A fairly old chestnut. But see why I'm asking below, if you already know it!

With every box of crunchy GlobalEvilCorpTM breakfast cereal you get a FREE! picture of an Everything2 noder. Suppose that there are N noders (and suppose further that the picture in every box is randomly chosen uniformly from the noders and independently of the other boxes). What is the expected number of boxes of cereal you have to buy to collect the whole set?

The above question has a nice answer. What about this one?

An "interesting" generalisation

Suppose I want not one complete set, but k complete sets. What's the expected number?

It's obviously bounded by k times the answer to the first problem. But it's also obviously a lot less (when you've collected one copy of each coupon, you'll already have many of the coupons twice!).

I'm interested in any solutions to this problem. Even for k=2!

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