Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing

Question

I had an interesting job interview experience a while back. The question started really easy:

Q1: We have a bag containing numbers

Answer 1

You will find it by reading the couple of pages of Muthukrishnan - Data Stream Algorithms: Puzzle 1: Finding Missing Numbers. It shows exactly the generalization you are looking for. Probably this is what your interviewer read and why he posed these questions.

Now, if only people would start deleting the answers that are subsumed or superseded by Muthukrishnan's treatment, and make this text easier to find. :)

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Also see sdcvvc's directly related answer, which also includes pseudocode (hurray! no need to read those tricky math formulations :)) (thanks, great work!).