Question

A chess tournament is planned for teams, each of which has exactly three players. Each player in a team will play exactly once against each player from all the other teams. For organizational reasons, no more than 250 games can be played in total. At most, how many teams can enter the tournament?

a) 6
b) 7
c) 8
d) 9

Answer 1

The maximum number of teams that can enter the chess tournament without exceeding 250 games is 8 teams.

Step-by-step explanation:

Given the question about a chess tournament where each team has three players and each player plays against every player from the other teams, we want to calculate the maximum number of teams that can enter the tournament without exceeding 250 games in total. Each player will play 3 games against each player from the other teams, so if there are 'n' teams, each team will play 3(n-1) games. Thus, each team plays against the other teams one time. The formula for the total number of games is then 3 × n × (n - 1). We need to solve for 'n' such that this product is less than or equal to 250.

Calculating this for different values of 'n', we find that for n=7, the total number of games is 3 × 7 × (7 - 1) = 126, which is within the 250 limit. However, if we try n=8, the total number of games would be 3 × 8 × (8 - 1) = 168, which still fits within the constraint. But for n=9, the total would be 3 × 9 × (8 - 1) = 216, which exceeds 250. Hence, the maximum number of teams that can enter is 8 teams.