The first season of [The Melancholy of Haruhi Suzumiya] consists of 14 episodes that were designed so that you can watch them in any order you like. At some point in a 2011 discussion of the series on 4chan, someone asked the minimum number of episodes they would have to watch to have seen it in every possible order. In fact, this question is related to so-called superpermutations. And as it turns out, this mathematical area holds many puzzles: to this day, mathematicians are still unable to fully answer the problem that the 4chan user had posed.
The exact answer may be (at this time) unknowable, but in that 4chan /sci/ discussion, an anonymous person provided a formula for determining the lower bound of what that number could be. According to mathematician Robin Houston, "the author of the proof is not (to the best of my knowledge) a mathematician, nor does he have any apparent desire to publish his result in a conventional form, so it's still a pretty unexpected place for such a result to originate." Houston put that together with a recent proof from scifi author Greg Egan who had coincidentally arrived at a similar formula for the number's upper bound, and provided the world with an answer:
So the math works out that to watch all 14 episodes of Haruhi in all possible orders, you'd need to watch a minimum of 93,884,313,611 episodes and a maximum of 93,924,230,411. "But with an average episode length of around 24 minutes, it would take about 4 million years to sit through this superpermutation."
Quoting liberally from the Scientific American article which summarizes this: The exact answer may be (at this time) unknowable, but in that 4chan /sci/ discussion, an anonymous person provided a formula for determining the lower bound of what that number could be. According to mathematician Robin Houston, "the author of the proof is not (to the best of my knowledge) a mathematician, nor does he have any apparent desire to publish his result in a conventional form, so it's still a pretty unexpected place for such a result to originate." Houston put that together with a recent proof from scifi author Greg Egan who had coincidentally arrived at a similar formula for the number's upper bound, and provided the world with an answer:
Egan's upper bound formula: n! +(n – 1)! + (n – 2)! + (n – 3)! + n – 3
Anon's lower bound formula: n! +(n – 1)! + (n – 2)! + n – 3
So the math works out that to watch all 14 episodes of Haruhi in all possible orders, you'd need to watch a minimum of 93,884,313,611 episodes and a maximum of 93,924,230,411. "But with an average episode length of around 24 minutes, it would take about 4 million years to sit through this superpermutation."