[quote=@Kangaroo] I personally get 324 Sextillion by using a network diagram approach of 36^2 + 36^2 *37^n for n = 1:13 (as you can't start or finish with a space and you can end at each value of n). Seems much to simple compared to your maths though. Although I'm not sure on the potential for more than one space in a row for a username. I have my doubts about the validity of yours as it exceeds 37^15 = 333 Sextillion. [/quote] 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.