Question

Архипелаг состоит из N⩾8 островов. Любые два острова соединены не более чем одним мостом. Известно, что с каждого острова ведет не более чем 6 мостов, а среди любых 8 островов обязательно есть два, соединенные мостом. Какое наибольшее значение может принимать N?

Answer 1

Ответ:

12

Объяснение:

трудно

Answer 2

The maximum value of N in the given scenario

In this scenario, we are given that an archipelago consists of N≥8 islands, and any two islands are connected by at most one bridge. It is also known that each island has at most 6 bridges, and among any 8 islands, there are always two islands connected by a bridge.

To find the maximum value of N, we need to consider the given conditions. Let's analyze the information provided step by step:

1. Each island has at most 6 bridges. 2. Among any 8 islands, there are always two islands connected by a bridge.

To maximize the value of N, we need to ensure that each island has the maximum number of bridges (6) and that there are always two islands connected by a bridge among any 8 islands.

Let's consider a scenario where we have the maximum number of bridges (6) for each island. In this case, we can connect each island to the other 7 islands using a bridge. This way, we ensure that among any 8 islands, there are always two islands connected by a bridge.

Now, let's calculate the maximum value of N:

- Each island has 6 bridges, so the total number of bridges is 6N. - Among any 8 islands, there are always two islands connected by a bridge. So, the number of bridges connecting 8 islands is C(8, 2) = 28.

To maximize N, we need to ensure that the number of bridges connecting 8 islands is equal to the total number of bridges (6N):

28 = 6N

Solving this equation, we find:

N = 28/6 = 4.67

Since N represents the number of islands, it cannot be a fraction or a decimal. Therefore, the maximum value of N in this scenario is 4.

So, the maximum value that N can take in this scenario is 4.