The localities
![P_1, P_2, \dots, P_{1983}](/media/m/0/1/7/017686e372895ec8a3668c0d025f2a03.png)
are served by ten international airlines
![A_1,A_2, \dots , A_{10}](/media/m/8/c/3/8c3fb1f3a8bc87599cfbc0d5740a80b8.png)
. 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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The localities $P_1, P_2, \dots, P_{1983}$ are served by ten international airlines $A_1,A_2, \dots , A_{10}$. 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.