[0:00] Is it possible to mathematically calculate the 
fewest number of items of clothing you'll have  
[0:05] to own so you never repeat an outfit for 
an entire year? Well, you can and I have,  
[0:14] which is why for this video, really put in the 
effort. I keep a long list of video ideas. Oh,  
[0:20] so long. But on that list, when I was flicking 
through it the other day was just a Reddit URL.  
[0:26] So, I followed that and it was a post on the math 
subreddit that the mods had since removed and the  
[0:33] original poster had deleted it and then deleted 
their account. So, there wasn't much left for me  
[0:39] to work out why I'd saved that URL. But looking at 
the comments that survived, it seems the original  
[0:46] poster was asking how many items of clothing would 
they need to own. So across the course of a year,  
[0:53] they would never repeat an outfit by combining 
those bits of clothing. At least that's what I  
[0:57] choose to believe it said because that is a 
mathematically interesting question. Now my  
[1:03] first mathematical thought was regret. Maths 
regret that I'm no longer a high school math  
[1:09] teacher. Because if I came across this when I was 
teaching in a school, I absolutely would have got  
[1:14] 31 ties and like numbered them on the back and 
worn them in the same order every month and then  
[1:19] had 12 shirts and worn them. Okay, washing. Let's 
not worry about that. But I would have worn a  
[1:25] different shirt per month and then I would have 
had a unique outfit for every single school day  
[1:30] and I would have found that so funny and I now 
miss being a teacher just a little. It was It's  
[1:36] a great career. And I was like, that would have 
been hilarious. But actually, that would have been  
[1:40] inefficient because 31 ties times 12 shirts is 372 
possible combinations. Can we be more efficient?  
[1:50] We'll break down the case for exactly 365 outfits. 
365 is not a prime number. It is 73* 5. They're  
[2:00] both prime numbers. That's as far as you can break 
it down. So you would need to own 73 of something,  
[2:07] maybe shirts, and then five of something else. 
So if you don't wear ties, which is fine,  
[2:13] that would be like five trousers. You can choose 
your own categories. And that would be exactly  
[2:19] 365 outfits. Ah, leapers though, they're 366 days. 
So I guess your options are to either go full 366.  
[2:27] So that would be uh 2 * 3 * 61. So, two trousers, 
three shirts, 61 hats, and that will cover you.  
[2:37] And there's an outfit that only comes out once 
a year, or you stick with 365. Once every four  
[2:42] years, go naked. That said, uh, for all of these 
categories, there is like the null whatever. And  
[2:50] some categories do and don't lend themselves to 
that. Particularly if you're a math teacher, you  
[2:54] could probably get away with the null tie, maybe 
a null hat. That's probably about it. The point is  
[3:02] choosing to not wear something is also an option. 
So, we're splitting numbers into their prime  
[3:06] factors and then you've got to have categories 
that have as many options as each of those prime  
[3:12] values. And you might choose one of those options 
is just not wearing that thing. Right? Let's  
[3:17] talk about efficiency. Here's the thing. We don't 
care about how many outfits. As long as we've got  
[3:21] enough to cover a year surplus, that's fine. We 
care about the fewest number of items of clothing.  
[3:29] And the 365 one, that's 78 items of clothing if 
you add up all the prime factors. And for 366,  
[3:35] that's actually better. That's come down to 66 
items of clothing. Although the hilarious 31 ties,  
[3:43] 12 shirts, that's a mere 43 items of 
clothing. So actually, by overshooting the  
[3:49] number of combinations, we can reduce potentially 
dramatically the number of items of clothing. What  
[3:54] we'll need to do is just sum the prime factors for 
all the numbers bigger than 366 and see what's the  
[4:04] smallest, which I did. And I put them all in a 
spreadsheet. First of all, over here, I plotted  
[4:13] what this looks like as you increase the number 
of outfits. And you can see the primes are just  
[4:18] these spikes at the top. And there's no rhyme or 
reason to them. They're primes. classic primes and  
[4:25] even the in between ones. There's just not much of 
a pattern because we're it's prime factors. Like  
[4:31] primes defy nice neat patterns. So the easiest 
answer here is just to sort. So you know what?  
[4:40] Going to select everything. Sort by number of 
items, smallest to largest. Here we go. 17. You're  
[4:49] not going to beat 17 items. In fact, there are 
four different ways you can do 17. That's pretty  
[4:54] sweet. So, oh my goodness, you can just have two 
in like seven categories and then three in one.  
[5:02] Or you could have fewer categories here. Maybe you 
want to minimize categories because you can do 17  
[5:06] and get 405 outfits with only five categories. 
A 3x3x 3x3 by five. That would do it. So,  
[5:14] we kind of want to maximize outfits. Although, as 
long as it's more than a year, we're satisfied the  
[5:19] conditions. We want to minimize items, but we also 
want to minimize potentially number of categories  
[5:27] because then you've got fewer different things you 
got to change in your outfit every day. Although,  
[5:32] do we want to minimize the biggest number in one 
of the categories? Because if you're prepared to  
[5:37] have a few more items, you could down here do 
a 5 by 7 by 11. That's only 23 and you've only  
[5:44] got to very three different categories. But 
11 in one category. Oh, wait a minute. We've  
[5:51] just reached the end of maths and the beginning of 
shopping. I will of course link to the spreadsheet  
[5:58] in the description below if you want to have 
a look at the numbers for yourself. However,  
[6:01] I think I can't carry on this analysis any 
further without actually going shopping.  
[6:07] I've got to discover what are the practicalities 
of buying clothing in different categories that  
[6:13] can then be swapped to get a certain number of 
outfits. You know what's even easier to change  
[6:19] than your outfits? It's me business mat. And that 
picture up there is from this plate. So easy to  
[6:24] change. In fact, regular mat, can you go grab the 
other ones? Great. Now, this plate, those things  
[6:30] held up by magnets. Yes, thanks to displate. 
toolf-free, safe for walls, quick swapping  
[6:37] magnet system. You can easily switch between the 
over 2 million different artworks available on  
[6:44] their unique metal canvases. Now, if you can't 
find the designs you want, they do have a custom  
[6:49] display option for your own artwork, but we 
were easily able to find multiple display plates  
[6:55] that we wanted here at Standup Matts. It was 
producer Nicole who went for this classy number,  
[6:59] whereas camera person Alex picked this. I think 
it's from Warhammer. And which one did I get? Oh,  
[7:06] thanks, Regular Matt. He's definitely standing 
right there. I went for Pac-Man. And this month,  
[7:12] this plate have a Black Friday deal for up to two 
plates, 37% off, up to four plates, 43% off, and  
[7:20] more than four plates, 46% off. That's basically 
half of them free, rounded to the nearest whole  
[7:26] metal plate. if you use the code standup or click 
the link in the description. I imagine there's a  
[7:32] QR code on the screen somewhere. And that discount 
includes the texture plates. Those are plates with  
[7:39] an extra 3D effect that really makes them pop. 
So, please do check out Displate. Use code stand  
[7:46] up for a tiered structure of discounts. And thank 
you so much to Displate for sponsoring this video.  
[7:53] Okay. And can we get the original? Thank you. 
Anyway, so I'm going to have to hit the actual  
[8:03] high street and see what clothes cost. So, let's 
go shopping now. While we have no idea who the  
[8:09] person is, we can use me as a substitute. And we 
don't know where they would have bought clothes.  
[8:15] So, I figure I'll go to Oxford Street. This is one 
of the most iconic shopping districts for clothes  
[8:21] in the world, definitely in the UK. And I'm going 
to spend as little money as possible within my  
[8:27] fashion and ethical limitations and see if I 
can uh buy a year's worth of outfits. I realized  
[8:34] pretty quickly once you're dealing with a serious 
item of clothing in like a hoodie or something,  
[8:39] you're not getting that for under £30. And if you 
want a shirt or trousers, that's definitely north  
[8:45] of £50. For a nice one, you're touching 100 quid. 
So, so if I strayed into too many categories,  
[8:52] had to get multiple jumpers or something, I'm 
going to blow the budget real fast. And I found  
[8:58] the sock loophole. Pack of five socks from John 
Lewis. £15. That's three quid each. Oh, but does  
[9:06] that count? Socks. H. Either way, Small Things 
might be the winner as long as I can still make  
[9:11] it count as a proper outfit. Okay, some of you may 
have seen this coming. I've instantly run into the  
[9:16] problem of style. So, I could just, you know, this 
is my classic kind of G core look. I could shop  
[9:23] for my everyday wear, or I could try and shop to 
dress like a math teacher. What I mainly want to  
[9:29] do is not just spend money unnecessarily. So, 
I'm either going to buy things I will continue  
[9:34] to wear, or I'll buy stuff that I figure I 
can sell on eBay afterwards for charity. So,  
[9:42] if you're shopping for the math teacher in your 
life, keep an eye out at the end of the video.  
[9:47] Okay, I've hit math teacher P here with Oh, 
come on. with the ties. Look at this. So, I  
[9:55] could easily rack up, you know, as many as I need 
from here. I could do So, the 1175, we're talking  
[10:05] 23 items, but only three categories. So, I could 
pick cheap categories. I could stuck up on tithe.  
[10:11] I could do maybe socks. 385 outfits. What I would 
like to do though is get down like I meanh it's  
[10:22] still a lot in the one category though where I can 
get down to the 5553. There's only 18 items. We're  
[10:27] talking 375 outfits. But now I got to find like 
four different categories. It' be like five ties,  
[10:33] five shirts, five socks. I mean socks feel like 
a they're so cheap. Three trousers. I don't know.  
[10:44] We'll see. Do I go for fewer categories but a 
lot of them in each category or more categories  
[10:50] fewer in each one? I mean, the one thing that's 
not up for debate is I'm buying. I'm buying that  
[10:55] tie and at least two of these. Okay. In 
the end, I've gone full math teacher. So,  
[11:03] I only got five ties, and I could have got them as 
cheap as £10 each, but I went for ones that I feel  
[11:10] uh have more visual difference and more likely for 
other people to buy them once the video is done.  
[11:14] They averaged me £12 and I think like4 each. 
Again, could have got that down. And then I  
[11:21] went for shirts and the multiack shirts were the 
ticket. Uh they came down to £1820 each for five  
[11:29] shirts. I think the idea of changing categories. 
So instead of doing 17 in the same category, the  
[11:35] fact that I pay basically the same for the shirts 
and the ties, but because I switched categories,  
[11:40] combinations go up. So I think in the end that's 
the right decision. Now I am going to cheat and  
[11:46] go for the sock loophole. I'm going to get the 
five socks for £3 each. Come on. I got to get  
[11:51] this cost down. Uh and then finally, hats. 
I mean, I genuinely need Well, I'm already  
[11:56] wearing the null hat. I'm going to allow that. And 
I genuinely need two new hats. They're for me. So,  
[12:02] that's the plan. Total will appear on the screen 
in a second. I now own enough items of clothing  
[12:09] to wear 375 different outfits. But, of course, 
I can't put on 375 outfits in one YouTube video.  
[12:17] I mean, to do that, it would take a whole 
day. I need to hire a studio so I could do  
[12:22] a elaborate stop motion catwalk sequence, which 
of course we've done. Here are all 375 outfits.
[12:56] Take me home.
[13:31] We ran out of time. We We literally got kicked out 
of the studio. You think four hours is enough, but  
[13:38] no. So, I mean, I was going to catch the ball. We 
had a whole final routine. The only thing we could  
[13:43] do now, I guess, is just keep going as planned 
here in the office. So, I'm going to do that.
[14:18] And that's how it's done. Never wearing 
a tie again. Two days of my life. I think  
[14:28] we can all agree it was worth it. Hope you 
enjoyed it. 375 outfits. Although, fun fact,  
[14:33] we missed one. If you can, I saw it when I 
reviewed the footage. If you can find it,  
[14:38] uh, comment below. I'll be very impressed. So, 
the in conclusion, the fewest number of items you  
[14:43] can own and not repeat outfit for a year is nine. 
It's because if you go back to the 384 solution,  
[14:49] which is the one with the most categories for any 
17 items because there's so many categories, if  
[14:55] you put a null in every single category, you got 
seven binary. You either wear it or you don't. And  
[15:01] then you got a single three. So that's two items 
in the null. So there you are. Nine. Although  
[15:06] actually you can get 512 outfits out of nine items 
because if you just have nine binary categories,  
[15:14] you wear it or you don't. If you can find nine 
categories of clothing where it's acceptable  
[15:19] to just not wear it, you can't own other items. 
Don't forget. Maybe you can. I don't know. Anyway,  
[15:26] uh 512. Two to the nine. There you are. Nine 
items. That is the absolute minimum. Although  
[15:32] practically as I discovered because not all 
categories of clothing cost the same. You  
[15:37] want to also balance off minimizing the number 
of categories so you're not once you're buying  
[15:42] trousers and jackets it gets so expensive. So I 
would say in in reality 17 or 18 items although  
[15:47] if you want to go your entire life never wearing 
the same outfit twice. 29 items. Yeah. 29 items.  
[15:56] You got nine categories with three each. single 
two item category and that will give you 39,366  
[16:03] individual outfits. That's over 107 years. I mean, 
you'll have to pick a size and commit to it for  
[16:11] life and as they wear out. I guess you can replace 
them. No, I don't know. I don't know the rules.  
[16:17] Anyway, combinotaurics, eh? Woo! Things things 
explode real quick. 29 items for a lifetime over  
[16:23] a century of clothes. There you are. Um, that's 
basically it. Thank you so much for watching.  
[16:27] If you do want any of the clothes from this video, 
imagine buying one of these for your math teacher.  
[16:33] Now, there's a Christmas gift or you if you are 
a math teacher, I will um sell these will all be  
[16:39] on eBay. All the money goes to Water Aid or for 
charity. I'll put up all the socks as well and  
[16:44] the shirts. I will wash them all. That's not you 
know, don't get weird. Uh and you can buy them for  
[16:50] yourself or for the math teacher in your life. And 
on Patreon, I'll give you the behind the scenes.  
[16:55] Yes, we could have done the stop motion better. 
I automated it with terrible Python code. I'll  
[17:00] do the behind the scenes on Patreon cuz 
if uh things have no educational value,  
[17:05] I don't mind putting them on Patreon. But 
the fine Patreon people support these videos,  
[17:09] so the content's out there for everyone, the 
useful bits. Uh and that's it. Thank you uh so  
[17:14] much for watching. Uh happy Christmas shopping 
for your new incredibly efficient wardrobe.