Credit for this problem goes to Sander Parawira
A container holds $N$ coupons. You draw successive coupons from the container, observe the coupon drawn, and then replace the coupon. What is the expected number of draws needed until all $N$ coupons have been seen at least once?
Solution here: http://dharmath.thehendrata.com/2010/01/12/solution-coupon-drawing/