# 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.

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