Problems Section: Problems 1511--1520

Q1511 In a certain country (see Q1494 and Q1502), between every pair of towns there is a highway going in one direction but not in the other direction. A town is called ``central'' if it can be reached from every other town either directly, or with just one intermediate town.

  (a) Show that if there are 8 towns in this country, then it is possible for every town to be central.
  (b) Show that the same is true for any number of towns except 2 or 4.