Math solutions can be found in amazing places, including the dark spheres on the Internet. In 2011, an anonymous poster, infamenly controversy image table 4Chan raised a math puzzle about the classic classic anime series Haruhi Suzumiya’s melancholy. Although the bulletin table contain hatred, violent and extreme, this original message gave him a solution to the sophisticated math problem.
The first season of this Anime series was made up of 14 episodes that were designed to be seen in any time you want. (For people who are not known with the anime world: eight-part direct action is called thriller Kaleidoscope Follows the same principle of netflix.
In fact, this question is linked to the very so-called superpermuts. And it seems that this mathematical field has plenty of puzzles: Currently, mathematicians cannot answer the problem raised by 4Chan.
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But horrible, in this discussion, an anonymous user estimated the minimum amount of all the passages observed with a approach to mathematics. “I need this (practice) this in many posts. Please check out any clap. Then other users took and discussed arguments, but out of 4chan, which did not make waves. No one took any notice.
Extreme binge observation
In math, two objects are permlated when they are rearranged or reconnected. For example, you can allow AB. If a series of anime was only two parts, the first and then you can see the second section (1-2) or the second and the second (2-1).
If you want to see a series in multiple sets, perhaps the passage sequence is the greatest sense. This is a sequence of possible permutations. Imagine the first section that shows the marathon that you see, and then the second and then saw the second section, and then the first (1-2-2-1). To avoid viewing the second section twice, the shorter superpermy would be 1-2-1; You should see three episodes to cover all possible order.
If a series is made up of three passages, it becomes more difficult to find the shortest superperm. In this case, there are 3! = 6 different sequences: 1-2-3, 1-3-2, 2-3-1, 2-1-3, 3-1-2, 3-2-1. Zorionez, ez duzu 3 × 6 = 18 pieza ikusi behar, baina lasterbide garbia aurki daiteke, kasu honetan: 1-2-3-1-2-1-2-1-2-1. This request has 1, 2 and 3. It has all possible permutations of numbers, but you just need to see nine episodes!
The mathematician also calculated the shortest superpermutations of the series n = 4 and n = 5 episodes (33 to 153 episodes, respectively). Beyond that, however, they are in the dark. Shortest Superpermutations n > 5 are not known.
In fact, in algorithmic challenges, it relates to one of the most intracted problems: Travel seller problem. In this problem, a person wants to visit different cities and return to his hometown. The task is to find the shortest route that connects all cities. The shortest superpermacy is the variation of this problem, which represents individual permutations from different cities. In this case, it assigns you different distances between cities by determining the overlap of permutations. For example, 1-2-3 and 2-3-1 cities have a great overlay: the last two digits of the first permutation matches two second numbers, so they can be combined to complete 1-2-3-1. So we can give a short distance between these two cities. On the other hand, 1-2-3 and 2-1-3 do not overlap. (To see the two sequences, you need to look into six parts; it is not a shortcut possible.) Thus, these cities have a great distance between them.
To find the shortest route within the permutations, you link the most overlapping permutations. There is only one difficulty: No known algorithm that solves the problem of travel vendors quickly. If you are talking about some cities, or, in the case of an anime series, some episodes are not a great inconvenience. But as soon as n They become large, the computer fails to the task because computer science is exponentially grown n.
Computers are able to calculate superpermutations n = 4 and n = 5 but not beyond that. Although it is possible to calculate elaborate superpermutations for larger numbers, it becomes more difficult to find the shortest superpermutation.
Experts must therefore do with estimates. For example, there is an algorithm that helps calculate the length of the shortest possible superpermutation n Objects: 1! + 2! + 3! + … + n! Using this algorithm, then n = 2, 1 + 2 = 3 you get the superpermutation of length. For n = 3, which is 1 + 2 + 6 = 9. It gets in length. For n You get = 4, 33. And n You get = 5, 153, corresponding to the shortest superpermutation in each case.
For larger n, However, this algorithm is no longer applied: computers could find shorter superpermutations. In fact, 1. Formula! + 2! + 3! + … + n! has exceeded the length of the greatest superpermutation n. Although the algorithm offers an approximate response, mathematicians use them as a starting place with the aim of reducing the chances of finding more specific answers.
Coincidences and discourses
In 2013, Nathaniel Johnston, now Mathematical Professor at Brunswick New Allison University landed Haruhi Suzumiya’s melancholy Fandom page. Johnston himself was not anime fan. Reached the site after some search terms related to superpermutations. There, he found the discussion of 4Chan nearly two years earlier, a user copied to the Fandom site.
Johnston did not do math But he mentioned the fandom post on his blog. This comment also went unnoticed for several years.
Then in October 2018, the mathematician Robin Houston entered his colleague blog through a strange coincidence. Houston recently learned Australian fictional science fiction authors Greg Egan found a new maximum Length for shortest superpermutings, indicated:
n! + (n -1)! + (n – 2)! + (n – 3)! + n – 3
He was inherently curious. When Houston began learning more about this result, a minimum length of theaters gave a new value of an anonymous anime fandom (at the time he didn’t know the origin of 4chan). The minimum length formula is:
n! + (n – 1)! + (n – 2)! + n – 3
Houston Share His discovery on Twitter (now x) on October 23rd of that year. “Strange situation. The best lowest low length of superpermutations proved an anonymous user dedicated to an anonymous user of a wiki,” he wrote.
Along with his colleagues, along with mathematicians Jay Pantone and Vince Vatter, Houston decided to check the 4Chan’s proof of user and write in a mathematical way. Researchers published their mathematical work Online encyclopedia of the whole sequences in the same month, and the first author appears as “4CHAN poster”.
So what do these formulas tell us? If you want to see all episodes n-Part series all possible combinations, you need to sit at least n! + (n – 1)! + (n – 2)! + n – 3 episodes – that is the contribution of 4CHAN to the user- and maximum n! + (n – 1)! + (n – 2)! + (n – 3)! + n – 3, we know through the work of Egan.
In the case of the series of eight sections Kaleidoscope, You should see at least 46,085 and up to 46,205 episodes. For Haruhi Suzumiya’s melancholy, or Haruhi, With 14 passages, the number increases significantly: at least 93,884.313.611 passages and up to 93.924.230.411. Let us remember that there is a complete solution – which would make it effectively to see the series effectively.
Fortunately, EGAN also gave the algorithm to build the appropriate superpermutation. This allows Haruhi fans to see the best passage order. But with an average passage about 24 minutes, it would last about 4 million years to sit through this superperm.
