YouTube / John “Hehe” Smith
A simple comment on a social network has made an anonymous user in a genius of mathematics. And all because of an anime series.
The first season of the worship anime series The Melancholy of Haruhi Suzumiya There are 14 episodes that can be seen in any order.
In the controversial 4chan Forum, a user left a question in 2011: what is the minimum number of episodes you would have to see to have seen the series on all possible orders?
In mathematics, two objects exchange when they are reorganized or recombined. For example, it can turn AB into BA. If an anime series was made up of two parts only, it could see the first and then the second episode (1-2) or the second and then the first (2-1). So explains to.
To a sequence of all possible permits, it is called Superpermutation. This was what sought the anime fan, who turned into the image discussion forum into a true mathematician. “I will have to elaborate this in several posts. Please see if there is any flaws that may have escaped me, ”he wrote.
If there are 3 episodes, for example, the case changes figure. It is not necessary to see 3 × 6 (18) episodes to achieve the 6 different sequences, which would be 1-2-3, 1-3-2, 2-3-1, 2-1-3, 3-1-2, 3-2-1. There is an easier way to do it: 1-2-3-1-2-1-3-2-1. With only 9 episodes viewed, you can see 1 after 2 and 3, 2 after 1 and 3 and 3 after 1 and 2 (in the three possible “orders”).
Mathematicians have already calculated the shorter superpermutations possible for a series composed of n = 4 (33) e n = 5 (153) episodes.
But for cases of large series, such as this anime, there are no answers even an algorithm. This problem is a variation of Problem of the Right Caixeiro: A person wants to visit different cities and eventually return to his hometown. The task is to find the shortest way that connects all cities: a kind of superpermation.
To find the shortest way within permutations, you must connect the most overlapping permutations. But There is no formula that quickly solves the problem.
But it was in 2013 that a mathematician happened to find the commentary on the 4can of this anonymous user. Cited the post on your blog. Only 5 years later, in 2018, that mathematician Robin Houston came across the publication.
Surprisingly, the anime fan had discovered a formula for calculating the smaller superpermation for each number:
n! +(n – 1)! + (n – 2)! + n – 3
Together with his mathematical colleagues Jay Pantone and Vince Vatter, Houston decided Check the 4chan user proof and write it in a mathematical way. Researchers their mathematical work in Online Encyclopedia of Integer Sequences. The first author of the article is the “anonymous user of 4chan”.
And if it was curious about how many episodes you need to see to have a supermutation of The Melancholy of Haruhi Suzumiya, Don’t be alarmed: you just have to see 93,884,313,611.
