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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
В стране 17 городов. Каждый с каждым соединен авиалинией. Каждая авиалиния, соединяющая любые 2 города, обслуживается ровно одной авиакомпанией. Всего в стране работают 3 авиакомпании. Докажите, что найдутся 3 города, которые можно облететь последовательно и вернуться в исходный пункт, не заезжая в другие и пользуясь рейсами только одной авиакомпании.
Обращаю внимание экспертов, что эта задача входит в программу заочного тура олимпиады по математике здесь. Этот тур продлён до 5 января 2019 года. Поэтому прошу желающих решить задачу не показывать её решения до 6 января.
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