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

Concept: In a round-robin or league tournament format, every participating team must play a match against every other team exactly once. The mathematical formula used to calculate the total number of matches (\( M \)) required for a league tournament is: \[ M = \frac{N(N - 1)}{2} \] where \( N \) represents the total number of participating teams.

Step 1: Substitute the given team parameter into the league formula.
We are given that the total number of competing teams is \( N = 8 \). Placed into our equation: \[ M = \frac{8 \cdot (8 - 1)}{2} \]

Step 2: Simplify the arithmetic expression to find the final match count.
\[ M = \frac{8 \cdot 7}{2} = \frac{56}{2} = 28 \text{ matches} \] Thus, 28 distinct matches must be scheduled to complete the single league rotation.