The following fun exercises appeared on p. 134 of Hofstadter's Metamagical Themas, a collection of his Scientific American articles from the early 1980s (the title is a play on Martin Gardner's column, "Mathematical Games").

I have not sought permission to reprint them here, although I doubt he would be upset if more people explored—and became fluent with—really big numbers. I encourage you to buy the book, which has the same élan vitale that made GEB a classic.

Note: In case anyone is interested I have posted my "solutions." If you don't care about my thought process, you can grab my results as a list of tuples for easy processing; it might be interesting to aggregate people's answers.