Question

The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year?

Answer 1

The conference commissioner would have to schedule 90 games each year.

Step-by-step explanation:

Number of teams in the conference = 10 teams

Since each team is to play every other team, and there are 10 teams in the conference, then each team will play against 9 opponents each.

Number of games played per team = 9 games

Total number of games to be played = Number of teams × Number of games per team

= 10 × 9 = 90 games

Therefore the conference commissioner would have to schedule 90 games each year.

Answer 2

It would be necessary to schedule 45 games.

Step-by-step explanation:

As shown in the question above, the Super Ten Football Conference has ten teams. Each team will have to play with all the others for the champion to be considered.

Based on this, we can conclude that 45 games will be necessary, because for all teams to play each other, the following scheme would need to be formed:

• Team 1: play with 9 other teams.
• Team 2: play with 8 other teams.
• Team 3 would play with 7 other teams.
• Team 4: play with 6 other teams.
• Team 5 would play with 5 other teams.
• Team 6: play with 4 other teams.
• Team 7: play with 3 other teams.
• Team 8: play with 2 other teams.
• Team 9: would play with 1 other team.
• Team 10: participated in the games of all teams.

The sum of the games of each team would give a total of 45 games.