Question

1. find the number of games played in a round robin tournament for the given numbers of teams. in a round robin tournament every team plays every other team once.

number of teams | number of games played
3 teams | 3 games
4 teams | 6 games
5 teams | 10 games
6 teams | __ games
7 teams | __ games

look for a pattern. find the number of games played in a round robin tournament involving ( n ) teams. find the number of games played in a round robin tournament involving 14 teams.

Explanation:

Step1: Identify the pattern formula

In a round-robin tournament, the number of games is the number of unique pairs of teams, given by the combination formula:
$$C(n,2) = \frac{n(n-1)}{2}$$
where $n$ = number of teams.

Step2: Calculate for 6 teams

Substitute $n=6$ into the formula:
$$\frac{6(6-1)}{2} = \frac{6 \times 5}{2} = 15$$

Step3: Calculate for 7 teams

Substitute $n=7$ into the formula:
$$\frac{7(7-1)}{2} = \frac{7 \times 6}{2} = 21$$

Step4: Calculate for 14 teams

Substitute $n=14$ into the formula:
$$\frac{14(14-1)}{2} = \frac{14 \times 13}{2} = 91$$

Answer:

• 6 teams: 15 games
• 7 teams: 21 games
• 14 teams: 91 games
• General formula for $n$ teams: $\frac{n(n-1)}{2}$ games