Ex 0: Prove that b(n)>=2n-3.
Ex 1: Compute a and b for the following system: n-m+d hyperplanes in general position and m-d very big sets.
Ex 2: Very hard! (Schweitzer 2011: http://mathproblems123.wordpress.com/2012/03/06/miklos-schweitzer-2011/)
Let C_1,...,C_d be compact and connected sets in R^d, and suppose that the convex hull of any C_i contains the origin.
Prove that for all i there exists c_i from C_i such that the convex hull of {c_1,c_2,..,c_d} contains the origin.
For d=2 it is not hard.
Ex 3: Tverberg implies Centerpoint theorem.