# Let's Play A Game

**Discrete Mathematics**Level 3

You make a guess of any subset \(T\), and I will then tell you how many elements there are in \( T \cap S \).

You continue making different choices of \(T\) until you are able to exactly determine \(S\). What is the minimum number of guesses that are necessary?

Note: You do not need to pick \(S\) as one of your choices.