Games And Tournament
Direction: There are five teams Paraguay, Qatar, Russia, Spain and Turkey playing in a tournament where each team plays against every other team only once. These are the following possibilities: each match can result in a draw where it scores three points, while the losing team scores one point
 If Paraguay has won all the matches and Turkey has lost all the matches and all the remaining three teams score equal points, how many points have each of the three remaining teams scored?

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Each match has 4 points and each team plays 4 matches. Hence total number of points is 40
Paraguay wins all matches. So it scores 3 x 4 = 12 points.
Turkey loses all matches. So it scores 1 x 4 = 4 points.
16 points are scored by Turkey and Paraguay
The other teams score 40  16 = 24 points
As all other teams score equal points, each team scores 24/3 = 8 pointsCorrect Option: C
Each match has 4 points and each team plays 4 matches. Hence total number of points is 40
Paraguay wins all matches. So it scores 3 x 4 = 12 points.
Turkey loses all matches. So it scores 1 x 4 = 4 points.
16 points are scored by Turkey and Paraguay
The other teams score 40  16 = 24 points
As all other teams score equal points, each team scores 24/3 = 8 points
 If all the five teams have an equal score, what is the number of points scored by each team?

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The total score is 40 points. If each team scores equally, each team scores 40/5 = 8 points
Correct Option: D
The total score is 40 points. If each team scores equally, each team scores 40/5 = 8 points
Direction: Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is 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 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 one points 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 tiebreaking rules so that exactly four teams from each group advance to the next stage.
 What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?

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The team which gets 1 point at 1st stage would be eliminated because the combination may be 6 points for the team and 2 times each for remaining. There are some more cases that supports the idea.
Correct Option: A
The team which gets 1 point at 1st stage would be eliminated because the combination may be 6 points for the team and 2 times each for remaining. There are some more cases that supports the idea.
 What is the number of rounds in the second stage of the tournament?

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Since there are 8 teams and we know that 8 = 2^{3} hence there are 3 rounds in 2nd stage.
Correct Option: C
Since there are 8 teams and we know that 8 = 2^{3} hence there are 3 rounds in 2nd stage.
 Which of the following statements is true?

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From the discussion above we can say that. It is possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.
Correct Option: C
From the discussion above we can say that. It is possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.