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

I haven't checked the maths, but I suspect that computing Σ(n^2) in the same pass as we compute Σ(n) would provide enough info to get two missing numbers, Do Σ(n^3) as well if there are three, and so on.