Question

в футбольном турнире участвовало  8 команд ,при чем каждая сыграла с каждой ровно по одному разу . Известно, что любые две команды , сыгравшие между собой вничью,набрали в итоге разное число очков.Найдите наибольшее возможное общее число ничьих в этом турнире.(За выигрыш матче команде начисляется 3 очка , за ничью- 1,за поражение -0)

Answer 1

Calculation of the Maximum Number of Draws in a Football Tournament

To find the maximum number of draws in the given football tournament, we need to consider the number of teams and the number of matches played.

Given: - There are 8 teams participating in the tournament. - Each team plays exactly one match against every other team.

To calculate the maximum number of draws, we need to determine the number of matches played and the number of possible outcomes for each match.

Number of Matches Played

In a tournament with 8 teams, each team plays against every other team exactly once. To calculate the number of matches played, we can use the formula for the number of combinations:

Number of Matches Played = nC2 = (n * (n - 1)) / 2

where n is the number of teams.

Substituting the value of n = 8, we get:

Number of Matches Played = (8 * (8 - 1)) / 2 = 28

Therefore, there are a total of 28 matches played in the tournament.

Number of Possible Outcomes for Each Match

In a football match, there are three possible outcomes: win, draw, or loss. However, we are interested in finding the maximum number of draws. To maximize the number of draws, we need to minimize the number of wins and losses.

Since each match can have only one outcome, the maximum number of draws is obtained when all matches end in a draw. Therefore, the number of possible outcomes for each match is 1.

Calculation of the Maximum Number of Draws

To calculate the maximum number of draws, we need to multiply the number of matches played by the number of possible outcomes for each match.

Maximum Number of Draws = Number of Matches Played * Number of Possible Outcomes for Each Match

Substituting the values, we get:

Maximum Number of Draws = 28 * 1 = 28

Therefore, the maximum possible number of draws in this football tournament is 28.

Please let me know if you need any further assistance.