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Given any $30$ points in the plane, what is the smallest number of subsets in a subdivision of the set of $30$ points into subsets such that all the points in each subset are on the boundary of the convex hull of the subset, and how about $60$ points? Thanks a lot.

Given any $30$ points in the plane, what is the smallest number of subsets in a subdivision of the set of $30$ points into subsets such that all the points in each subset are on the boundary of the convex hull of the subset? and how about $60$ points? Thanks a lot.

Given any $3k$ points in the plane, what is the smallest number of subsets in a subdivision of the set of $3k$ points into subsets such that all the points in each subset are on the boundary of the convex hull of the subset? Thanks a lot.

Given any $30$ points in the plane, what is the smallest number of subsets in a subdivision of the set of $30$ points into subsets such that all the points in each subset are on the boundary of the convex hull of the subset, and how about $60$ points? Thanks a lot.