Given fi nitely many open half planes on the Euclidean plane. The boundary lines of these half planes divide the plane into convex domains. Find a polynomial C(q) of degree two so that the following holds: for any q≥1 integer, if the half planes cover each point of the plane at least q times, then the set of points covered exactly q times is the union of at most C(q) domains.(translated by L. Erdős) college contestsMiklos Schweitzeralgebrafunctiondomain