0Question:
In a Cricket Tournament, there are 8 Teams. Each Team plays every other team once, in the group stages of the competition. The teams accumulate points as follows in the Grp stages- Win-2, Loss-0.
Every match must have a result, with either of the teams being victorious, and the other conceding defeat. This is ensured by a Super-Over for Tied score matches, and Spin of the Coin for Washed out games.
Top 4 Teams on the basis of Points, and Net Run Rate in case of Tie in Points, qualify to the Play-Offs, whose fixtures are as follows:
Qualifier 1: Rank 1 vs Rank 2
Eliminator- Rank 3 vs Rank 4
Qualifer 2: Loser(Qualifier 1) vs Winner (Eliminator)
Finals- Winner (Qualifier 1) vs Winner (Qualifier 2)
1) What is the minimum number of wins a team requires in the Grp Stage to ensure Qualification to the Play-Offs, irrespective of the outcome of other matches?
A) 4 B) 5 C) 3 D) 6
2) What is the maximum number of matches a team can afford to lose across the entire tournament (Grp Stage + Play-Offs), and yet earn themselves the label of ‘Champions’?
A) 2 B) 5 C) 4 D) 3
3) For a Team, to achieve the feat mentioned in Question 2) with the maximum number of Defeats across the entire Tournament, what must be their Team Rank in the Grp Stages?
A) 2nd B) 4th C) 3rd or 4th D) 2nd or 4th
Answer:
Solutions
1) Total Matches = 7C2 =28. This situation of will arise if Top 5 Teams win as many points as possible, and Bottom 3 lose all their matches. Hence All top 5 Teams have won 3 matches each against bottom 3, and amongst the 5C2=10 matches between themselves, they have won 2 each. So in that case, all 5 Teams have won 5 matches. But only 4 Teams can Qualify, and 1 team could crash out on Net Run Rate, even with 5 wins. Hence Only 6 wins could
ensure a qualification into the Play-Offs... Option D
2) Total Matches = 7C2 =28. This situation can arise in 2 possible scenarios:
i) 1 team wins all 7 matches, Rest 6 teams win 3 matches each. Team finishing 2nd has lost 4 matches in Grp-Stage
ii) Top 3 teams win 7 , 6, 5 matches respectively, beating all the other 5 teams(Ranked 4th to 8th). These Teams 4th to 8th all win 2 of the 5C2=10 matches between themselves. One of them qualifies on the basis of Net Run-Rate.
In Case i) Team has lost 4 matches, and can afford to lose another match in Play-Offs since it finished 2nd in the grp
In Case ii) Team has lost 5 matches and has qualified as the 4th team, hence they must win all their Play-Off games.
Hence in either case Team can afford to lose a maximum of 5 matches... Option B
3) As shown above, the Team can finish either 2nd or 4th in the grp stages... Option D.
