Question

A movie company wants to make movies featuring various monsters. They want each movie to have at least 2 different monsters and no two movies to have the exact same set of monsters. What is the minimum number of monsters the company must use in order to make a million movies?

Answer 1

If they have n>=2k monsters to choose from, then we need

C(n,2) + C(n,3) + C(n,4) + ... + C(n,k) >= 500,000

10
∑ C(20,k) = 616,665
k=1

Answer 2

20