Recently smart phones using Android have provided a new feature that you can draw a pattern to unlock the screen, so here is the question, how many patterns you can create with 9 dots? By pattern we mean a connected path between 9 dots that you don't go through the same dot more than once. Is my definition of pattern clear? I guess that would be a nice question to be studied in combinatorics. How many such patterns can you have with n2 dots in general? (Assuming that the dots are numbered and can be distinguished).