Question

What is the total number of matches that will be played in a single league tournament containing 8 participating teams?

• A. \( 28 \)
• B. \( 56 \)
• C. \( 7 \)
• D. \( 32 \)

Hint:

Be sure to check whether the problem specifies a single league or a double league tournament format. A single league uses \( \frac{N(N-1)}{2} \), while a double league requires you to skip the division step entirely, using the formula \( N(N-1) \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A league tournament, or Round-Robin tournament, is a competition format where every participant plays against every other participant.
In a "Single League" format, each team meets every other team exactly once.
This format is widely considered the fairest way to determine a champion because it eliminates the element of luck associated with a single bad game (as in knockout tournaments).
The number of matches required increases significantly as the number of teams grows, following the mathematical principle of combinations.
Step 2: Key Formula or Approach:
The number of matches ($M$) in a single league tournament with $N$ teams is calculated using the formula:
\[ M = \frac{N(N - 1)}{2} \]
If the tournament were a "Double League" (where teams play each other twice, home and away), the formula would be:
\[ M = N(N - 1) \]
Step 3: Detailed Explanation:
In this question, $N = 8$.
Using the single league formula:
\[ M = \frac{8(8 - 1)}{2} \]
\[ M = \frac{8 \times 7}{2} \]
\[ M = \frac{56}{2} \]
\[ M = 28 \text{ matches} \]
The reason we divide by 2 is because a match between Team A and Team B is the same match as Team B vs. Team A. We don't want to count the same match twice.
Another way to think about it is:
Team 1 plays 7 matches.
Team 2 plays 6 matches (we already counted the match against Team 1).
Team 3 plays 5 matches... and so on.
Sum = $7 + 6 + 5 + 4 + 3 + 2 + 1 = 28$.
Step 4: Final Answer:
For 8 teams in a single league rotation, 28 matches must be scheduled.