IMO Shortlist 1990 problem 22


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2. travnja 2012.
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Ten localities are served by two international airlines such that there exists a direct service (without stops) between any two of these localities and all airline schedules offer round-trip service between the cities they serve. Prove that at least one of the airlines can offer two disjoint round trips each containing an odd number of landings.
Izvor: Međunarodna matematička olimpijada, shortlist 1990