesday celebrate on the weekend wednesday be pretty pretty grim actually do you know what no i think the worst day to have a birthday is a Sunday. Oh. Yeah. Because then you're burning all your energy and then Monday you're even lower in energy. Yeah.

So that's my take. Best day, Friday. Worst day, Sunday. I had, growing up in Australia, my birthday is pretty much on the summer solstice, which is the longest day of the year. So as a child, when the birthday is really all about the day, let's say, I had the longest day of the year so as a child when the birthday is really all about the day let's say i had the longest day for my birthday yeah and then roughly coinciding with adulthood i moved to the uk oh yeah and then i got the longest night of the year when you're an

adult it's all about the evening that's true i think that's that's you'd probably prefer a birthday beer a hundred percent just some candles floating in it or fizzled out I want a beer big enough you can get a tea candle So basically beer but served in a cake tin. Yes, there you are With a bunch of candles. I mean, what is bread if not improperly

fermented beer? I mean, still. Breakfast toast But bread is not a birthday You don't have birthday bread. What? I mean, that kind of is what But bread is not a birthday. You don't have birthday bread. What? I mean, that kind of is what cake is. My parents lied to me. Not only do you have to wait until Christmas to have your birthday present.

Here's your birthday toast, son. Friday. Right. That's my answer for me. I can't answer on behalf of anyone else. That's true. I mean, I would agree a Friday is a winner. You know, you can either ignore it or celebrate it at your work and or place of education.

But thankfully. That's our official answer. Thankfully it rolls. It rolls throughout the week. So throughout your life, you'll get to sample. I'm pretty confident to say every different day. Yeah. I was about to ask, is there a date where it falls on the same day every time?

No. No. No, that's not how time dates work. No. And that's because actually there are 365 days in the year. And from memory, that's one more than a multiple of seven. And I've got a video about this coming out in a bit. Everyone's like, how many days in a year?

365. How many weeks in the year? 52. Yeah. How many days in a year 365 how many weeks in the year 52 yeah how many days no wait seven not because seven days times 52 weeks is 364 which is a day short yes there's one more now if the year had accidentally been 364 days no that's the opposite that's one extra i just want to describe the look that matt just gave me which was which was a sort of slight wide-eyed but also you're going to realize in about two seconds and uh it was correct no yeah well it's also that's the anyone who's done anything involving programming and dates lives in fear of leap years and time zones. But so if the Earth orbited the sun a little bit faster, got a little bit closer in, and our year was 364 days,

then your birthday would fall on the same day of the week every single time. Or if our week was five days long, which is a factor of 365, it would fall on the same day of the week every single time. It's only because the year is not a nice multiple of a week that it drifts. And because there's one extra day, your birthday drifts by one day every year. So let's say your birthday was a Wednesday this year. It'll be the day after that the next year. It'd be Thursday the next year. It'd be Friday the year after. Saturday next year be thursday the next year yeah it'll be friday the year after sad day the year after except leaped years leap years bump you too oh oh bum

so then you skip one wait when's the next leap year 2024 oh next one next one oh my gosh do you know what this means because last year my birthday was on a friday there you go this year my birthday will be on a saturday correct guess who's skipping the worst day of the week sunday look at you go straight to monday nice yeah and that's because you know there's just one extra day to make up the whole year and so that means you're a day you've done an extra day so you've got a whole multiple of weeks plus an extra day from birthday to birthday and that means you've moved forward one yeah if you've got a leap year you've got an extra day from birthday to birthday. And that means you've moved forward one. Yeah. If you've got a leap year, you've got two extra days in there.

And it depends if your birthday is before or after the end of Feb when you skip the day. Because it's only on the year that has the actual leap date in it. So if your birthday is 2024 before the end of Feb, you won't skip two until your 2025 birthday. Oh, yeah, of course. That's when you go over the hump as such. Gotcha. Yeah. So that's how you can work out when your birthday is year on year.

It'll fall into this nice pattern. And for the rest of our conceivable lives, there is a leap year every four years. They occasionally get messed around with, but that's like once a century at the most frequent. And so you have to worry about this until the year 2100 between now and then yeah you go up one three times so you if from the beginning of the week you do monday tuesday wednesday then you'd skip one thursday friday saturday skip one this is where you are in your cycle yeah monday tuesday wednesday skip thursday friday saturday sunday skip mond, Friday, Sunday, Sunday, skip Monday, Tuesday, Wednesday, Thursday, skip Friday.

Okay. And that will roll through all the days at some point. Yeah. Okay. So now I've got a base. As long as I can remember what day my birthday was last year, I can work out what day my birthday will be on next year or this year. Yep.

So if you know what day your birthday is going to be on, and then let's say we want to know what, what day of the week june 13 is going to be i just picked that randomly so but if we want to know what day of the week june 13 is going to be yeah but in relation to my birthday oh because that was the question wasn't it is there a way of is there an easy way to work out what day of the week something's going to be if you already know what day of the week something else is going to be also not just year on year like within a year if you give me if you give two days within a year well yes because i mean arguably now we know it doesn't just work for birthdays presumably you're saying anything that happens annually correct like

christmas follows the same pattern or new year's day all these things follow the same pattern or New Year's Day, all these things follow the same pattern. Yes. Tell you what, do you know off the top of your head how many days are in each month? Because I don't. Oh, as in 30 days for September, April, June, and November. So the ones that have 30 are April, June, November, and September. I've written down. All I care about is difference from seven.

And so I've written down all the remainders mod seven of all the months. You want to know the 13th of June and where are we starting from? Well, the one that I know is that the, spoiler alert, my birthday is on the 4th of November, which will be a Saturday. So that's a Saturday. Okay. Here's what we're going to do. I'm going to do the remainder of November after your birthday.

You're born on the 4th, so you're four days in. Yep. And then after that, there are another 26 days. So I can start at 26, but I'm doing everything mod 7, and that equals 5. So there's 5 left. Okay. And your birthday, what day of the week was it in November? Saturday.

Saturday. Saturday. I'm encoding Saturday as 6. Add them together, what day of the week was it in November? Saturday. Saturday. I'm encoding Saturday as six. Add them together. That's 11. Then chuck off the remaining. That's four. Okay, cool. Four at the end of November.

Got it. What's our target now? Okay. Let's try May 16th. May 16th. Okay, hang on. Let me just label May 16th. I got to get from November with a remainder of four. So December's three.

Oh, that's easy because that's going to end the year on zero. So you're going to end on a, you're going to finish the year on a Sunday. That's handy. Okay. Which means we start fresh over here. So January's going to add three. March is going to add three because we can skip Feb. That's now six. April's going to add three. March is going to add three because we can skip Feb. That's now six.

April is going to add two. Just so listeners know, I'm watching Matt do this and I am so lost. I have no idea what he's doing. And you wanted the 16th of May. Yep. Which I add up to give me. So the 16th is remainder two. That's three.

Wednesday. It is a Tuesday. No, it's not. It is. I've gotten off by one error somewhere. I'm okay with that. What date of the year did you say that the year was going to end on? I said the last day of the year would be a Sunday.

Yeah, it is a Sunday. Yeah, I got that right. Then I messed up the next bit. Just for me to understand the maths that you're doing and translate it back into Beck language, you've worked out how many lots of seven are in each month. Yes. Because that then explains how many times that day pops up in the month. Well, I don't care about how many times there's seven. I care about anything that's different to seven. Because if there's seven days, you're back where you started. So each time there's

seven, there's no change. Okay. Yes, I understand. So I'm now looking at things that deviate from seven. So does that would then move the days? Does January end on a Wednesday? Or did January end on a Wednesday? Yeah. No, it ended on Tuesday. So that's where I'm going wrong. So Sunday, Monday, Tuesday, Wednesday. And so the last day of the year was a? Sunday. Oh, I know what I'm doing wrong. No, last day of this year is a Sunday.

I know what I'm doing wrong. I'm going to the date next year as opposed to back to that. So I got Wednesday because if you could do me one consolation prize, if you look up at the 16th of May next year. Well, it should be one day later. Yeah, so that's why I was off by a day. Yeah. Whereas, yep, yep, yep, yep.

I was working forward. So you work your way forwards. Yep. And then if it's before the date that you know you take off one day. Yeah. Or I could have gone backwards, but then you're doing negative in modulant. It's doable. I mean, I've got a bit of paper here, so I should be able to do it.

So I feel like that's a terrible way of doing it. You can do a much, I mean, it doesn't get less complicated than that. It gets worse, in fact. There's a thing called the doomsday calculation, which is where you're given any date, and you can then say what day of the week it was. And I can't do that. A friend of mine can. A james grime can do it it's very impressive that is impressive and that's a similar thing where for example you know what day the year 1600 starts in or something or you know what day 2000 is and then you go forwards or backwards because but you've learned for each where the leap years

are and you shift everything around as you go and you can get the new um day but it's all kind of built into a calculator you learn the calculation you don't have to do the logic yourself you just crunch it but what it's doing is it's calculating the remainder mod seven so i guess see i think if i was doing it i would do it the long way well i mean i can go from my birthday so i would do it the long way. Well, I mean, I can go from my birthday. So I would do this. I'd go, all right. So the fourth to the end, that's 26 days. And then, uh, that's another 22 days until your birthday. So that's 48 days. Yep. And so then I would just on my fingers. Yeah. Sunday, Monday, Tuesday, Wednesday, Friday, Sunday, Sunday, Monday, Tuesday, Friday, Saturday, Sunday, Monday, Tuesday is one less than Friday, Saturday, Sunday, Monday, Tuesday, Wednesday. Friday, Sunday, Sunday. Monday, Tuesday. Friday, Saturday, Sunday.

Monday, Tuesday. 48 is one less than seven squared. Friday, Saturday, Sunday. Monday, Tuesday. Friday, Saturday, Sunday. It's going to be the day before. Tuesday, Friday, Saturday, Sunday. You're going to be on a Sunday? Oh, I think it's going to be.

What day is your birthday on? Saturday. I think it's going to be a Friday. Oh. We're both checking our calendars. Yeah, it is a Friday. But in fairness, I was trying to count while you were talking. I think you rushed.

I was talking, trying to count. That would have worked. That's the safer way of doing it. Well, I feel like, you know, the real birthday gift. I mean, considering that this is for a four-year-old. Exactly. I think maybe the way I did it. I think counting on your fingers is correct.

I think the important gift out of all of this, though, is to Lauren, our editor, who's going to make sense out of this. Wait. Hang on. Whose birthday? Oh, when's your birthday? Well, I know it.

I won't say in case she doesn't want people to know. Write it down. I know what it is. I know how many days it is difference from mine. Here we go. I feel like I'm doing a magic trick. I think it's a Thursday. I think she just mouthed almost.

Oh, I got your birthday wrong. We would make the worst magic show. We are doing this by cold reading. Wait,'s a thursday no hang on i'm getting i'm getting a day during the week there you are i hope that's cleared it up for the for a four-year-old oh wow yep i've given up that fast for that coming okay first bit of any other business we did our champagne experiment a while ago yes with controversial results i just want to let everyone know we are on the case and we're planning a much bigger event where we can get a lot of people together and have, you know, multiple bottles. And to avoid us having to buy them, we're trying to partner up with a pre-existing champagne event.

And so the Royal Institution do science of champagne events. And so our current plan is to just have like a side experiment on one of their events. So it'll be in london it'll be later in the year but uh if it doesn't end up there at some point we're going to put on a big event and we'll announce it so everyone can come along yeah it should be good fun hooray yeah i just wanted to say loads of you sent in your findings on the bath thing oh yes after i complained yep and really really great stuff. Like genuinely fantastic scientific explanations. Oh, I've seen them flooding on the problem posing page.

I just skimmed right over them. I'm like, eh, back thing, back thing. No, they're really good. But I need proper time to sit down and measure them against each other and everything. So I just want to say thank you to those people who sent them in. I've seen them. We've both seen them.

They're very impressive. And we will talk about them on a later episode. Probably not the next one, but sometime after that. We should also say that the pre-orders, pre-orders, we're taking the money. Orders. Orders for our commemorative plate and our commemorative bowl for 1 million downloads are still going. The website had a bit of a wobble a while ago. People who contacted us on Twitter, all fixed.

So we'll close that at the eclipse. As the sun disappears behind the moon, we will close pre-orders for the Commemorative Plate and Bowl. 20th of April. 20th of April. So you've got 10 days from the time of this podcast. That's not long. You get onto it. Yeah.

Finally, we did mention this earlier, but you got your medal. I did. And some people, some listeners came along. We had listeners there. I was very touched. And they said, he didn't give us a chance to say ding. I realized because I did it. You got a shout out on a minimum of two occasions.

You gave me a shout out on stage. Yep. In front of hundreds of people. Yes. Because you were sort of saying. At the Royal Society. You were like, oh, everyone was great. And then I noticed you go, like Beck, for example.

And I instantly was like, I've done nothing to help you get a medal. Hey, I thanked you for the podcast because what we're doing right now. Yes. Not that this was part of the award. No. But then I forgot to do a call and response ding because a bunch of my Patreon supporters came along, which was very nice. So hi to them.

And a bunch of listeners did come and see me afterwards and say hi and say they'd come along because we mentioned it on the podcast. So for those of you we got to meet in person, that was great. Thank hi to them. And a bunch of listeners did come and see me afterwards and say hi and say they'd come along because we mentioned it on the podcast. So for those of you we got to meet in person, that was great. Thank you for coming. Everyone else, there will be other events in the future, which brings me nicely to our last bit of any other business. Yes. We're going back to New York.

Woohoo! So. So yeah, we're going to go do an evening of unnecessary detail in New York again. And we'll link to it below. Yeah, I will be on. You're doing a thing. I'm doing a thing. And other guests.

Yes. Which I'm still confirming. But I imagine when the podcast comes out, we'll be able to say for definite. Yes. And the tickets could literally go on sale today. So I told Caveat, don't start selling the tickets until we can mention it in the podcast so all our favorite listeners have first chance to book. Because it's not a very big room.

So today is the first day they're out. If you want to come along, don't dawdle is what I'm trying to say. Yes. Come along. If there's anything that you think that we should definitely do in New York. Yeah. And that maybe Matt and I can turn into a problem that we should definitely do in new york yeah and that maybe matt and i can turn into a problem that we yeah yeah yeah if it can have enough solving a problem we

can justify it for the podcast but also a fun day out i've also i've already floated the idea of it being a roller coaster based problem you just want to go to coney island i want to go to coney island again yeah and now is the time on every episode where we like to thank three of our patreon supporters at random because uh even though this podcast is free to listen to and we don't expect anyone to pay for it we also cannot provide it without financial assistance we expect some people to pay for it but voluntary basis yes yeah the ones who can we very much appreciate it so that everyone else gets to enjoy this and today we want to specifically thank oliver townshend james mcnaughton john adams do you what? I think maybe that is the first time we've almost got them. I'm not 100% confident on John because it's J-H-O-N.

Sean. Sean. John. If I've mispronounced that, I apologize. As I do for all the names. Yeah. I mean, basically what happens is if you support us on Patreon, there is a chance that we might mispronounce your name publicly.

I would describe that as a perk. Yeah. One of the many features available. In fact, look, we will do our best to purposefully. Do you know what? I feel like, look, James, you're Yarmus McNorgen now. That's your name now. Okay, Oliver.

T'Ownshend. mcnogton now that's your name now okay oliver t own shen and other people i want to thank are matt parker thank you um i've been back hill and we definitely want to thank uh my fellow scorpio and our producer la Lauren Armstrong Carter. Rebecca, I'm going to need to ask you. I'm just scrolling down there. Which Muppet are you? Quiz. Okay. If you want to play along, link in the description. It's got the Swedishedish chef as the as the muppet that represents this question okay and then there are nine spaghetti yeah so so uh what

do you value in a friend shall we i'll read them out yeah bravery the ability to chill okay musical talent who has ever valued musical talent in a friend? If anything, I think that I am friends with people despite the fact that some of them are musically talented. Wow. I want music, but I want to pay for it. I want to befriend someone with musical talent. Loyalty. Brains. Sarcasm.

How can you value? Puns. Oh, yeah. I mean. Parties. Pizza. how can you value puns oh oh yeah i mean parties pizza oh wait didn't they just show up with pizza or the pizza is in them they are pizza like i value the pizza that is in them yeah i value you because you eat pizza um wow oh that's become real tough now. Ha. I think I have to go puns though. Really? I pun-derstand. See?

See, I felt the pressure. I thought our friendship hanging in the balance. Well, it's obviously not brains. Clearly. Yeah, no, I think, yeah, pizza is I think I'm at heart. Yeah. Pizza is good. Pizza is quite up there. I will, I will forgive someone for not. I'll get you pizza tonight. Oh my goodness.

Okay, good. Thank you. That's what I was getting at. That's what I got. You know what? I would pick the ability to chill. Well, that's lucky because that is, uh, a certain percentage of my name. There you go.

Exactly. I was going to try and do the math. What is it? It's how many letters in your name? You've got seven letters. Seven. Yeah. That's going to be a.

Five out of seven. Yeah. That's like around 62%. A little over that. Yeah. It's more than that. Six. Five out of seven.

Two point. Yeah.2 point. Yeah. No, wait. 72. Sorry. There we go. What's. That's why you didn't pick brains.

Yeah, that's true. 7. What? Rough. Somewhere in the vicinity of 71. 71. 71. Point 8. 5 eight five seven percent.

Yeah. If I had to pin it down. Oh man, you owe me so much pizza.