Ex 1: Show that (d+1)(r-1)+1 is sharp in the Tverberg thm, i.e. there are (d+1)(r-1) points that cannot be partitioned into r sets.
Ex 2: For each I from {0,..,d} there is a hyperplane separating {C_i: i from I} from {C_i: i not from I} if and only if
there is no hyperplane intersecting all C_i (where C_i are convex).
Ex 3: Prove pos-frac Erdos-Szekeres: For all k exists c>0 from any point set with n points we can select k disjoint sets,
each of size cn, such that any transversal is in convex position.