Sixteen teams have been invited to participate in the ABC Gold Cup cricket…

2024

Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament was conducted in two stages. In the first stage, the teams are divided into two

groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group

advance to the second stage while the rest are eliminated. The second stage comprised several rounds. A round involves one match for each team, while the loser is eliminated. The

team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.

The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss.

At the end of the first stage, teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.

What is the number of rounds in the second stage of the tournament?

  1. A.

    3

  2. B.

    1

  3. C.

    2

  4. D.

    4

Attempted by 1 students.

Show answer & explanation

Correct answer: A

Concept: In a single-elimination (knockout) format, every round pairs up the remaining teams; the winner advances and the loser is eliminated, so each round exactly halves the number of teams still in contention.

Application:

  1. The two groups send their top four teams each into the knockout stage, so 4 + 4 = 8 teams begin the second stage.

  2. Round 1 (quarter-finals): 8 teams play 4 matches, halving the field to 4 teams.

  3. Round 2 (semi-finals): 4 teams play 2 matches, halving the field to 2 teams.

  4. Round 3 (final): the remaining 2 teams play 1 match, producing the single undefeated winner.

Cross-check: halving 8 teams down to 1 champion takes log28 = 3 halvings, matching the three rounds traced above; the total number of matches played (4 + 2 + 1 = 7) also equals the expected teams − 1 = 7 for a single-elimination bracket of 8 teams.

Hence, the second stage has 3 rounds.

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