Question

Каждый ученик школы занимается хотя бы в одном из 30 кружков, но не более чем в двух из них.Окозалось,что в каждом кружке занимается ровно 30 человек, а для каждых двух кружков есть ученик, который посещает оба этих кружка. Какое наибольшее количество кчеников может быть в этой школе?

Answer 1

64 надеюсь помогла, обращался в вк

Answer 2

Problem Analysis

We are given that each student in a school participates in at least one of 30 clubs, but no more than two. It is also mentioned that each club has exactly 30 members, and for every pair of clubs, there is a student who attends both clubs. We need to determine the maximum number of students that can be in this school.

Solution

To find the maximum number of students in the school, we need to consider the different scenarios that satisfy the given conditions.

Let's analyze the possible scenarios:

1. Each student participates in exactly one club: - In this scenario, there would be a total of 30 students in the school, with each club having exactly 30 members.

2. Each student participates in two clubs: - In this scenario, there would be a total of 15 students in the school, as each student can only participate in a maximum of two clubs. - Since there are 30 clubs, we can pair them up in such a way that each pair has one student who attends both clubs. - This means that there would be 15 pairs of clubs, and each pair would have one student attending both clubs. - Therefore, the maximum number of students in this scenario is 15.

To find the overall maximum number of students in the school, we need to consider the maximum number of students from both scenarios. Since the second scenario has a higher number of students, the maximum number of students in the school is 15.

Answer

The maximum number of students that can be in this school is 15.