Don't worry, it's nothing as malevolant as cracking passwords... While talking to a friend, I had a silly idea to create a Net::AIM bot that worked through all the AOL screen names to figure out the percentages of the 4 user types, and maybe how many screen names are actually still available. I did the math using the same base 36 idea as you, so I realized it was pretty much futile doing it like this. But I still wanted to write the code for it, even if the sun would explode before it finished... *shrug* Maybe in a few years when we have super nano quantum processors, I'll pull it off the shelf and run it then... Anyway, it was an interesting idea, sorta.

"We're experiencing some Godzilla-related turbulence..."

If you want to work out percentages, what you *really* want to be doing is to randomly pick valid usernames and go from there.

The code to randomly generate a username is left as an exercise for the reader. (minus 3 points for saying "Use the loop above to generate an array and then pick random elements from that", although I do grant that is how a mathematician would approach the problem.)

Q: How does a mathematician boil an empty kettle?
A: S/He fills the kettle, switches it on and waits for it to boil.

Q: How does a mathematician boil a kettle full of water?
A: S/He empties the kettle, reducing it to the previous problem.

Disclaimer: I may have studied mathematics in the past...