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Behold, here is how we made the sequence where I wear 375 outfits. It took two days. Totally worth it.

Behind the scenes: https://youtu.be/KDqGkEQvgswOriginal video: https://www.youtube.com/watch?v=yoR2obq4YUw

Files

Behind the clothes

This is a behind the scenes video for my fine patreon supporters. From this post: https://www.patreon.com/standupmaths Original video over here: https://www.youtube.com/watch?v=yoR2obq4YUw

Comments

Rich Holmes

In the original video you briefly mentioned the laundry problem; when you're going through 375 outfits in two days you can wear the same shirt for five consecutive outfits but when you're a math teacher wearing a different outfit every day, wearing the same shirt five days in a row is another matter. This led me to think, could you order all the outfits such that no item is worn two days in a row? A couple of things are obvious: One is that if the numbers of items in each clothing category are relatively prime, you can. Just cycle through all categories and you won't repeat an outfit until you go through all of them. On the other hand if every category has two items, you can't go more than two days without either repeating an outfit or wearing something two days in a row. But it's not obvious to me whether you can avoid the same item on consecutive days when you have, for instance, 3, 5, 5, and 5 items.

Rich Holmes

Terrible Python code®, which does an ad hoc sort of search that may not always find such an ordering even when one exists, says it can be done for the [3, 5, 5, 5] case and for any other case I've tried unless it has two or more 2-item categories (which, I think it's evident, must always fail). But I have no proof it can otherwise always be done, nor a systematic way to generate such an ordering.

Origami Alice Zhang

Is it... Too late to back out from the team now? 😅🤣

Magnasium

Okay, this is much more systematic and automated than I was expected. More complicated than it needed to be? Perhaps; but I also share that joy of automating a process not necessarily because it's efficient, but because it's cool.