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

Not sure, if it's the most efficient solution, but I would loop over all entries, and use a bitset to remember, which numbers are set, and then test for 0 bits.

I like simple solutions - and I even believe, that it might be faster than calculating the sum, or the sum of squares etc.