Source: Peter Winkler book, Placement quant company interview, Wikipedia
1) How many times do you need to flip a coin before you expect to see both heads and tails?
2) How many times do you need to roll a die before you expect to see all the numbers 1-6?
3) A company — say Coca-Cola, for concreteness — is holding a contest where everyone who collects one each of n different "coupons" wins some prize. You get a coupon with each purchase of a Coke, and each coupon is equally likely. What’s the expected number of Cokes you have to buy in order to collect all the coupons?
Update (10/01/10): Solution posted by Giridhar (IITK alumnus, Yahoo! Engineer) in comments!!