# A Game Of Circles

Alice has two circles on the plane that intersect each other twice. Bob wants to know these circles. To do that, Alice plays a game with Bob. Alice selects $$n$$ points from each circle in such a way that both intersections are selected (so Alice selects $$2n-2$$ points). Bob then asks for the identities of $$k$$ of them.

What is the smallest value of $$k$$ required so that Bob can always determine the circles, even if Alice tries to prevent it? Enter your answer for the following three problems:

1. $$n = 6$$
2. $$n = 5$$
3. $$n = 4$$

If Bob cannot figure out the circles with any $$k$$, enter 0. Otherwise, enter the minimum value of $$k$$ such that Bob can always determine the circles. Concatenate your answers for all three problems. For example, if the answers are 0, 10, 100 in that order, enter $$010100 = 10100$$.

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