Question

У каждого ребёнка в группе детского сада ровно два друга – мальчика и ровно две подруги – девочки. Известно, что у любых подруг нет общего друга, а любых друзей мальчиков нет общей подруги. Какое наименьшее количество детей может быть в группе?

Answer 1

Как так но я считаю что 6 детей

Answer 2

Problem Analysis

We are given that each child in a daycare group has exactly two friends who are boys and exactly two friends who are girls. It is also known that any two girls do not have a common boy friend, and any two boys do not have a common girl friend. We need to determine the minimum number of children in the group.

Solution

To find the minimum number of children in the group, we need to consider the scenario where each child has the minimum number of friends required.

Let's assume there are n children in the group. Each child has exactly two boy friends and two girl friends. Therefore, the total number of boy-girl friendships in the group is equal to 2n.

Now, let's consider the scenario where each girl is friends with exactly two boys. In this case, the total number of girl-boy friendships is equal to 2n.

Since any two girls do not have a common boy friend and any two boys do not have a common girl friend, the total number of friendships in the group is equal to the sum of boy-girl friendships and girl-boy friendships, which is 4n.

However, we have counted each friendship twice (once as a boy-girl friendship and once as a girl-boy friendship). Therefore, the actual number of unique friendships in the group is equal to 2n.

Since the total number of friendships in the group is equal to 4n and the actual number of unique friendships is equal to 2n, we can set up the following equation:

4n = 2n

Simplifying the equation, we find:

2n = 0

This equation implies that the minimum number of children in the group is 0.

Therefore, the minimum number of children in the group is 0.

Answer

The minimum number of children in the group can be 0.