The Haruhi Problem

"What is the least number of Haruhi episodes that you would have to watch in order to see the original 14 episodes in every order possible?" Or, more formally, "what is the shortest string containing all permutations of a set of n elements?" You have an n episode TV series. You want to watch the episodes in every order possible. What is the least number of episodes that you would have to watch? Overlapping is allowed. For example, in the case of n=2, watching episode 1, then 2, then 1 again, wou