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Здравствуйте, уважаемые эксперты! Помогите решить задачу В стране 10 городов, некоторые из них соединены дорогой с односторонним движением, в каждый город ровно одна дорога входит и из каждого города ровно одна дорога выходит. В каждом городе находится по автомобилисту. Каждый день каждый автомобилист проезжает одну дорогу. Найдите наименьшее натуральное N такое, что ровно через N дней все автомобилисты будут в тех городах, из которых начинали движение, вне зависимости от того, как именно проложены дороги
Такая прокладка дорог возможна, если они образуют кольца. Может быть одно кольцо, включающее все города, два кольца, в одно из которых входит, например 7 городов, в другое - 3, и так далее. Чтобы при обходе кольца автомобилист вернулся в исходный пункт, необходимо, чтобы количество дней N было кратно числу городов в кольце. При произвольной раскладке дорог, в одно из колец могжет войти любое число городов от 2 до 10. Поэтому наименьшее N должно быть наименьшим общим кратным этих чисел, N = 5*7*8*9 = 2520.
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Лангваген Сергей Евгеньевич 
