---
title: 'The fewest items of clothes to never repeat an outfit.'
source: 'https://youtube.com/watch?v=yoR2obq4YUw'
video_id: 'yoR2obq4YUw'
date: 2026-06-28
duration_sec: 1040
---

# The fewest items of clothes to never repeat an outfit.

> Source: [The fewest items of clothes to never repeat an outfit.](https://youtube.com/watch?v=yoR2obq4YUw)

## Summary

This video explores the mathematical problem of minimizing the number of clothing items needed to never repeat an outfit for an entire year. Using prime factorization and combinatorial optimization, the creator calculates theoretical minima and then tests them with a practical shopping trip. The conclusion reveals that 9 items are theoretically sufficient, but 17-18 items are more realistic.

### Key Points

- **Prime Factorization of 365** [1:50] — 365 = 73 × 5, so you need 73 of one item and 5 of another for exactly 365 outfits.
- **Efficiency Through Overshooting** [3:29] — Overshooting the number of outfits can reduce total items; e.g., 31 ties and 12 shirts give 372 outfits with only 43 items.
- **Minimum Items: 17** [4:49] — The minimum number of items found is 17, which yields 405 outfits.
- **Practical Shopping Result** [10:55] — Practical shopping on Oxford Street led to buying 5 ties, 5 shirts, 5 socks, and 2 hats for 18 items and 375 outfits.
- **Theoretical Minimum: 9 Items** [14:43] — The absolute theoretical minimum is 9 items using binary categories (wear or don't wear), giving 512 outfits.
- **Lifetime Solution: 29 Items** [15:56] — For a lifetime (107 years), 29 items in 10 categories provide over 39,000 unique outfits.

## Transcript

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