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Airlines

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September 9, 2010
combinatoricsExtremal combinatoricsRamsey Theorygraph theoryExtremal Graph TheoryIMO Shortlist

Problem Statement

The localities P1,P2,…,P1983P_1, P_2, \dots, P_{1983} are served by ten international airlines A1,A2,…,A10A_1,A_2, \dots , A_{10}. It is noticed that there is direct service (without stops) between any two of these localities and that all airline schedules offer round-trip flights. Prove that at least one of the airlines can offer a round trip with an odd number of landings.
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