[MichaelCrawford]

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.