Question

В королевстве 2017 городов. Король приказал проложить между городами дороги так, чтобы из каждого города выходило ровно 5 дорог. Смогут ли подданные справиться с приказом короля? Ответ обоснуйте.

Answer 1

Всего в королевстве 2017 городов. Из каждого города должно выходить ровно 5 городов.
Общее количество дорог=2017*5=10085
Каждую дорогу в общем количестве мы посчитали дважды, потому что у каждой дороги есть начало и конец.
Значит, что поданным нужно проложить 10085/2 дороги. Деление нечетного числа на чётное дает частное с остатком (10085:2=5042,5). А нам нужно целое число.  Значит поданные не смогут справиться с приказом короля (число дорог должно быть  чётным числом: 4,6 и т.д.)
ОТВЕТ: ПОДАННЫЕ НЕ СМОГУТ СПРАВИТЬСЯ С ПРИКАЗОМ.

Answer 2

Analysis of the King's Order

The King of the Kingdom in 2017 has ordered the construction of roads between cities in such a way that each city has exactly 5 roads leading out of it. The question is whether the subjects of the kingdom will be able to fulfill the King's order.

Possibility of Fulfilling the King's Order

To determine whether the subjects of the kingdom can fulfill the King's order, we need to consider the number of cities and the number of roads required.

Unfortunately, the exact number of cities in the kingdom is not provided in the question. Therefore, we cannot provide a definitive answer based on the information given.

However, we can make some observations based on the given information:

1. If the number of cities is divisible by 5, it would be possible to construct the required number of roads. For example, if there are 10 cities, each city can have 5 roads leading out of it, resulting in a total of 50 roads.

2. If the number of cities is not divisible by 5, it would not be possible to construct the exact number of roads required. For example, if there are 12 cities, it would not be possible to have exactly 5 roads leading out of each city.

Without knowing the exact number of cities in the kingdom, we cannot determine with certainty whether the subjects will be able to fulfill the King's order. The feasibility of the order depends on the specific number of cities and whether that number is divisible by 5.

Conclusion

In conclusion, the ability of the subjects to fulfill the King's order of constructing roads between cities with exactly 5 roads leading out of each city depends on the specific number of cities in the kingdom. If the number of cities is divisible by 5, it would be possible to fulfill the order. However, if the number of cities is not divisible by 5, it would not be possible to construct the exact number of roads required.