Question

When drafting league tournament fixtures containing an odd number of participating teams, how many total operational rounds must be scheduled if the coordinator chooses the standard 'Staircase Method'?

• A. \( N - 1 \text{ rounds} \)
• B. \( N \text{ rounds} \)
• C. \( N + 1 \text{ rounds} \)
• D. \( \frac{N(N-1)}{2} \text{ rounds} \)

Hint:

The Staircase Method is the most straightforward way to schedule a league tournament because it completely avoids the need to distribute "Byes," and the number of rounds always simplifies to \( N - 1 \).

Answer 1

The Correct Option is A

Concept: The Staircase Method organizes league fixtures by arranging pairings in a step-like visual sequence. A unique advantage of this layout is that it operates independently of standard odd or even team-count rules.

Step 1: Analyze round counts within the Staircase framework.
Unlike the Cyclic or Tabular methods—where an odd number of teams forces the number of rounds to equal \( N \)—the Staircase Method always requires exactly \( N - 1 \) structural steps or rounds to complete all matches, regardless of whether the total team count is odd or even.

Step 2: Differentiate from total match calculations. The formula \( \frac{N(N-1)}{2} \) calculates the *total number of matches* played across the entire tournament, rather than the number of administrative rounds scheduled.