Let's Play A Game

I pick a subset \(S\) of {Sue, Arron, Pete, Dan, Calvin}.

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.

Image credit: Cece Yu

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