Direction: 16 teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in 2 stages. In the first stage, the teams are divided into two groups. Each group consists of 8 teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top 4 teams from each group advance to the 2nd stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, 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 1 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 4 teams from each group advance to the next stage.
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What is the total number of matches played in the tournament?
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- 28
- 55
- 63
- 35
Correct Option: C
First Stage: There is two groups of 8 teams each. In each group, each team plays with every other team and hence total number of matches are 8c2 = 8 × ( 7/2 ) = 28 matches So, in both the groups the total number of matches played at the first stage are 28. And hence 56 matches are played in 1st stage
Second Stage: In this stage there are 8 teams playing in such a way that in one round 4 teams play with 4 other teams. 4 teams win and go to the next round. That is called knock out tournament.
In the 1st round no of matches ( 8/2 ) = 4,
In the 2nd round no of matches = ( 4/2 ) = 2,
In the third or the last round number of match = ( 2/2 ) = 1,
So , total no. of matches in 2nd stage is 4 + 2 + 1 = 7
Hence total match in the tournament = 56 + 7 = 63
