Route Cause

A problem submitted by France and shortlisted for the 17th International Mathematical Olympiad, Burgas-Sofia, Bulgaria, 1975:

A lake has six ports. Is it possible to arrange a series of routes that satisfy the following conditions?

  1. Each route must include exactly three ports.
  2. No two routes may contain the same three ports.
  3. Any tourist who wants to visit two different arbitrary ports has a choice of exactly two routes.
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