  Hegselmann and Krause introduced a discrete-time model of opinion dynamics
with agents having limit confidence. It is well known that the dynamics reaches
a stable state in a polynomial number of time steps. However, the gap between
the known lower and upper bounds for the worst case is still immense. In this
paper exact values for the maximum time, needed to reach consensus or to
discover that consensus is impossible, are determined for small number of
agents using an integer linear programming approach.
