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 asked a 4-year-old to solve this problem. He sorted the numbers and then counted along. This has a space requirement of O(kitchen floor), and it works just as easy however many balls are missing.