Games and Tournament - Logical Reasoning (MCQ) Questions for Q. 29091
Q. 16 teams participated in a cricket tournament.
The tournament was conducted in two stages.
First stage- In the first stage, the teams are divided into two equal groups.
- Each team plays every other team in its group exactly once.
- At the end of first stage, the top four teams from each group advance to the second stage.
- Rest teams are eliminated.
Second stage- The second stage comprised 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.
Rules- The tournament rules 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 advanced to the next stage.
What would be the total number of matches in the tournament?- Published on 07 Jul 17a. 55
b. 56
c. 63
d. 66
ANSWER: 63
In first stage, teams are divided into two groups of 8 teams each.
They play a match against everyone exactly one i.e. 8C2 matches in every group.
So,
2 x 8C2 = 56 matches for the first stage.
8C2 = 8! / (2!)(6!) = 4 x 7 = 28
In second stage, there are 8 teams in a “knockout stage”.
There will be one winner, so 8 – 1 = 7
So, total number of matches is 56 + 7 = 63
