Question

На соревнованиях по борьбе каждый участник должен провести ровно один бой с каждым другим участником. Но двое участников получили травмы, из-за чего не могут продолжать участие в соревнованиях. Каждый из них провел по 4 боя. Всего было проведено 62 боя. Сколько всего участников всего было на соревнованиях? Помогите, пожалуйста!!​

Answer 1

Ответ:

13

Пошаговое объяснение:

В турнире n игроков

Один бой каждого с каждым - это n-1 боёв для одного участника.

И это n(n-1)/2 боёв за весь турнир.

Проведя по 4 боя два участника не смогли принять участие в

2*(n - 1 - 4) = 2n - 10 боях, а общее число поединков

n(n-1)/2 - (2n - 10) = 62

n(n-1)/2 - 2n + 10 = 62

n(n-1)/2 - 2n - 52 = 0

n² - n - 4n - 104 = 0

n² - 5n - 104 = 0

n₁₂ = (5 ± √(5² + 4*104))/2 = (5 ± √441)/2 = (5 ± 21)/2

n₁ = (5 - 21)/2 = -16/2 = -8

Отрицательный корень отбросим

n₂ = (5 + 21)/2 = 26/2 = 13
Всего было 13 участников

Answer 2

Calculating the Total Number of Participants in the Wrestling Competition

To calculate the total number of participants in the wrestling competition, we can use the information provided about the number of fights and the number of fights each injured participant had. Let's break it down step by step.

1. Total Number of Fights - The total number of fights can be calculated using the formula for the sum of the first n natural numbers, which is n * (n + 1) / 2. - In this case, the total number of fights is given as 62.

2. Number of Fights per Injured Participant - Each injured participant had 4 fights.

3. Calculating the Total Number of Participants - We can use algebra to solve for the total number of participants.

Let's proceed with the calculation.

Calculation

We can use the given information to set up an equation to solve for the total number of participants.

Let's assume the total number of participants is represented by 'n'.

The total number of fights can be expressed as the sum of the first n natural numbers, which is n * (n + 1) / 2.

Given: - Total number of fights = 62 - Each injured participant had 4 fights

We can set up the equation: n * (n + 1) / 2 - 8 = 62

Solving for 'n': n * (n + 1) / 2 = 70 n * (n + 1) = 140 n^2 + n - 140 = 0

Using the quadratic formula: n = (-1 + sqrt(1 + 4*140)) / 2 n = (-1 + sqrt(561)) / 2 n ≈ 11.83

Since the number of participants must be a whole number, we take the positive value: n ≈ 12

Conclusion

Based on the given information, the total number of participants in the wrestling competition was approximately 12.