Question

На первом острове 15 городов, а на втором острове 18 городов. Между некоторыми городами есть дороги, при этом любые два города соединены не более чем одной дорогой. Каждая дорога соединяет ровно два различных города. Жители этих двух островов решили построить 280 дорог. а) Какое наибольшее количество дорог можно построить между городами первого острова? Укажите ТОЛЬКО число.б) Какое наименьшее количество дорог можно построить между городами первого острова? Укажите ТОЛЬКО число.​

Answer 1

Ответ:

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Answer 2

Question Analysis

The question asks for the maximum and minimum number of roads that can be built between the cities on the first island, given that there are 15 cities on the first island and 18 cities on the second island. It is also mentioned that any two cities are connected by at most one road, and the total number of roads to be built is 280.

Maximum Number of Roads

To find the maximum number of roads that can be built between the cities on the first island, we need to consider the worst-case scenario, where each city on the first island is connected to every city on the second island. In this case, each city on the first island will have 18 roads connecting it to the cities on the second island. Since there are 15 cities on the first island, the maximum number of roads that can be built is 15 * 18 = 270.

Minimum Number of Roads

To find the minimum number of roads that can be built between the cities on the first island, we need to consider the best-case scenario, where each city on the first island is connected to only one city on the second island. In this case, each city on the first island will have exactly one road connecting it to a city on the second island. Since there are 15 cities on the first island, the minimum number of roads that can be built is 15.

Conclusion

In summary, the maximum number of roads that can be built between the cities on the first island is 270, while the minimum number of roads that can be built is 15.