CRE 3 - Round Robin Tournament | DI - Games & Tournaments

Answer: Option B

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Explanation :

As there are eight teams in a pool, the number of matches = 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28.

A → B, C, D, E, F, G and H, i.e., 7 matches

B → C, D, E, F, G and H, i.e., 6 matches

C → D, E, F, G and H, i.e., 5 matches

D → E, F, G and H, i.e., 4 matches

E → F, G and H, i.e., 3 matches

F → G and H, i.e., 2 matches

G → H, i.e., 1 match

Alternately,

Number of matches in each pool = ⁸C₂ = (8 × 7)/2 = 28.

Hence, option (b).

Answer: Option D

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Explanation :

The total number of matches = 28 + 28 + 2 + 1 = 59

⇒ Pool matches = 28 + 28,

⇒ Semifinals = 2

⇒ Final = 1

Hence, option (d).

Answer: Option A

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Explanation :

Let A and B advance to next round with B qualiying with least possible score.

To minimise the points scored by B we will have to maximise the points of the teams above it i.e., of A. A plays a total of 7 matches hence maximum points A scores will be 14.

Total points to be score in the pool stage = 28 × 2 = 56.

Remaining points = 56 – 14 = 42.

Now, these points are to be distributed amongst B to H such that B who is the best of these 7 teams gets least number of points.

The best team cannot receive less than the average, hence points when shared equally by the seven teams, each team would get 42/7 = 6 points.

Since all 7 teams have same points, B can advance based on net runrate.

∴ A team with six points can advance to the semifinals.

Hence, option (a).

Answer: Option A

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Explanation :

If three teams end up with the maximum points, then one of them would be eliminated. 

Total points to be score in the pool stage = 2 × 28 = 56.

Now, bottom 5 teams will play = ⁵C₂ = 10 matches between them i.e., they will get minimum 10 × 2 = 20 points between them.

Now, maximum total points that the top 3 teams get is 56 – 20 = 36.

Let’s distribute these 36 points equally among the top 3 teams. Based on net run-rate 2 of these 3 teams will advance and 3rd team will be eliminated.

So, maximum score a team can get when three teams finish with highest points is 12.

∴ A team with 12 points can be eliminated.

Hence, option (a).

Answer: Option C

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Explanation :

If all teams score the same number of points, each team will have 56/8 = 7 points, but as there are no draws and ties, some teams would score 8 and some teams would score 6 points. 

A team with 6 points can end up as last in the pool.

Hence, option (c).

Answer: 6

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Explanation :

Instead of calculating the minimum number of wins required to guarantee qualification to the next round, let us focus on maximum numbers of wins despite a team can be eliminated.

Total number of matches in a pool = ⁸C₂ = 28 matches.

Now, 4 teams will qualify for next round and the 5th team despite wining a lot of matches would get disqualified.

The bottom 3 teams will play 3 matches.
∴ The top 5 teams will play a total of 28 - 3 = 25 matches i.e., they can win a maximum of 25 matches.

Now to maximise the number of matches team 5 wins, we will distribute these 25 wins equally amongst all 5 teams. Now there are 5 teams with 5 wins each. Since only 4 teams can qualify there will be one team that would get disqualified.

Hence, even after winning 5 matches a team can get disqualified.

∴ To gurantee qualification to next round a team will have to win at least 6 matches.

[Note: A team may be able to qualify even with less than 6 wins, but that would not be a guaranteed qualification.]

Hence, 6.

Answer: 0

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Explanation :

Since draws are allowed, it is possible that all 28 matches in the pool are drawn and based on net runrate top 4 teams will qualify to next round.

Hence, 0.