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IMO 1975 — Shortlisted Problems Question 1

IMO Shortlist · IMO 1975 — Shortlisted Problems

Question 1

(FRA) There are six ports on a lake. Is it possible to organize a series of routes satisfying the following conditions:
(i) Every route includes exactly three ports;
(ii) No two routes contain the same three ports;
(iii) The series offers exactly two routes to each tourist who desires to visit two different arbitrary ports?