Question

В турнірі брали участь N учасників, з яких було 3 дівчини.В кожній грі грають 3 учасникі. У першій грали 3 дівчини. У кожній наступній грі брала участь принаймі одна з них. Результати показали, що кожні два учасникі(хлопці чи дівчата) один з одним грали лише в одній грі. Для якого найбільшого значення N це можливо

Answer 1

Ответ:

34 можливо (пожалуста 10 баллов)

Answer 2

Problem Analysis

We are given that there are N participants in a tournament, out of which 3 are girls. In each game, 3 participants play, and in the first game, all 3 girls played. In each subsequent game, at least one girl participated. The results showed that every pair of participants (boys or girls) played together in exactly one game. We need to determine the maximum possible value of N.

Solution

To find the maximum possible value of N, we need to consider the scenario where every pair of participants (boys or girls) plays together in exactly one game. Let's analyze the given information step by step:

1. In the first game, all 3 girls played. This means that there were 3 boys as well, as each game involves 3 participants. 2. In each subsequent game, at least one girl participated. This means that in each game after the first, there were at least 2 boys and 1 girl playing. 3. The results showed that every pair of participants (boys or girls) played together in exactly one game. This means that each boy played with each girl exactly once.

To maximize the value of N, we need to maximize the number of games played. Since each game involves 3 participants, the number of games played will be equal to the total number of participants divided by 3.

Let's consider the number of games played: - In the first game, 3 girls played. - In each subsequent game, at least one girl participated. Since each girl needs to play with each boy exactly once, there will be a total of 3 games for each girl-boy pair. - The number of girl-boy pairs is given by the product of the number of girls and the number of boys, which is 3 * 3 = 9.

Therefore, the total number of games played is 1 (first game) + 3 (games for each girl-boy pair) * 9 (number of girl-boy pairs) = 1 + 27 = 28.

Since each game involves 3 participants, the total number of participants (N) will be equal to the total number of games played multiplied by 3, which is 28 * 3 = 84.

Hence, the maximum possible value of N is 84.