Question

Шахматист занявший 1 место в турнире в котором каждый игрок сыграл с каждым из остальных по одному разу, набрал 3,5 очка, занявший 2 место 3 очка, 3 место 2 очка. сколько очков набрали все остальные шахматисты вместе (за победу 1 очко, ничья полочка, поражение 0 очков) варианты ответов а)1 б) 1,5 в)6,5 г) определить невозможно (ответ писать с объяснением!!!)

Answer 1

Ответ "В": 6,5 очков

Если в турнире приняло участие 15 игроков, то число матчей составляет 6(6-1)/2=15. За каждый матч, вне зависимости от результата, число очков в таблице увеличивается на 1 (1+0; 0,5+0,5 или 0+1). Следовательно, число очков равно числу сыгранных матчей. Занявшие первые места в сумме набрали 8,5 очков. 15-8,5=6,5 очков.

Answer 2

Problem Analysis

We are given information about the scores of the top three chess players in a tournament where each player played against every other player exactly once. The player who finished first scored 3.5 points, the player who finished second scored 3 points, and the player who finished third scored 2 points. We need to determine the total number of points scored by all the other chess players combined.

Solution

Let's assume there were 'n' total players in the tournament, including the top three players. We know that each player played against every other player exactly once. In a tournament with 'n' players, each player plays 'n-1' games. Since each game results in either a win, a draw, or a loss, the total number of points scored by all the players combined is equal to the total number of games played.

To find the total number of games played, we can use the formula for the sum of the first 'n' natural numbers: `sum = n * (n-1) / 2`.

Let's substitute the values we know into the formula: - The player who finished first scored 3.5 points, so they won 3.5 games. - The player who finished second scored 3 points, so they won 3 games. - The player who finished third scored 2 points, so they won 2 games.

We can calculate the total number of games played by summing up the games won by the top three players: `total_games = 3.5 + 3 + 2 = 8.5`.

Now, we can solve for 'n' using the formula for the sum of the first 'n' natural numbers: `8.5 = n * (n-1) / 2`.

To solve this equation, we can multiply both sides by 2: `17 = n * (n-1)`.

Expanding the equation: `n^2 - n - 17 = 0`.

Using the quadratic formula, we can solve for 'n': `n = (-b ± √(b^2 - 4ac)) / 2a`.

In this case, 'a' is 1, 'b' is -1, and 'c' is -17. Plugging in these values, we get: `n = (-(-1) ± √((-1)^2 - 4(1)(-17))) / (2(1))`.

Simplifying the equation: `n = (1 ± √(1 + 68)) / 2`.

Calculating the discriminant: `n = (1 ± √69) / 2`.

Since the number of players cannot be negative, we can ignore the negative solution: `n = (1 + √69) / 2`.

Now that we have the value of 'n', we can calculate the total number of points scored by all the other chess players combined. Each win is worth 1 point, so the total number of points scored by all the other players is equal to the total number of games played minus the points scored by the top three players: `total_points = total_games - (3.5 + 3 + 2)`.

Substituting the value of 'total_games' and simplifying the equation: `total_points = 8.5 - 8.5 = 0`.

Therefore, the total number of points scored by all the other chess players combined is 0.

Answer

The total number of points scored by all the other chess players combined is 0.