Question

in a football tournament, each team played exactly one game against each other teams. in each game the winner was awarded 2 points, and the loser gets 0 point. if the game is a tie, each of the two team earned 1 point. assume that the score of the team a is maximal, but the number of games in which a wins is minimal. find the smallest value of the number of teams in this tournament.

Answer 1

The smallest value for the number of teams in the tournament is 2.

Step-by-step explanation:

To find the smallest value of the number of teams in the tournament, we need to minimize the number of games in which team A wins while maximizing the score of team A.

Let's assume that there are n teams in the tournament.

Each team plays n-1 games (one game against each other team).

Since team A has the maximal score, it must win all the games except one, which it ties.

So, if team A wins n-2 games and ties 1 game, its score would be 2(n-2) + 1 = 2n-3.

In order to maximize this score, we want to minimize n-2.

This means that the smallest possible value for the number of teams in the tournament is 2.