# Anonymous anime fan might just have solved a question that's stumped maths experts for 25 years

Greg Evans
Wednesday 31 October 2018 16:45
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Somehow, someway, a fan of an obscure Japanese anime series has managed to inadvertently solve a complex maths question which has stumped experts for years.

Unless you are well versed in the medium of anime, you've probably never heard of The Melancholy of Haruhi Suzumiya, which ran between 2006 and 2009 and only has two seasons to its name.

This bizarre show features all sort of goings on including time travel, paranormal activity and philosophical paradoxes (sounds like an average Wednesday night in, right?).

However, the show, which has a cult following, was originally broadcast in a non-linear order and was presented in an entirely different order when released on DVD.

Since then, fans have been trying to figure out what order they should watch the series in and, more to the point, what is the quickest way to watch the series in every possible order?

This is where the notorious forum 4Chan comes into the equation, as one anonymous fan on the website claimed that they had solved this problem; simply watch fewer episodes as you have no chance of watching it in every possible order.

## Still with us? Good. Now it's time for the mathematical side of the story.

Allow us to introduce you to the world of combinatorics, a branch of mathematics that deals with permutations and superpermutations.

To present it in it's most digestible form, this is a way of listing a collection of things or elements - in this case, it is numbers.

For instance, a permutation of numbers less than 4 can be listed like 123 or 312. A superpermutation involves every possible permutation of a set.

Therefore for numbers less than 4 there are six different permutations and, when written out in an order, it reads as follows: 123121321

As you can imagine, the denser a set of numbers the more complicated a superpermutation becomes. A set of just five numbers results in a list which is 153 characters long.

So, mathematicians wanted to find a way to make these superpermutations as short and easy to find as possible, but until recently had come up short.

That was until the mathematician Robin Houston managed to stumble across the anime fans theory, which is now known as The Haruhi Problem.

Once he found this and shared the discovery on social media, his peers and researchers began reviewing the anime fan's theory and it actually works out for them.

Now the anonymous anime fans work has been referenced in a paper on the subject and combined with the research by Greg Egan, the researchers are now to devise a formula for the problem once and for all.

Jay Pantone, a mathematician at Marquette University and who also worked on the aforementioned paper, told The Verge: