Let's Play A Game

I pick a subset SS of {Sue, Arron, Pete, Dan, Calvin}.

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

You continue making different choices of TT until you are able to exactly determine SS. What is the minimum number of guesses that are necessary?

Note: You do not need to pick SS as one of your choices.

Image credit: Cece Yu
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