[quote=@Alex] My answer is definitely too big I worked under the assumption that the cases that weren't allowed would be so few that they would be insignificant - I'm probably [s]very lazy[/s] wrong for doing so. But by the time I realized the problem looked like a geometric series I was going crazy (I was trying to brute force it as a programming exercise) I'm not sure I completely understand your approach or what you meant by "network diagram approach" tbh Wouldn't it be 36^4*37^n for n= 0:13? n= 1:13 ignored the two character usernames for n=0. I'm not sure why you add the 36^2 instead of adding them either? idk it's been a while since I've done this sort of maths Wouldn't it exceed 37^15 since I'm basically summing 37^15+37^14+37^13+...+37^2? And anyways you're right about multiple spaces in a row - that isn't allowed either. Honestly without knowing [b]all[/b] the rules it's difficult to make an estimate. [/quote] I didn't consider disallowing multiple spaces myself but the network diagram approach is looking at it where every step has 'x' possible future steps. The 36^2 is all of the two alphanumeric usernames possibilities. 36^2*37 is all of the three alphanumeric username possibilities and so on until n=13 which is all of the 15 alphanumeric usernames. So basically you have 14 different sets of potential usernames from 2-15 characters long.