I've been trying to solve this problem since 1975. I just glanced at the linked page, yes it is indeed the same problem, but I don't want to know the answer, I want to solve it myself.
I'm pretty sure I know how it's done now, but I haven't had the headspace to deal with it yet.
Here is a related problem. I think it's related anyway:
WITHOUT USING A CALCULATOR!
How many chocolate chips must one mix into the dough used to bake one hundred thousand chocolate chip cookies, such that ninety-eight percent of the cookies contain at least two chips?
I don't recall the precise numerical answer but I do know how it's done; I solved that problem in a final exam at Caltech in less than fifteen minutes.
I'm pretty sure I know how it's done now, but I haven't had the headspace to deal with it yet.