Lower Bound on the Length of the Shortest Superpermutation aka "The Haruhi Problem" by Anonymous

Video explaining the problem and solution

tl;dr if you have the numbers 1 and 2 you can make two permutations with them: 12 and 21. You can also make a "Superpermutation" with something like 1221 which is a sequence that contains all permutations of 1 and 2. A shorter sequence would be 121 or 212. Finding the shortest sequence that contains all permutations of any given set of numbers was an unsolved math problem. Someone posted on 4chan's anime board asking for the most efficient way to watch every permutation of "the endless 8", which are 8 nearly identical epsiodes of The Melancholy of Haruhi Suzumiya. Anime nerds pride themselves on watching these episodes over and over. Someone posted a sequence with a math proof for why it is the shortest. In essence, they posted the shortest superpermutation for a set of 8. The method can be used on any sized set and doesn't just apply to sets of 8.