Robin Round Matches… DI Tournament based Data Interpretation

There are 16 teams and they are divided into 2 pools of 8 each. Each team in a group plays against one another on a round-robin basis. Draws in the competition are not allowed. The top four teams from each group will qualify for the next round i.e round 2. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead. Find –
Question 1 – Minimum number of wins required to qualify for the next round ?
Question 2 – Minimum number of wins required to guarantee qualification in the next round ?

Solution 1 – Each group consists of 8 teams. So each team will play 7 match each. Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win. So the number of wins for the 8 teams would be 7, 6, 5, 4, 3, 2, 1, 0 with highest seeded team winning all and lowest seeded team losing all. For minimum number of wins we allow 3 teams to win maximum number of matches. Of the remaining 5 teams just find out the mean of their number of wins. In this case it would be – (4+3+2+1+0)/5=2. So 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.

Solution 2 – In this case consider the mean of first 5 higher seeded teams (7+6+5+4+3)/5=5 So it may be the case that 5 teams can end up having 5 wins each. And hence 1 team will miss the second round birth. So minimum number of wins to guarantee a place would be 6.
Knockout Tennis type matches…DI Tournament based Data Interpretation

Normally in such questions, there are 64 players in a knock out tournament and every player is ranked (seeded) from 1 – 64. The matches are played in such a manner that in round one the 1st seeded player plays with the 64th, 2nd with the 63rd and so on. The players who win move on to the next round whereas others are out of the competition. In second round, the winner of match 1 will play winner of the last match (which was between seed 32 and seed 33), and winner of match 2 will meet the winner of second last match in round 1 and so forth. Thus after N number of rounds winner is declared.

NOTE: In these Questions: the term UPSET means when a lower seeded player beats the higher seed.

Question: Which seeds will play Match no 4 and Match no 9 in Round 1 of a 32 player tournament ?

Ans: Easy: 4 Vs 29 & 9 Vs 24 resp

Time for trick: Notice one thing the sum of the seedings in every match will be equal to total players + 1. i.e. 1 + 32 = 33, 2 + 31 = 33.

In round of 64, sum of seeds will be 65, and in round of 16, sum of seeds will be 17. And so forth. (This will be useful in solving complicated questions) This way we can easily calculate the opponents in any round.

Question: In a tournament of 128 players who will play 36 in round II if there are no upsets?

Ans: No need to do any back calculations, Just see – in Round 2 there will be 64 players. So the opponent of 36 will be = 65-36 = 29. Similarly u can calculate for anyone.

Question: Who will meet Seed 68 in the Quaterfinal’s of a 128 format tournament, if seed 5 lost in
the pre-quarters and there was no other upset?

Ans: Now the ques seems complicated but its not if we go step by step using the above method:
try once to solve the question yourself and then read further:

So We know Seed 68 is in Quarters that means he has defeated Seed 129 – 68 = 61 in round 1. Now 61 would have played 65 – 61 = 4 in round 2 (Which now 68 will be playing). Now, 68 has defeated 4 as well as he is in quarters.

Now look at the quarters opponent of 4 (68 will be playing with him) – its 9-4 = 5. We know 5 has lost in pre quarters where his opponent was 17 – 5 = 12.

So opponent of 68 will be 12.