Suppose we toss balls into N bins until some bin contains two balls. Each toss is independent, and each ball is equally likely to end up in any bin. What is the expected number of ball tosses?

Exits on an interstate are numbered consecutively. the distance between exit 12 and exit 13 is 2.7 miles. the distance between exit 13 and exit 14 is 0.9 mile farther than the distance between exit 12 and exit 13. the distance between exit 13 and exit 15 is 6.8 miles farther than the distance between exit 12 and exit 14. the distance between exit 14 and exit 15 is miles.